Quantum-classical multi-stage optimization method for unit combination and transmission line switching

Abstract

The invention provides a quantum-classical multi-stage optimization method for unit commitment and transmission line switching, and the method comprises the steps: decomposing an original model into a plurality of modules, introducing consensus variables between nodes into the modules, further decomposing the modules into a plurality of sub-problem models, and coordinating the unit power generation and transmission line switching through the external circulation between the modules and the internal circulation of the modules, and the optimal unit scheduling scheme of the power system and the corresponding optimal power grid topology can be obtained. According to the method, a main problem for optimizing discrete variables is converted into an equivalent Hamiltonian in a secondary unconstrained binary optimization form suitable for quantum calculation, the Hamiltonian is efficiently solved through a quantum computer, and the solving speed is increased; the modules of the method are subjected to efficient iterative interaction through cutting plane Hamiltonian, so that the global search capability is improved; according to the method, a sensitivity analysis theory is applied to the construction of the cutting plane, and the effectiveness of the cutting plane and the convergence of the method are ensured; the optimal unit scheduling and the power grid topology can be quickly searched, and the power generation energy consumption is reduced.

Description

Technical Field

[0001] The present invention belongs to the fields of quantum computing, classical decomposition methods and power systems, and relates to a quantum-classical multi-stage optimization method for unit combination and transmission line switching, which is suitable for accelerating the search for transmission line topology and unit power generation plans that both meet node load requirements and minimize power generation energy consumption. Background Art

[0002] A typical scenario of the optimization scheduling problem in the power system is the unit combination problem, which aims to determine the day-ahead dispatching plan for the generator sets to minimize the power generation energy consumption of the power system while meeting the safety constraints. The optimal transmission line switching problem determines the optimal topology of the power grid. When the power grid encounters safety-related problems related to power flow exceeding the limit, the power grid topology can be flexibly changed through transmission line switching to alleviate power flow congestion without affecting the node load supply. This is a flexible and reliable control method. However, the operation model of the power system does not consider the static network of the power grid topology. In order to adapt to the instability brought about by the continuous development of the power grid, it is necessary to improve the controllability and flexibility of the transmission system while considering the minimum energy consumption of the generator sets. For this purpose, a dynamic model of joint optimization of unit combination and transmission line switching under variable topology is constructed, which is essentially a more complex mixed integer nonlinear programming problem.

[0003] Existing methods for solving mixed integer nonlinear programming problems are divided into two categories: exact methods and intelligent methods. Exact methods include branch and bound method, cutting plane method, dynamic programming method and Lagrange multiplier method. These methods find the exact solution of the problem through mathematical formula derivation, structural recursive relationship or step-by-step enumeration. However, exact methods have great computing time and resource requirements for complex joint optimization problems. Complex constraints lead to poor quality of solutions found within a reasonable time, which may cause unacceptable delays for power system optimization problems. Intelligent methods include genetic method and particle swarm optimization method. These methods use heuristic and random search strategies and are suitable for problems with complex or incomplete information. They are particularly outstanding in solving large-scale and high-dimensional problems and tend to find a balance between solution quality and computational efficiency. However, intelligent methods are highly dependent on parameter settings and cannot guarantee the quality and stability of solutions. For power system optimization problems, they will lead to fluctuating suboptimal solutions, thus affecting system reliability, and require a large amount of memory.

[0004] Hedman first proposed a joint optimization model to ensure unit combination and transmission line switching. Through decomposition and iterative solution, he successfully verified the positive effect of optimizing network topology on power grid dispatching. Under the premise of not affecting the node load supply, building the optimal power grid topology to reduce the system operation cost and increase the reliability of the power grid against accidents is the development direction of smart grid. However, this joint optimization model needs to introduce a large number of binary variables to represent the start and stop status of the unit and the on and off status of the transmission line, which leads to the "exponential explosion" problem of the model solution as the scale expands, thus bringing huge computing power challenges to classical computers. Hedman's decomposition process did not utilize the interactive relationship between unit combination and optimal transmission line switching, resulting in low efficiency of decomposition and solution. At the same time, the decomposed sub-problems still belong to MINLP like the original problem, which has great optimization difficulty. Lin uses sensitivity linearization constraints and a step-by-step solution strategy to achieve efficient solution of the model. However, its model only fixes a single transmission line state, fails to achieve dynamic network topology optimization, and avoids the exponential explosion complexity of the binary variable search space.

[0005] Therefore, a quantum-classical multi-stage optimization method of unit combination combined with transmission line switching is proposed to solve the above shortcomings and quickly and stably search for the optimal transmission line topology and unit power generation plan, which is helpful to improve the stability and reliability of the power system and reduce power generation energy consumption. Summary of the invention

[0006] The present invention proposes a quantum-classical multi-stage optimization method for unit combination and transmission line switching, which combines model decomposition and cutting plane Hamiltonian construction, and combines classical optimization methods with quantum computing, for joint control of unit scheduling and transmission line switching in power systems, and realizes the function of quickly searching for the optimal unit scheduling and power grid topology of power systems, improves the solution speed of unit combination and transmission line switching models, improves the reliability and flexibility of power systems, reduces power system power generation energy consumption and reduces pollution; the steps of the method during use are:

[0007] Step (1): The joint optimization model of unit combination and transmission line switching is set according to different optimization functions: an upper consensus unit combination module responsible for optimizing unit start and stop and output power; a lower consensus transmission line switching module responsible for optimizing transmission line connectivity, system power flow and node phase angle; and an accident verification module considering N-1 accident conditions;

[0008] A joint optimization model of unit commitment and transmission line switching considering N-1 safety constraints is constructed, which specifically includes the objective function and operation constraints:

[0009] The mathematical model of the objective function of the joint optimization problem of unit commitment and transmission line switching is:

