CN116842669A - Quantum computation-based power network topology optimization method - Google Patents
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Abstract
The invention relates to the technical field of power, in particular to a power network topology optimization method based on quantum computation, which comprises the following steps of: step 1: defining a power network topology optimization problem; step 2: designing an initial Hamiltonian amount and a target Hamiltonian amount; step 3: setting an initial state of a quantum bit in a quantum state space, wherein the initial state is used for representing an initial state of a power network; step 4: by adjusting the parameters of the quantum bits, the target Hamiltonian amount is gradually evolved; step 5: monitoring the change of the energy of the quantum system along with time by monitoring an expected value of the target Hamiltonian quantity; step 6: different strategies are adopted to adjust and adjust parameters of the quantum bits so as to balance rapid convergence and avoid sinking into local minimum values; step 7: the final state of the quantum system is extracted, which state will correspond to a power network topology. Through quantum evolution and annealing strategies, high-efficiency global optimization is realized, and the stability and reliability of the power network are improved.
Description
Technical Field
The present disclosure relates to, but not limited to, the field of power technology, and in particular to a method for optimizing power network topology based on quantum computing.
Background
With the ever-increasing scale of power networks and increasing power loads, the problem of optimizing power networks has become increasingly complex and important. Conventional power network topology optimization methods are generally based on conventional optimization algorithms, such as genetic algorithms, particle swarm optimization, and the like, and can find out a better solution of a topology structure to a certain extent, but are often limited by the problem of the dimension of a search space and a local optimal solution. In practical applications, many factors, such as current transmission loss, node power supply and demand balance, etc., often need to be considered in optimizing the power network, so that the problem is more complex.
However, conventional optimization algorithms present challenges in solving the power network topology optimization problem. First, the size and complexity of the power network results in a huge search space, and it is difficult for conventional algorithms to find the optimal solution in a reasonable time. Secondly, because the power network topology involves the trade-off of a plurality of factors, the traditional algorithm is difficult to fully consider the comprehensive influence of the factors, and is easy to fall into a local optimal solution, so that the optimal result is not satisfactory. Furthermore, the power network is subject to the influence of external environment during operation, and conventional algorithms have difficulty in adjusting the optimization strategy in real time to cope with such changes.
In recent years, with the development of quantum computing technology, quantum computing has shown great potential in solving complex optimization problems. Quantum computation can have natural advantages in searching for large-scale solution spaces by taking advantage of the parallel computation of the quantum bits and the nature of the quantum superposition states. However, existing methods of power network topology optimization based on quantum computing still face some challenges. On the one hand, quantum computing is still in the development stage in terms of hardware and algorithms, limiting its application in practical problems. Quantum computing, on the other hand, may require more advanced algorithms and methods for the complexity and diversity of the power network.
Thus, there is a need for a more efficient and accurate method to address the power network topology optimization problem. The method needs to comprehensively consider the complex relation of various factors in the power network, and can find the global optimal solution in reasonable time. Meanwhile, the method needs to fully utilize the advantages of quantum computation, overcomes the limitations in the prior art, and enables the quantum computation to play a larger role in the field of power network optimization.
Disclosure of Invention
The power network topology optimization method based on quantum computation is provided, the quantum parallel computation and superposition state characteristics are utilized, and various optimization factors are comprehensively considered through quantum evolution and dynamic annealing scheduling, so that efficient global optimization is realized, and the stability, reliability and efficiency of a power network are remarkably improved.
In order to solve the problems, the technical scheme of the invention is realized as follows: a method for optimizing a power network topology based on quantum computation, the method performing the steps of:
step 1: defining a power network topology optimization problem;
step 2: designing an initial Hamiltonian amount and a target Hamiltonian amount, and mapping an optimization target of the power network topology optimization problem to a quantum state space to form a quantum system;
step 3: setting an initial state of a quantum bit in a quantum state space, wherein the initial state is used for representing an initial state of a power network;
step 4: gradually evolving the target Hamiltonian amount by adjusting parameters of the quantum bit so as to guide the quantum system to approach an optimized target;
step 5: monitoring the change of the energy of the quantum system along with time by monitoring an expected value of the target Hamiltonian quantity; setting a convergence judgment threshold range, and executing step 6 if the change value of the energy change along with time is within the set convergence judgment threshold range; if the change value of the energy change along with time is outside the set convergence judgment threshold value range, returning to the step 4 to continue execution;
step 6: different strategies are adopted to adjust and adjust parameters of the quantum bits so as to balance rapid convergence and avoid sinking into local minimum values;
step 7: extracting a final state of the quantum system, the state corresponding to an electrical network topology; and decoding the final state of the quantum system into an optimal solution of the power network to finish the topology optimization of the power network.