[0010] (1)

[0011] (2)

[0012] (3)

[0013] (4)

[0014] In the formula, is a function of the fuel cost of the generator set; is the unit startup cost function; is the transmission line switching cost function; are the number of units, time periods and transmission lines respectively; continuous variables Indicates timing group exist Output power at the moment; unit start and stop variables Indicates the unit exist The start and stop status at any time, when the unit is in the start state , when closed ; Transmission line on-off variable Represents a transmission line exist The on-off state at the moment, when the transmission line is connected , the transmission line is cut off ;parameter , and For each unit The secondary coefficient, primary coefficient and startup cost coefficient of power generation fuel cost; parameters For transmission line switching costs;

[0015] The mathematical model of the power balance constraint of each node is:

[0016] (5)

[0017] In the formula, Representation Node The set of units configured in; , , Respectively represent nodes The outgoing, incoming and total transmission lines of ; Represents a transmission line exist Current power at the moment; Is a node At the moment Load;

[0018] The mathematical model of unit power capacity constraint is:

[0019] (6)

[0020] (7)

[0021] In the formula, the parameters , The lower and upper limits of the unit's output power; Binary parameters of unit accidents Indicates that in the accident Medium Unit exist The state of the moment, represents a regular event, i.e. ;

[0022] The mathematical model of the minimum start-stop time constraint of the unit is:

[0023] (8)

[0024] (9)

[0025] In the formula, the parameters , Indicates the unit Minimum start and stop time;

[0026] The mathematical model of the power flow capacity constraint of the transmission line is:

[0027] (10)

[0028] (11)

[0029] In the formula, the parameters Represents a transmission line Maximum power flow; Binary parameters of transmission line accidents Indicates that in the accident Transmission line exist The state of the moment, represents a regular event, i.e. ;

[0030] The power flow constraint follows Kirchhoff's law. The mathematical model of simulating the system network power flow using the DC power flow equation is:

[0031] (12)

[0032] (13)

[0033] (14)

[0034] In the formula, Representation Node exist The phase angle of the moment; For transmission line reactance. is a sufficiently large constant introduced by the big-M method to satisfy ;

[0035] The mathematical model of the upper limit constraint of transmission line switching is:

[0036] (15)

[0037] In the formula, is the maximum number of disconnected transmission lines allowed in the network at any time;

[0038] The mathematical model of anti-islanding constraint is:

[0039] (16)

[0040] Step (2): The upper unit combination module is decomposed into the consensus-based local unit combination optimal sub-problem, the unit combination relaxation sub-problem and the local unit combination main problem according to the different types of variables;

[0041] Step (3): Randomly generate the initial start and stop variables of the unit For nodes equipped with generators, the connection relationship of these nodes is preset according to the transmission line topology, and the interactive power between adjacent nodes is introduced. As a consensus amount, for nodes Construct the optimal sub-problem of unit commitment based on consensus;

[0042] The mathematical model of the optimal sub-problem of unit commitment is:

[0043] (17)

[0044] (18)

[0045] (19)

[0046] (20)

[0047] In the formula, Representation Node A collection of configured units; Representation and Node A set of nodes with adjacent relationships; , are the dual multiplier and penalty term of consensus constraints respectively; and subscript Together with the node and nodes The relevant quantity is at the node A copy of Representation Node , The interaction power between global variables; Representation Node , The interaction power local variable between nodes, that is, the interaction power at the node Replicas in local subproblems; consensus amount The preceding symbol is determined by the preset node connection and represents the node in the preset connection. With adjacent nodes The power flow direction, Indicates that in the preset connection, the power is provided by the local node Flow to adjacent nodes , It indicates the opposite situation;

[0048] Step (4): If there is a feasible solution to the optimal subproblem of unit commitment, the consensus variables of each node are made to converge to the same through consensus iteration between nodes, and the local dual variables corresponding to constraints (19) and (20) are obtained by solving them. , and the optimal solution for local continuous variables , update the upper bound of the objective function of the upper unit combination module , construct node The optimality cutting plane of unit commitment;

[0049] The mathematical model of the optimal cutting plane of unit commitment is:

[0050] (twenty one)

[0051] In the formula, is the feasible domain of the optimal cutting plane of local unit commitment; is the dual variable corresponding to constraint (19); is the dual variable corresponding to constraint (20); is the continuous variable solution obtained by solving the optimal subproblem of local unit commitment; is the constant term obtained by sorting in the cutting plane; is the unit start and stop variable obtained in the cutting plane The coefficient of

[0052] Step (5): If there is no feasible solution to the optimal subproblem of unit commitment, then introduce continuous slack variables The original unit combination relaxation subproblem is constructed, and the Karush-Kuhn-Tucker condition of the relaxation subproblem is used as the constraint to express optimality. At the same time, the system over-limit cost and relaxation variable restriction constraints are introduced to construct the improved unit combination relaxation subproblem. The improved relaxation subproblem is solved to obtain the dual variables of the relaxation constraint of the unit output within each node. and continuous variable solutions , construct the unit commitment feasibility cutting plane at the node level;

[0053] The mathematical model of the original unit combination relaxation subproblem is:

[0054] (twenty two)

[0055] (twenty three)

[0056] (twenty four)

[0057] (25)

[0058] (26)

[0059] In the formula, is the slack variable of the unit minimum power constraint (19); is the slack variable of the unit maximum power constraint (20); Is the system in the period Total load;

[0060] The mathematical model of the improved unit commitment relaxation subproblem is:

[0061] (27)

[0062] (28)

[0063] (29)

[0064] The mathematical model of the unit commitment feasibility cutting plane is:

[0065] (30)

[0066] In the formula, is the dual multiplier of the unit minimum power constraint (19); is the dual multiplier of the unit maximum power constraint (20); is the continuous variable solution obtained by solving the improved unit commitment relaxation subproblem model; is the constant term obtained by sorting in the cutting plane; is the unit start and stop variable obtained in the cutting plane The coefficient of

[0067] Step (6): Convert the unit combination optimality cutting plane obtained in step (4) and the unit combination feasibility cutting plane obtained in step (5) into a Hamiltonian in the form of quadratic unconstrained binary optimization, and construct the node The main problem Hamiltonian is solved efficiently using quantum computers to obtain the optimized unit start and stop variables and update the lower bound of the objective function of the upper unit combination module. ;

[0068] The mathematical model of the cutting plane Hamiltonian of the unit commitment optimality in the quadratic unconstrained binary optimization form is:

[0069] (31)

[0070] In the formula, Is a node The cutting plane Hamiltonian of unit commitment optimality; is the number of internal iterations of the upper unit combination module; It is The constant term of the unit commitment optimality cutting plane for the iteration; It is The variables of the optimal cutting plane of unit commitment for the iteration The coefficient of It is The upper bound of the upper unit combination module in the iteration; It is the penalty term introduced in the process of transforming the unit commitment optimality cutting plane into a quadratic unconstrained binary optimization form;

[0071] The mathematical model of the Hamiltonian of the unit commitment feasibility cutting plane in the form of quadratic unconstrained binary optimization is:

[0072] (32)

[0073] In the formula, Is a node The Hamiltonian of the unit commitment feasibility cutting plane; is the number of auxiliary binary variables required for the unit commitment feasibility cutting plane; It is an auxiliary binary variable introduced by the unit commitment feasibility cutting plane; It is The constant term of the unit commitment feasibility cutting plane of the iteration; It is The variables of the unit commitment feasibility cutting plane for the iteration The coefficient of

[0074] Step (7): Update the unit start and stop variables , repeat steps (3), (4), (5), and (6) until the upper and lower bounds of the upper unit combination module converge to the set error limit, and then output the optimal unit start and stop state and unit output power;

[0075] Step (8): Determine the unit scheduling plan It is passed down to the lower-level consensus transmission line switching module, which is decomposed into consensus-based transmission line optimal subproblem, transmission line relaxation subproblem, node relaxation subproblem and transmission line switching main problem according to different variable types.

[0076] Step (9): Input the unit start and stop variables determined in step (8) , generating the initial transmission line topology state , based on the transmission line topology, the transmission line power flow between adjacent nodes is introduced and node phase As a consensus amount, for nodes Construct the consensus-based optimal subproblem of transmission lines;

[0077] The mathematical model of the optimal sub-problem of the transmission line is:

[0078] (33)

[0079] (34)

[0080] (35)

[0081] (36)

[0082] (37)

[0083] (38)

[0084] (39)

[0085] (40)

[0086] (41)

[0087] In the formula, is the objective function value of this subproblem; Representation and Node A collection of related transmission lines; , denotes the local copy of the interaction power at the local node and the local copy of the phase angle at the adjacent node, respectively. The subscript and superscript together denote the transmission line or Node The local node corresponding to the physical quantity a copy of; , denote the dual variable and penalty coefficient of the power flow consensus constraint respectively; , denote the dual variable and penalty coefficient of the phase angle consensus constraint respectively;

[0088] Step (10): If there is a feasible solution to the optimal subproblem of the transmission line, the consensus variables of each node are made to converge to the same through consensus iteration between nodes, and the effect of each transmission line state on the system node is calculated. The upper bound of the objective function of the lower transmission line switching module is updated based on the sensitivity of the operating cost , construct the optimality cutting plane of transmission line based on sensitivity;

[0089] The mathematical model of the optimal cutting plane of the transmission line is:

[0090] (42)

[0091] In the formula, Indicates the node corresponding to the current system topology under a given unit scheduling plan The objective function value of Represents a transmission line In the period Sensitivity to system operating costs when states change; is the constant term obtained by sorting in the cutting plane; is the state variable of the transmission line obtained in the cutting plane The coefficient of

[0092] Step (11): If there is no feasible solution to the transmission line optimal subproblem, then relax the unit power capacity constraint and the transmission line power flow capacity constraint on the basis of the transmission line optimal subproblem, and construct a transmission line relaxation subproblem based on consensus. If the relaxation subproblem has a solution, obtain the state of each transmission line for the nodes in the system. The sensitivity of the over-limit is calculated, and the feasibility cutting plane of the transmission line is constructed based on the sensitivity;

[0093] The mathematical model of the objective function of the relaxed transmission line relaxation subproblem is:

[0094] (43)

[0095] In the formula, the slack variable of unit capacity constraint is , Respectively represent the unit exist The reverse and forward relaxation power at time t. Transmission line capacity relaxation variable , Represents transmission line exist The sum of all slack variables represents the system node Local over-limit ;

[0096] The mathematical model for relaxing the unit power capacity constraint and the transmission line power flow capacity constraint is:

[0097] (44)

[0098] (45)

[0099] (46)

[0100] (47)

[0101] (48)

[0102] (49)

[0103] The mathematical model of the transmission line feasibility cutting plane constructed based on sensitivity is:

[0104] (50)

[0105] In the formula, is the state of each transmission line for each node in the system The sensitivity of the over-limit; is the constant term obtained by sorting in the cutting plane; is the state variable of the transmission line obtained in the cutting plane The coefficient of

[0106] Step (12): Convert the optimality cutting plane of the transmission line obtained in step (10) and the feasibility cutting plane of the transmission line obtained in step (11) into a Hamiltonian in the form of quadratic unconstrained binary optimization, and construct the node The Hamiltonian of the main problem of transmission line switching is efficiently solved using a quantum computer to obtain the optimized transmission line on-off state variables and update the lower bound of the objective function of the lower transmission line switching module. ;