Further, the step 1 specifically includes:
step 1.1: node set defining a power networkAnd connection set->Wherein each node represents a point in the power network and each connection represents a relationship between nodes;
step 1.2: construction of adjacency matrixThe adjacency matrix->Element->Representing node->And node->Connection state between (I) and (II)>Indicating connection(s)>Indicating a final connection;
step 1.3: for each connectionIntroducing a current variable->Representing by connection +.>At the same time +.>Distribution resistor->；
Step 1.4: defining a current transfer loss function as:the current transfer loss function represents the connection +.>Energy loss on the same.
Further, the step 2 specifically includes:
step 2.1: building energy loss terms using the following formula：
；
wherein ,is a connection->A power transfer loss function thereon;
step 2.2: construction of node power supply and demand balance term using the following formula：
；
wherein ,is an element of the adjacency matrix representing the node +.>And node->Connection state between (I) and (II)>Is node-> andA difference in power supply and demand between them;
step 2.3: constructing a target Hamiltonian volumeThe method specifically comprises the following steps: energy loss term->And other optimization factors->Taken together, the target Hamiltonian amount is constructed>：
；
wherein ,is a weight factor for balancing different items, and has a value ranging from 0.1 to 1.
Further, the step 3 specifically includes:
step 3.1: for each power network nodeIntroducing a quantum bit to represent the quantum state of the node; the qubits are represented using a binary representation, wherein +.>Indicating that node is not connected, +.>Representing node connections;
step 3.2: setting the initial quantum state of each qubit to be a state of an equal probability distribution:
；
wherein ,is the total number of qubits, +.>Indicate->Quantum states of the individual nodes;Is an initial quantum state and is used for representing the initial state of the power network.
Further, the step 4 specifically includes:
step 4,1: setting an annealing time table and scheduling evolution time: an annealing schedule is set, wherein the annealing schedule comprises a plurality of time points, which are respectively:the method comprises the steps of carrying out a first treatment on the surface of the The time point corresponds to the adjustment time of the qubit parameter in the annealing process;An upper limit for the number of set time points;
step 4.2: for each point in timeConstructing a quantum annealing operator>For adjusting the state of the qubit, said quantum annealing operator->The expression is used as follows:
；
wherein ,is the target hamiltonian,>is the current annealing time, +.>Is imaginary unit, ++>Takes the subscript as a positive integer and takes the value range of 0 to +.>；Is the initial hamilton amount;A scheduling function for annealing.
Step 4.3: during the annealing process, from the initial stateInitially, each quantum annealing operator is applied in turn using the following formula>Evolution is carried out:
；
over time, the state of the quantum system evolves gradually to guide the quantum system to approach the optimization objective.
Further, the step 5 specifically includes:
step 5.1: at each annealing time pointCalculating the current quantum state->Corresponding target Hamiltonian amountIs a desired value of (2):
；
wherein ,is at the time +.>Energy expectancy of ∈ ->Is->Is a conjugate transpose of (2);
step 5.2: setting a convergence judgment threshold range, and executing step 6 if the change value of the energy change along with time is within the set convergence judgment threshold range; if the change value of the energy change along with time is outside the set convergence judgment threshold value range, returning to the step 4 to continue execution.