[0107] The mathematical model of the optimality cutting plane Hamiltonian of the transmission line in the form of quadratic unconstrained binary optimization is:

[0108] (51)

[0109] In the formula, Is a node The transmission line optimality cutting plane Hamiltonian; is the internal iteration number of the lower transmission line switching module; It is The constant term of the optimality cutting plane of the transmission line at the iteration; It is The variable of the optimality cutting plane of the transmission line for the iteration The coefficient of It is The upper bound of the switching module of the lower transmission line in the iteration; It is the penalty term introduced in the process of transforming the optimality cutting plane of the transmission line into a quadratic unconstrained binary optimization form;

[0110] The mathematical model of the transmission line feasibility cutting plane Hamiltonian in the form of quadratic unconstrained binary optimization is:

[0111] (52)

[0112] In the formula, Is a node The Hamiltonian of the unit commitment feasibility cutting plane; is the number of auxiliary binary variables required for the feasibility cutting plane of the transmission line; is an auxiliary binary variable introduced by the feasibility cutting plane of the transmission line; It is The constant term of the transmission line feasibility cutting plane for the iteration; It is The variables of the feasibility cut plane of the transmission line for the iteration The coefficient of It is the penalty term introduced in the process of transforming the feasibility cutting plane of the transmission line into a quadratic unconstrained binary optimization form;

[0113] Step (13): Update the on / off status of the transmission line , repeat steps (9), (10), (11), and (12) until the upper and lower bounds of the lower transmission line switching module converge to the set error limit, then output the optimal transmission line topology and system power flow, and input the obtained unit scheduling plan, transmission line topology, and system power flow solution into the accident verification module;

[0114] Step (14): If the transmission line relaxation subproblem after relaxation still has no feasible solution, then on the basis of the local transmission line optimal subproblem, all transmission lines are fixed to a connected state, and the node power balance constraint is relaxed to ensure that the subproblem has a feasible solution, and the node relaxation subproblem is constructed. The dual multiplier of the node minimum crossing limit and the constraint is solved, and the unit combination safety cutting plane for correcting the unit scheduling is constructed;

[0115] The mathematical model of the relaxed node relaxation subproblem is:

[0116] (53)

[0117] (54)

[0118] (55)

[0119] (56)

[0120] (57)

[0121] (58)

[0122] (59)

[0123] In the formula, represents the minimum violation of the node power balance constraint; node power relaxation variable , Respectively represent nodes exist surplus and loss of relaxation power at the moment;

[0124] The mathematical model of the unit combination safety cutting plane is:

[0125] (60)

[0126] In the formula, is the minimum crossing limit obtained by solving the node relaxation subproblem; is the dual multiplier corresponding to the unit scheduling constraint (55);

[0127] Step (15): Convert the unit combination safety cutting plane into a Hamiltonian in the form of a quadratic unconstrained binary optimization, and add it to the Hamiltonian of the main problem of the upper unit combination module in step (6) to obtain the updated unit start-stop variable solution , repeat steps (7), (8), (9), (10), (11), (12), (13), and (14) until step (13) can successfully output the optimal transmission line topology and system power flow and enter the accident verification module;

[0128] The mathematical model of the unit commitment safety cutting plane Hamiltonian in the form of quadratic unconstrained binary optimization is:

[0129] (61)

[0130] In the formula, is the Hamiltonian of the unit combination safety cutting plane; is the number of auxiliary binary variables required for the unit combination safety cutting plane; It is an auxiliary binary variable introduced by the unit combination safety cutting plane; It is the penalty term introduced in the process of transforming the unit combination safety cutting plane into a quadratic unconstrained binary optimization form;

[0131] Step (16): Enter the accident verification module, and change the unit power capacity relaxation constraints (47)(48), the transmission line power flow capacity constraints (49)(50) and the power flow constraints (43)(44) to accident variant constraints. Then perform an accident feasibility check, which is essentially a relaxation problem. If there is no feasible solution to this check, construct the machine safety cutting plane through the accident node relaxation subproblem and return to the upper unit combination module to correct the temporary unit scheduling corresponding to the accident, and repeat step (15). If there is a feasible solution, further determine whether the system over-limit under the accident is zero at this time: if not, return to the accident transmission line relaxation subproblem of the lower transmission line switching module, and redetermine the system topology through the internal loop of the lower transmission line switching module, and repeat steps (11), (12), and (13); if so, it indicates that the current given unit scheduling and transmission line topology are still applicable to the accident situation, and output the optimal solution for the unit and transmission line;

[0132] The mathematical model for accident feasibility check is:

[0133] (62)

[0134] (63)

[0135] (64)

[0136] (65)

[0137] (66)

[0138] (67)

[0139] (68)

[0140] (69)

[0141] (70)

[0142] (71)

[0143] In the formula, Indicates that the system is in an accident The minimum amount of over-limit in the case.

[0144] Compared with the prior art, the present invention has the following advantages and effects:

[0145] (1) The existing classical methods are slow in solving problems, while the present invention combines quantum computing to accelerate the solution of combinatorial optimization problems and decomposition ideas, which can quickly search for the optimal power grid topology and power generation decisions.

[0146] (2) The existing decomposition and coordination methods are less effective in solving complex mixed integer nonlinear programming problems and do not consider the direct mutual influence between the unit combination problem and the transmission line switching. The present invention decomposes the original problem into different modules, which are further decomposed into multiple sub-problems and main problems, thereby reducing the optimization complexity of the decomposed model.

[0147] (3) The existing alternating direction multiplier method, Lagrange dual method, and Benders decomposition method have poor convergence in solving mixed integer nonlinear programming problems. However, the different modules of the present invention interact efficiently through the cutting plane Hamiltonian, and ultimately influence each other to approach the global optimal solution, thereby ensuring the convergence of the method.