Further, the step 6 specifically includes:
step 6.1: setting an initial temperatureAnd termination temperature->The method comprises the steps of carrying out a first treatment on the surface of the Said initial temperature->A state higher than a set first value so as to be able to accept high energy in an initial stage; the termination temperature->A non-zero value infinitely close to zero to converge to a low energy state at the end of annealing;
step 6.2: setting an exponentially decaying temperature decay scheme at each annealing time stepThe temperature was adjusted using the following formula:
；
wherein ,is time->Temperature at (I)>Is an attenuation factor;
step 6.3: determining whether to accept the new state by Mei Teluo wave lites criterion specifically includes: at the time ofFrom the current state->Generating a new state->If the energy of the new state +.>Lower, accept new state; if the energy is higher, determining whether to accept according to the set probability function, if the probability value calculated by the probability function exceeds the set acceptance threshold, accepting, otherwise, not accepting.
Further, the expression of the probability function is expressed using the following formula:
；
wherein ,for the calculated probability value.
Further, the step 7 specifically includes:
step 7.1: after the annealing process is finished, the final quantum state is extracted from the quantum system；
Step 7.2: will be in the final quantum stateThe conversion to an electrical power network specifically comprises: for each qubit in the qustates, determining the connection state of the corresponding node from its state if the state of the qubit is +.>Representing the corresponding node connection; if the state is +.>Indicating that the corresponding node is not connected.
Further, the annealing scheduling functionThe expression is used as follows:
；
wherein ,as hyperbolic tangent function, +.>The value range is 0.3 to 0.8 for the slope coefficient.
The power network topology optimization method based on quantum computation has the following beneficial effects:
the invention adopts an optimization method based on quantum computation, and overcomes the difficulty of the traditional algorithm in the aspects of search space limitation and local optimal solution. The parallel nature of quantum computation enables the algorithm to consider multiple solutions simultaneously, thereby significantly speeding up the search process. Meanwhile, through the characteristic of quantum superposition state, the algorithm can carry out jump search among different solutions, and the situation that the solution falls into a local optimal solution is avoided, so that more global optimization is realized.
The invention considers the complex relation of a plurality of factors in the power network, such as current transmission loss, node power supply and demand balance and the like. By introducing the target Hamiltonian amount and the initial Hamiltonian amount and combining a quantum annealing algorithm, various optimization factors can be comprehensively evolved in one quantum system, so that various optimization targets are balanced better, and a better topology solution is obtained.
The annealing scheduling function can adjust the evolution mode of the quantum system according to the annealing time, so that the requirements of global exploration and local optimization can be balanced in different stages. The dynamic adaptability enables the algorithm to better cope with changes in the operation of the power network, and stability and robustness of the algorithm are improved.
The annealing scheduling function and the probability function ensure that the algorithm advances towards the direction of energy reduction in the evolution process of the quantum system. The probability function controls whether to accept a new state or not through the temperature parameter, so that the new state can be gradually converged to a lower energy state in the evolution process, and the convergence of the algorithm is improved.
Drawings
Fig. 1 is a schematic flow chart of a power network topology optimization method based on quantum computation according to an embodiment of the present invention.
Description of the embodiments
In order to make the technical problems, technical solutions and advantageous effects to be solved by the present disclosure more clear and obvious, the present disclosure is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present disclosure and are not intended to limit the present disclosure.
Example 1: referring to fig. 1, a method for optimizing a power network topology based on quantum computing, the method performs the steps of:
step 1: defining a power network topology optimization problem;
in this step, the aim is to transform the actual problem of the power network into an optimization problem. This means that information about nodes, lines, loads etc. of the power network is mapped into a mathematical model in order to find an optimal solution.
Step 2: designing an initial Hamiltonian amount and a target Hamiltonian amount, and mapping an optimization target of the power network topology optimization problem to a quantum state space to form a quantum system;
the basis of quantum computation is hamiltonian, which represents the energy and interactions of the system. The design of the initial and target hamiltonians is a key step in mapping the power network problem into the quantum system. The initial hamiltonian may be set to a simple state and the target hamiltonian corresponds to an objective function of the power network optimization problem.
Step 3: setting an initial state of a quantum bit in a quantum state space, wherein the initial state is used for representing an initial state of a power network;
key to quantum computation is entanglement and unitary time evolution between qubits. By applying proper quantum gate operation, the qubit state of the system will evolve in the quantum state space, thereby gradually approaching the optimization objective.
Step 4: gradually evolving the target Hamiltonian amount by adjusting parameters of the quantum bit so as to guide the quantum system to approach an optimized target;
by applying quantum gate operation, the state of the quantum system evolves in the quantum state space. This is based on the core principle of quantum computing, which exploits the entanglement and coherence properties between qubits. The purpose of this step is to gradually adjust the state of the quantum system to a state that can approach the power network optimization objective through an adaptive evolution process.
Step 5: monitoring the change of the energy of the quantum system along with time by monitoring an expected value of the target Hamiltonian quantity; setting a convergence judgment threshold range, and executing step 6 if the change value of the energy change along with time is within the set convergence judgment threshold range; if the change value of the energy change along with time is outside the set convergence judgment threshold value range, returning to the step 4 to continue execution;
step 6: different strategies are adopted to adjust and adjust parameters of the quantum bits so as to balance rapid convergence and avoid sinking into local minimum values;
the nature of quantum computing may cause the algorithm to sink to local minima, and not easily jump out. In this step, by adjusting the evolution parameters or introducing noise, a balance can be struck between fast convergence and avoiding trapping in local minima. The purpose of this step is to increase the robustness of the algorithm, ensuring a more comprehensive search in the solution space.
Step 7: extracting a final state of the quantum system, the state corresponding to an electrical network topology; and decoding the final state of the quantum system into an optimal solution of the power network to finish the topology optimization of the power network.
In particular, conventional power network optimization problems are introduced into the quantum computing framework. By exploiting the parallel computing and coherence properties of the qubits, the optimal solution can be searched more efficiently in the quantum state space. Compared with the traditional optimization algorithm, the quantum computation-based method can find the globally optimal solution more quickly in some cases, so that the efficiency and stability of the power network are improved. In addition, this approach can also cope with complex power network topologies and changes.
Example 2: on the basis of the above embodiment, the step 1 specifically includes:
step 1.1: node set defining a power networkAnd connection set->Wherein each node represents a point in the power network and each connection represents a relationship between nodes;
step 1.2: construction of adjacency matrixThe adjacency matrix->Element->Representing node->And node->Connection state between (I) and (II)>Indicating connection(s)>Indicating a final connection;
step 1.3: for each connectionIntroducing a current variable->Representing by connection +.>At the same time +.>Distribution resistor->；
Step 1.4: defining a current transfer loss function as:the current transfer loss function represents the energy loss on the connection.
Specifically, assume a simplified power network in which there are 5 nodes: A. b, C, D, E and 6 connections: AB. AC, BC, CD, DE, EA. These nodes and connections can be represented as the following set:
node set：
；
Connection set：
；
Adjacency matrixIs a matrix representing the connection relationships between nodes. For the above example of nodes and connections, adjacency matrix +.>The following is shown:
；
wherein ,representing node->And node->The connection state between the two is 1, 0 is unconnected.
One current variable is introduced for each connection. For the above connection set, the following current variables were introduced:the method comprises the steps of carrying out a first treatment on the surface of the Each current variable represents the current in the corresponding connection.
A current transfer loss function is defined for each connection. Assuming the resistance of each connectionFor a uniform value, the loss function may be defined as follows:
；
these loss functions represent the energy loss of the current transfer on each connection, which will be used in the subsequent optimization problem to calculate the energy loss and power.
Example 3: based on the above embodiment, the step 2 specifically includes:
step 2.1: building energy loss terms using the following formula：
；
wherein ,is a connection->A power transfer loss function thereon;
step 2.2: the section is constructed using the following formulaPoint power supply and demand balance item：
；
wherein ,is an element of the adjacency matrix representing the node +.>And node->Connection state between (I) and (II)>Is node-> andA difference in power supply and demand between them;
step 2.3: constructing a target Hamiltonian volumeThe method specifically comprises the following steps: energy loss term->And other optimization factors->Taken together, the target Hamiltonian amount is constructed>：
；
wherein ,is a weight factor for balancing different items, and has a value ranging from 0.1 to 1.