[0148] (4) The present invention was tested on a quantum real machine platform. The comparison results with other methods showed that this method had the lowest power generation energy consumption and the shortest solution time. BRIEF DESCRIPTION OF THE DRAWINGS

[0149] Figure 1 It is a module framework diagram of the method of the present invention.

[0150] Figure 2 It is a flow chart of the upper unit combination module of the method of the present invention.

[0151] Figure 3 It is a flow chart of the lower layer transmission line switching module of the method of the present invention.

[0152] Figure 4 It is a flow chart of the accident verification module of the method of the present invention. DETAILED DESCRIPTION

[0153] The present invention proposes a quantum-classical multi-stage optimization method for unit combination and transmission line switching, which is described in detail in conjunction with the accompanying drawings as follows:

[0154] Figure 1 This is a module framework diagram of the method of the present invention. The method consists of an upper unit combination module, a lower transmission line switching module and an accident verification module. The upper unit combination module is responsible for outputting the optimal unit power generation scheduling on the day before. After the internal circulation of the upper unit combination module, a set of unit scheduling is obtained. And sent to the lower transmission line switching module. When the unit scheduling does not meet the power flow safety, the corresponding optimal network topology and system power flow are generated through the internal loop of the lower layer. If there is no adaptive system topology under the unit scheduling scheme, the lower transmission line switching module will construct the unit safety cutting plane and return it to the upper unit combination module to further correct the unit scheduling. Through the internal and external loops of the upper unit combination module and the lower transmission line module, a set of optimal unit start and stop states, unit output power, transmission line switching states and system power flows under normal conditions are obtained. , and send the solution to the accident verification module. This module introduces parameters representing N-1 accidents in the relevant constraints, and constructs the unit combination safety cutting plane according to the different over-limit situations of the system and returns it to the upper unit combination module, or constructs the transmission line feasibility cutting plane and returns it to the lower transmission line switching module. The optimal solution for the conventional situation is re-corrected, and it is finally responsible for outputting the optimal solution in the case of N-1 accidents, realizing reactive intelligent error correction, and avoiding safety problems caused by N-1 accidents.

[0155] Figure 2 This is the flow chart of the upper unit combination module of the method of the present invention. It receives the input of the Hamiltonian of the unit combination safety cutting plane and is responsible for outputting the optimal unit power generation dispatch, that is, the unit start-stop state that minimizes the operating cost of the power system. And unit output . This module decomposes the unit combination problem into the unit combination optimal subproblem, the unit combination relaxation subproblem and the unit combination main problem Hamiltonian according to the variable type. Since the optimal subproblem and the relaxation subproblem have low optimization complexity, the continuous variable solution can be obtained by using mature classical solvers. The dual information provided by the subproblem is used to construct the cutting plane to reduce the feasible domain of binary variables. The exponential combination of discrete variables leads to high optimization complexity. Therefore, this method converts the cutting plane into the corresponding Hamiltonian in the form of quadratic unconstrained binary optimization to be suitable for quantum computer accelerated solution. If there is a feasible solution to the unit combination optimal subproblem, the upper bounds of the continuous variables and the objective function of the upper unit combination module are calculated, and the unit combination optimality cutting plane Hamiltonian is constructed according to the dual signal to return the unit combination main problem. If there is no feasible solution to the unit combination optimal subproblem, the slack variable is introduced to construct the unit combination relaxation subproblem, and the continuous slack variable is obtained by solving it. The unit combination feasibility cutting plane Hamiltonian is constructed according to the dual signal and the unit combination main problem is returned. Using quantum computers to accelerate the solution of the Hamiltonian of the unit combination master problem composed of cutting plane Hamiltonians to optimize the binary solution and the lower bound of the objective function of the upper unit combination module, and repeat the above steps until the upper and lower bounds of the objective function of the upper unit combination module converge to within the error limit.

[0156] Figure 3 The lower transmission line switching module flow chart of the method of the present invention. This block converts the unit scheduling provided by the upper unit combination module As input, it is responsible for outputting the optimal transmission line switching state adapted to it and system flow If there is no adapted system topology, the unit combination safety cutting plane Hamiltonian is output and returned to the upper unit combination module to further correct the unit scheduling. This module decomposes the transmission line switching problem into the transmission line optimal subproblem, transmission line relaxation subproblem, node relaxation subproblem and transmission line switching main problem Hamiltonian according to the variable type. If there is a feasible solution to the transmission line optimal subproblem, the continuous variable solution and the upper bound of the objective function of the lower transmission line switching module are calculated. The change in system operating cost caused by the state change of the transmission line is defined as the cost sensitivity of the transmission line to the system operating cost. Based on the sensitivity, the transmission line optimality cutting plane is constructed and converted into a Hamiltonian in the form of quadratic unconstrained binary optimization. If there is no feasible solution to the optimal subproblem of the transmission line, then relax the power capacity constraint of the unit and the power flow capacity constraint of the transmission line to construct a relaxed subproblem of the transmission line. If the relaxed subproblem has a solution, define the over-limit change of the system caused by the state change of the transmission line as the over-limit sensitivity of the transmission line to the system operation cost, and construct the feasibility cutting plane of the transmission line based on the sensitivity and transform it into a Hamiltonian in the form of quadratic unconstrained binary optimization; construct the Hamiltonian of the transmission line switching main problem from the transmission line optimality cutting plane and the feasibility cutting plane Hamiltonian, and use quantum computers to accelerate the solution of the main problem to obtain a binary solution and the lower bound of the objective function of the lower transmission line switching module. Repeat the above steps until the upper and lower bounds of the objective function of the lower transmission line switching module converge to within the error limit. If the transmission line relaxation subproblem after relaxation still has no solution, it means that the unit scheduling scheme provided by the upper unit combination module has no adaptive system topology. Further relax the node power balance constraint to construct the node relaxation subproblem, construct the unit safety cutting plane Hamiltonian based on its dual information, and return to the upper unit combination module.

[0157] Figure 4 This is the flow chart of the accident verification module of the method of the present invention. This module combines the upper unit combination module and the lower transmission line switching module to obtain the optimal solution for the normal situation. As input, responsible for outputting the optimal solution for N-1 accident situations , or output the unit combination safety cutting plane according to different situations and return it to the upper unit combination module and the transmission line feasibility cutting plane to return it to the lower transmission line switching module. This module introduces the parameter representing N-1 accident in the constraints of the node relaxation subproblem and the transmission line relaxation subproblem. , Therefore, this module consists of an accident feasibility check, an accident node relaxation subproblem, and an accident transmission line relaxation subproblem. First, an accident feasibility check is performed, which is essentially a relaxation problem, and the corresponding system over-limit is obtained by solving it. If there is no feasible solution to this check, it means that the violation of various safety constraints cannot be avoided by switching transmission lines in the case of this accident. Therefore, it is necessary to construct a machine safety cutting plane through the accident node relaxation subproblem and return to the upper unit combination module to correct the unit scheduling of the corresponding accident. If there is a feasible solution, it is further determined whether the system over-limit under the accident is zero at this time: if so, it indicates that the current given unit scheduling and transmission line topology are still applicable to the accident situation, and the optimal solution is output; if not, it returns to the accident transmission line relaxation subproblem of the lower transmission line switching module, and the system topology is re-determined through the internal loop of the lower transmission line switching module.