Specifically, energy loss termIs based on the current transfer loss function on the connection in the power network. These functions describe the energy loss of current through the connection in the power network and can be used to measure the efficiency of power transfer. The introduction of energy loss terms in the objective function allows the optimization process to take into account the energy loss of the current transmission in the power network. The optimization algorithm tends to reduce current transmission loss in the process of adjusting current distribution, so that the transmission efficiency of the power network is improved.
Node power supply and demand balance itemIs based on the adjacency matrix of the power network>And power supply and demand difference between nodes +.>. These elements represent the connection relationship between nodes and the power supply and demand difference. The node power supply and demand balance term takes into account the power supply and demand difference between nodes, which is a key problem in the operation of the power network. The optimization algorithm may tend to balance the supply and demand of power between the nodes during adjustment of the current distribution, thereby ensuring stable operation of the power network.
Target Hamiltonian volumeIs a linear combination of energy loss term and node power supply and demand balance term, wherein the energy loss term and the node power supply and demand balance term are determined by a weight factor +.>To balance the importance of both. The goal of the quantum optimization algorithm is to find the state with the lowest energy, corresponding to the optimal topology of the power network. Construction of the target Hamiltonian quantity->The function of (2) is to convert the optimization objective of the power network into the energy optimization problem of the quantum system. By finding the state with the lowest energy in the quantum state space, the optimization algorithm can find a power network topology structure to transmit power with the smallest energy loss and node power supply and demand difference.
The purpose of step 2 is to map the optimization objective of the power network to the energy optimization problem of the quantum system, and to achieve optimization of the power network by adjusting the current distribution and node supply and demand to minimize the energy loss and balance the power supply and demand difference between the nodes. The mapping and optimizing process utilizes the advantages of quantum computation, and can improve the efficiency and reliability of the power network to a certain extent.
Example 4: on the basis of the above embodiment, the step 3 specifically includes:
step 3.1: for each power network nodeIntroducing a quantum bit to represent the quantum state of the node; the qubits are represented using a binary representation, wherein +.>Indicating that node is not connected, +.>Representing node connections;
step 3.2: setting the initial quantum state of each qubit to be a state of an equal probability distribution:
；
wherein ,is the total number of qubits, +.>Indicate->Quantum states of the individual nodes;Is an initial quantum state and is used for representing the initial state of the power network.
Specifically, the qubit is a basic unit in quantum computing, and can represent different quantum states. In this step, each power network node is mapped onto a qubit state, representing the node's connection state in binary code. Mapping the power network nodes onto the qubits provides a basic unit representing the power network state for the subsequent quantum computing process.
In quantum computing, the initial quantum state is the starting point for the algorithm to run. In this step, the initial quantum state of each qubit is set to a state of an equiprobable distribution, representing an uncertainty of the initial state of the power network.
The initial quantum state is set to be in a state of equal probability distribution, and uncertainty of the initial state of the power network is reflected. This helps the algorithm to take into account the various possibilities in the search process, thereby finding an optimal solution more fully.
Example 5: based on the above embodiment, the step 4 specifically includes:
step 4,1: setting an annealing time table and scheduling evolution time: an annealing schedule is set, wherein the annealing schedule comprises a plurality of time points, which are respectively:the method comprises the steps of carrying out a first treatment on the surface of the The time point corresponds to the adjustment time of the qubit parameter in the annealing process;For setting timeAn upper limit on the number of dots;
step 4.2: for each point in timeConstructing a quantum annealing operator>For adjusting the state of the qubit, said quantum annealing operator->The expression is used as follows:
；
wherein ,is the target hamiltonian,>is the current annealing time, +.>Is imaginary unit, ++>Takes the subscript as a positive integer and takes the value range of 0 to +.>；Is the initial hamilton amount;A scheduling function for annealing.
Step 4.3: during the annealing process, from the initial stateInitially, each quantum is applied in turn using the following formulaAnnealing operator->Evolution is carried out:
；
over time, the state of the quantum system evolves gradually to guide the quantum system to approach the optimization objective.