[0158] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A quantum-classical multi-stage optimization method for unit combination and transmission line switching, characterized in that: Combining model decomposition and cutting plane Hamiltonian construction, combining classical optimization methods and quantum computing, for joint control of unit scheduling and transmission line switching in power systems, realizing the function of rapid search for optimal unit scheduling and grid topology of power systems, improving the solution speed of unit combination joint transmission line switching model, improving the reliability and flexibility of power systems, reducing power system power generation energy consumption and pollution; the steps in the use process are: Step (1): The joint optimization model of unit combination and transmission line switching is set according to different optimization functions: an upper consensus unit combination module responsible for optimizing unit start and stop and output power; a lower consensus transmission line switching module responsible for optimizing transmission line connectivity, system power flow and node phase angle; and an accident verification module considering N-1 accident conditions; A joint optimization model of unit commitment and transmission line switching considering N-1 safety constraints is constructed, which specifically includes the objective function and operation constraints: The mathematical model of the objective function of the joint optimization problem of unit commitment and transmission line switching is: (1) (2) (3) (4) In the formula, is a function of the fuel cost of the generator set; is the unit startup cost function; is the transmission line switching cost function; are the number of units, time periods and transmission lines respectively; Continuous variables Indicates timing group exist Output power at the moment; unit start and stop variables Indicates the unit exist The start and stop status at any time, when the unit is in the start state , when closed ; Transmission line on-off variable Represents a transmission line exist The on-off state at the moment, when the transmission line is connected , the transmission line is cut off ;parameter , and For each unit The secondary coefficient, primary coefficient and startup cost coefficient of power generation fuel cost; parameters For transmission line switching costs; The mathematical model of the power balance constraint of each node is: (5) In the formula, Representation Node The set of units configured in; , , Respectively represent nodes The outgoing, incoming and total transmission lines of ; Represents a transmission line exist Current power at the moment; Is a node At the moment Load; The mathematical model of unit power capacity constraint is: (6) (7) In the formula, the parameters , It is the lower and upper limits of the unit’s output power; Crew accident binary parameters Indicates that in the accident Medium Unit exist The state of the moment, represents a regular event, i.e. ; The mathematical model of the minimum start-stop time constraint of the unit is: (8) (9) In the formula, the parameters , Indicates the unit Minimum start and stop time; The mathematical model of the power flow capacity constraint of the transmission line is: (10) (11) In the formula, the parameters Represents a transmission line Maximum power flow; Binary parameters of transmission line accidents Indicates that in the accident Transmission line exist The state of the moment, represents a regular event, i.e. ; The power flow constraint follows Kirchhoff's law. The mathematical model of simulating the system network power flow using the DC power flow equation is: (12) (13) (14) In the formula, Representation Node exist The phase angle of the moment; For transmission line reactance. is a sufficiently large constant introduced by the big-M method to satisfy ; The mathematical model of the upper limit constraint of transmission line switching is: (15) In the formula, is the maximum number of disconnected transmission lines allowed in the network at any time; The mathematical model of anti-islanding constraint is: (16) Step (2): The upper unit combination module is decomposed into the consensus-based local unit combination optimal sub-problem, the unit combination relaxation sub-problem and the local unit combination main problem according to the different types of variables; Step (3): Randomly generate the initial start and stop variables of the unit For nodes equipped with generators, the connection relationship of these nodes is preset according to the transmission line topology, and the interactive power between adjacent nodes is introduced. As a consensus amount, for nodes Construct the optimal sub-problem of unit commitment based on consensus; The mathematical model of the optimal sub-problem of unit commitment is: (17) (18) (19) (20) In the formula, Representation Node A collection of configured units; Representation and Node A set of nodes with adjacent relationships; , are the dual multiplier and penalty term of consensus constraints respectively; and subscript Together with the node and nodes The relevant quantity is at the node A copy of Representation Node , The interaction power between global variables; Representation Node , The interaction power local variable between nodes, that is, the interaction power at the node Replicas in local subproblems; consensus amount The preceding symbol is determined by the preset node connection and represents the node in the preset connection. With adjacent nodes The power flow direction, Indicates that in the preset connection, the power is provided by the local node Flow to adjacent nodes , It indicates the opposite situation; Step (4): If there is a feasible solution to the optimal subproblem of unit commitment, the consensus variables of each node are made to converge to the same through consensus iteration between nodes, and the local dual variables corresponding to constraints (19) and (20) are obtained by solving them. , and the optimal solution for local continuous variables , update the upper bound of the objective function of the upper unit combination module , construct node The optimality cutting plane of unit commitment; The mathematical model of the optimal cutting plane of unit commitment is: (21) In the formula, is the feasible domain of the optimal cutting plane of local unit commitment; is the dual variable corresponding to constraint (19); is the dual variable corresponding to constraint (20); is the continuous variable solution obtained by solving the optimal subproblem of local unit commitment; is the constant term obtained by sorting in the cutting plane; is the unit start and stop variable obtained in the cutting plane The coefficient of Step (5): If there is no feasible solution to the optimal subproblem of unit commitment, then introduce continuous slack variables The original unit combination relaxation subproblem is constructed, and the Karush-Kuhn-Tucker condition of the relaxation subproblem is used as the constraint to express optimality. At the same time, the system over-limit cost and relaxation variable restriction constraints are introduced to construct the improved unit combination relaxation subproblem. The improved relaxation subproblem is solved to obtain the dual variables of the relaxation constraint of the unit output within each node. and continuous variable solutions , construct the unit commitment feasibility cutting plane at the node level; The mathematical model of the original unit combination relaxation subproblem is: (22) (23) (24) (25) (26) In the formula, is the slack variable of the unit minimum power constraint (19); is the slack variable of the unit maximum power constraint (20); Is the system in the period Total load; The mathematical model of the improved unit commitment relaxation subproblem is: (27) (28) (29) The mathematical model of the unit commitment feasibility cutting plane is: (30) In the formula, is the dual multiplier of the unit minimum power constraint (19); is the dual multiplier of the unit maximum power constraint (20); is the continuous variable solution obtained by solving the improved unit commitment relaxation subproblem model; is the constant term obtained by sorting in the cutting plane; is the unit start and stop variable obtained in the cutting plane The coefficient of Step (6): Convert the unit combination optimality cutting plane obtained in step (4) and the unit combination feasibility cutting plane obtained in step (5) into a Hamiltonian in the form of quadratic unconstrained binary optimization, and construct the node The Hamiltonian of the main problem is solved efficiently using a quantum computer to obtain the optimized start-stop variables of the unit and update the lower bound of the objective function of the upper unit combination module. ; The mathematical model of the cutting plane Hamiltonian of the unit commitment optimality in the form of quadratic unconstrained binary optimization is: (31) In the formula, Is a node The cutting plane Hamiltonian of unit commitment optimality; is the number of internal iterations of the upper unit combination module; It is The constant term of the unit commitment optimality cutting plane for the iteration; It is The variable of the optimal cutting plane of unit commitment for the iteration The coefficient of It is The upper bound of the upper unit combination module in the iteration; It is the penalty term introduced in the process of transforming the unit commitment optimality cutting plane into a quadratic unconstrained binary optimization form; The mathematical model of the Hamiltonian of the unit commitment feasibility cutting plane in the form of quadratic unconstrained binary optimization is: (32) In the formula, Is a node The Hamiltonian of the unit commitment feasibility cutting plane; is the number of auxiliary binary variables required for the unit commitment feasibility cutting plane; It is an auxiliary binary variable introduced by the unit commitment feasibility cutting plane; It is The constant term of the unit commitment feasibility cutting plane of the iteration; It is The variables of the unit commitment feasibility cutting plane for the iteration The coefficient of Step (7): Update the unit start and stop variables , repeat steps (3), (4), (5), and (6) until the upper and lower bounds of the upper unit combination module converge to the set error limit, and then output the optimal unit start and stop state and unit output power; Step (8): Determine the unit scheduling plan Passed down to the lower-level consensus transmission line switching module, which is decomposed into consensus-based transmission line optimal sub-problem, transmission line relaxation sub-problem, node relaxation sub-problem and transmission line switching main problem according to different variable types; Step (9): Input the unit start and stop variables determined in step (8) , generating the initial transmission line topology state , based on the transmission line topology, the transmission line power flow between adjacent nodes is introduced and node phase As a consensus amount, for nodes Construct the consensus-based optimal subproblem of transmission lines; The mathematical model of the optimal sub-problem of the transmission line is: (33) (34) (35) (36) (37) (38) (39) (40) (41) In the formula, is the objective function value of this subproblem; Representation and Node A collection of related transmission lines; , denotes the local copy of the interaction power at the local node and the local copy of the phase angle at the adjacent node, respectively. The subscript and superscript together denote the transmission line or Node The local node corresponding to the physical quantity a copy of; , denote the dual variable and penalty coefficient of the power flow consensus constraint respectively; , denote the dual variable and penalty coefficient of the phase angle consensus constraint respectively; Step (10): If there is a feasible solution to the optimal subproblem of the transmission line, the consensus variables of each node are made to converge to the same through consensus iteration between nodes, and the effect of each transmission line state on the system node is calculated. The upper bound of the objective function of the lower transmission line switching module is updated based on the sensitivity of the operating cost , construct the optimality cutting plane of transmission line based on sensitivity; The mathematical model of the optimal cutting plane of the transmission line is: (42) In the formula, Indicates the node corresponding to the current system topology under a given unit scheduling plan The objective function value of Represents a transmission line In the period Sensitivity to system operating costs when states change; is the constant term obtained by sorting in the cutting plane; is the state variable of the transmission line obtained in the cutting plane The coefficient of Step (11): If there is no feasible solution to the transmission line optimal subproblem, then relax the unit power capacity constraint and the transmission line power flow capacity constraint on the basis of the transmission line optimal subproblem, and construct a transmission line relaxation subproblem based on consensus. If the relaxation subproblem has a solution, obtain the state of each transmission line for the nodes in the system. The sensitivity of the over-limit is calculated, and the feasibility cutting plane of the transmission line is constructed based on the sensitivity; The mathematical model of the objective function of the relaxed transmission line relaxation subproblem is: (43) In the formula, the slack variable of unit capacity constraint is , Respectively represent the unit exist The reverse and forward relaxation power at time t. Transmission line capacity relaxation variable , Represents transmission line exist The sum of all slack variables represents the system node Local over-limit ; The mathematical model for relaxing the unit power capacity constraint and the transmission line power flow capacity constraint is: (44) (45) (46) (47) (48) (49) The mathematical model of the transmission line feasibility cutting plane constructed based on sensitivity is: (50) In the formula, is the state of each transmission line for each node in the system The sensitivity of the over-limit; is the constant term obtained by sorting in the cutting plane; is the state variable of the transmission line obtained in the cutting plane The coefficient of Step (12): Convert the optimality cutting plane of the transmission line obtained in step (10) and the feasibility cutting plane of the transmission line obtained in step (11) into a Hamiltonian in the form of quadratic unconstrained binary optimization, and construct the node The Hamiltonian of the main problem of transmission line switching is efficiently solved using a quantum computer to obtain the optimized transmission line on-off state variables and update the lower bound of the objective function of the lower transmission line switching module. ; The mathematical model of the optimality cutting plane Hamiltonian of the transmission line in the form of quadratic unconstrained binary optimization is: (51) In the formula, Is a node The transmission line optimality cutting plane Hamiltonian; is the internal iteration number of the lower transmission line switching module; It is The constant term of the optimality cutting plane of the transmission line at the iteration; It is The variable of the optimality cutting plane of the transmission line for the iteration The coefficient of It is The upper bound of the switching module of the lower transmission line in the iteration; It is the penalty term introduced in the process of transforming the optimality cutting plane of the transmission line into a quadratic unconstrained binary optimization form; The mathematical model of the Hamiltonian of the transmission line feasibility cutting plane in the form of quadratic unconstrained binary optimization is: (52) In the formula, Is a node The Hamiltonian of the unit commitment feasibility cutting plane; is the number of auxiliary binary variables required for the feasibility cutting plane of the transmission line; is an auxiliary binary variable introduced by the feasibility cutting plane of the transmission line; It is The constant term of the transmission line feasibility cutting plane for the iteration; It is The variables of the feasibility cut plane of the transmission line for the iteration The coefficient of It is the penalty term introduced in the process of transforming the feasibility cutting plane of the transmission line into a quadratic unconstrained binary optimization form; Step (13): Update the on / off status of the transmission line , repeat steps (9), (10), (11), and (12) until the upper and lower bounds of the lower transmission line switching module converge to the set error limit, then output the optimal transmission line topology and system power flow, and input the obtained unit scheduling plan, transmission line topology, and system power flow solution into the accident verification module; Step (14): If the transmission line relaxation subproblem after relaxation still has no feasible solution, then on the basis of the local transmission line optimal subproblem, all transmission lines are fixed to be connected, and the node power balance constraint is relaxed to ensure that the subproblem has a feasible solution, and the node relaxation subproblem is constructed. The dual multiplier of the node minimum crossing limit and the constraint is solved, and the unit combination safety cutting plane for correcting the unit scheduling is constructed; The mathematical model of the relaxed node relaxation subproblem is: (53) (54) (55) (56) (57) (58) (59) In the formula, represents the minimum violation of the node power balance constraint; node power relaxation variable , Respectively represent nodes exist surplus and loss of relaxation power at the moment; The mathematical model of the unit combination safety cutting plane is: (60) In the formula, is the minimum crossing limit obtained by solving the node relaxation subproblem; is the dual multiplier corresponding to the unit scheduling constraint (55); Step (15): Convert the unit combination safety cutting plane into a Hamiltonian in the form of a quadratic unconstrained binary optimization, and add it to the Hamiltonian of the main problem of the upper unit combination module in step (6) to obtain the updated unit start-stop variable solution , repeat steps (7), (8), (9), (10), (11), (12), (13), and (14) until step (13) can successfully output the optimal transmission line topology and system power flow and enter the accident verification module; The mathematical model of the unit commitment safety cutting plane Hamiltonian in the form of quadratic unconstrained binary optimization is: (61) In the formula, is the Hamiltonian of the unit combination safety cutting plane; is the number of auxiliary binary variables required for the unit combination safety cutting plane; It is an auxiliary binary variable introduced by the unit combination safety cutting plane; It is the penalty term introduced in the process of transforming the unit combination safety cutting plane into a quadratic unconstrained binary optimization form; Step (16): Enter the accident verification module and change the unit power capacity relaxation constraints (47)(48), transmission line power flow capacity constraints (49)(50) and power flow constraints (43)(44) to accident variant constraints. Then perform an accident feasibility check, which is essentially a relaxation problem. If there is no feasible solution to this check, construct a machine safety cutting plane through the accident node relaxation subproblem and return to the upper unit combination module to correct the temporary unit scheduling corresponding to the accident, and repeat step (15). If there is a feasible solution, it is further determined whether the system over-limit under the accident is zero. If not, it returns to the accident transmission line relaxation subproblem of the lower transmission line switching module, and the system topology is re-determined through the internal loop of the lower transmission line switching module, and steps (11), (12), and (13) are repeated. If so, it indicates that the current given unit scheduling and transmission line topology are still applicable to the accident situation, and the optimal solution of the unit and transmission line is output. The mathematical model for accident feasibility check is: (62) (63) (64) (65) (66) (67) (68) (69) (70) (71) In the formula, Indicates that the system is in an accident The minimum amount of over-limit in the case.

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