Specifically, the annealing schedule is a series of time points that represent the annealing process in the quantum optimization algorithm. During annealing, the parameters change gradually, allowing the system to slowly evolve from a high energy state (random state) to a low energy state (possible solution). The schedule determines the evolution steps in the annealing process. The annealing schedule controls the rate and timing of parameter adjustments. The parameter change of the earlier time point is smaller, and the system can fully explore the state space; over time, the parameter changes gradually increase, causing the system to gradually trend toward a low energy state. This process is similar to the decrease in temperature during metal annealing, causing the system to gradually go from a high energy state to a steady state.
Assume that an annealing schedule is set includingTime points:. These points in time correspond to the moments of adjustment of the parameters during annealing. For example, a->，，，，。
Quantum annealing operatorFor adjusting the state of the qubit to effect the evolution of the system. It is based on two Hamiltonian volumes +.> andBy parameter->To control the mixing ratio of the two hamiltonians. The quantum annealing operators guide the evolution of the quantum system in parameter space, bringing it gradually closer to the optimal solution. By reasonable choice of mixing parameters->The system can be made to explore the state space more initially and then gradually trend toward optimization goals during annealing.
Suppose at a certain point in timeThere are parameters-> and. At this time, the quantum annealing operator may be expressed as +.>。
During annealing, from the initial quantum stateInitially, by applying the quantum annealing operator +.>And (5) evolving the quantum state. Over time, the state of the quantum system evolves gradually, approaching from the initial state towards the optimization objective. The process of quantum annealing evolution is similar to classical simulated annealing, but due to the nature of the quantum states, it can explore multiple possibilities simultaneously. This allows the system to jump out of the local minimum, more likely to find the globally optimal solution. At a certain point in time->From the initial quantum state->Initially, a quantum annealing operator is applied>Evolution is carried out to obtain a new quantum state。
Example 6: on the basis of the above embodiment, the step 5 specifically includes:
step 5.1: at each annealing time pointCalculating the current quantum state->Corresponding target Hamiltonian amountIs a desired value of (2):
；
wherein ,is at the time +.>Energy expectancy of ∈ ->Is->Is a conjugate transpose of (2);
step 5.2: setting a convergence judgment threshold range, and executing step 6 if the change value of the energy change along with time is within the set convergence judgment threshold range; if the change value of the energy change along with time is outside the set convergence judgment threshold value range, returning to the step 4 to continue execution.
Specifically, at each annealing time pointCalculating the current quantum state->Corresponding target Hamiltonian quantity->Is a desired value of (2). The expected value calculation is the average energy of the quantum state under hamiltonian. By calculating the energy expectation value, the target Hamiltonian amount can be known in the current quantum state>Is a function of the average energy of the (c). The change in energy and trend may indicate whether the optimization algorithm is approaching towards a lower energy solution.
Suppose at a certain point in timeQuantum states +.>Then the energy expectations can be calculated. In each iteration, it may be determined whether the algorithm converges by comparing the changes in the energy expectations. If the change in energy is small enough, it can be considered thatThe system has approached a steady state. The convergence judgment threshold range is used for determining whether to terminate the optimization algorithm. If the energy change is within the set threshold, the system can be considered to be converged, a certain steady state is reached, and the next step can be entered. Assume that the convergence judgment threshold range is set to +.>. If the energy variation is less than +.>The algorithm considers that it has converged and can proceed to the next step. If the energy variation is greater thanThe algorithm considers that it has not converged and needs to continue the iterative annealing process.
Example 7: based on the above embodiment, the step 6 specifically includes:
step 6.1: setting an initial temperatureAnd termination temperature->The method comprises the steps of carrying out a first treatment on the surface of the Said initial temperature->A state higher than a set first value so as to be able to accept high energy in an initial stage; the termination temperature->A non-zero value infinitely close to zero to converge to a low energy state at the end of annealing;
step 6.2: setting an exponentially decaying temperature decay scheme at each annealing time stepThe temperature was adjusted using the following formula:
；
wherein ,is time->Temperature at (I)>Is an attenuation factor;
step 6.3: determining whether to accept the new state by Mei Teluo wave lites criterion specifically includes: at the time ofFrom the current state->Generating a new state->If the energy of the new state +.>Lower, accept new state; if the energy is higher, determining whether to accept according to the set probability function, if the probability value calculated by the probability function exceeds the set acceptance threshold, accepting, otherwise, not accepting.
Specifically, temperature is an analog parameter introduced during simulated annealing to simulate the "heat" variation of the system in the search space. Initial temperatureThe settings are higher, allowing the system to initially accept high energy states, potentially jumping out of the locally optimal solution, exploring a wider solution space. Termination temperature->Setting near zero but not zero means that at the end of the annealing process the system cools down gradually, tending to converge to a low energyQuantity state, find the best solution.
The settings of the initial temperature and the end temperature control the extent of the search and the end of the anneal. The higher initial temperature helps to overcome the potential local minima, while as annealing proceeds, the reduced temperature stabilizes the system gradually, helping to find a state closer to the globally optimal solution. Setting an initial temperatureAnd termination temperature->。
The temperature decay scheme determines the temperature change over time. An exponential decay scheme is typically employed in which the temperature gradually decreases with increasing time, speeding up the system entering steady state. The temperature decay scheme ensures that the system has a higher heat early in the search, allowing for a wider range of searches. Over time, the temperature gradually decreases, enabling the system to gradually approach a steady state. Setting an attenuation factor using an exponential decay scheme。
Mei Teluo Brix criterion decides whether to accept the new state based on the energy difference and the temperature. If the energy of the new state is lower, the new state is always accepted. If the new state energy is higher, it is accepted with a certain probability, so that the locally optimal solution can be overcome, and the globally optimal solution is more likely to be found.
Mei Teluo the Bolus criterion balances the chance of accepting poor solutions, which is important when searching for globally optimal solutions. By accepting a high energy state with a certain probability, the algorithm has the opportunity to jump out of the current local minimum.
Example 8: on the basis of the above embodiment, the expression of the probability function is expressed using the following formula:
；
wherein ,for the calculated probability value.
In particular, it is assumed that at a certain point in timeThe energy of the new state is +.>The energy of the current state is +.>The current temperature is +.>. Calculating probability function values:
；
example 9: based on the above embodiment, the step 7 specifically includes:
step 7.1: after the annealing process is finished, the final quantum state is extracted from the quantum system；
Step 7.2: will be in the final quantum stateThe conversion to an electrical power network specifically comprises: for each qubit in the qustates, determining the connection state of the corresponding node from its state if the state of the qubit is +.>Representing the corresponding node connection; if the state is +.>Indicating that the corresponding node is not connected.
Specifically, after the annealing process is finished, the amountFinal state of subsystemInformation in the optimization process is contained. This final quantum state will be used to decode into an optimal solution for the power network. Final Quantum state->The path and state change of the optimization algorithm in the searching process is recorded, wherein the path and state change comprises the optimal topology information of the power network. After the annealing process is finished, the final quantum state is obtained>. The state of each qubit in the final quantum state corresponds to a node connection state in the power network. If the state of the qubit is +.>The corresponding nodes are connected; if the status is +.>The corresponding node is unconnected. And converting the final quantum state into a power network, namely mapping the quantum information to a topological structure of the power network, so as to obtain an optimized power network topology.
Example 10: on the basis of the previous embodiment, the annealing scheduling functionThe expression is used as follows:
；/>
wherein ,as hyperbolic tangent function, +.>The value range is 0.3 to 0.8 for the slope coefficient.
Specifically, annealing scheduling functionIs an important parameter in the annealing algorithm, which determines the evolution mode of the quantum annealing operator during annealing, i.e. how to weigh the target Hamiltonian amount at different time points>Initial Hamiltonian volume. The scheduling function is implemented by adjusting the slope coefficient +.>And time parameter->To achieve it, it adjusts the quantum system from the initial state to the final state at different stages of the algorithm. The annealing scheduling function is used for controlling the evolution mode of the quantum system and balancing the target Hamiltonian amount and the initial Hamiltonian amount according to different time points. It makes the system more focused on global exploration or local optimization at different stages in the search process, helping to find the optimal solution faster.
Suppose at a certain point in time，，. Calculating an annealing scheduling function value:
；
if it isCalculated to obtain. This means that at this point in time, the quantum annealing operator will uniformly trade off the effect of the target hamiltonian and the initial hamiltonian. During the annealing algorithm, the quantum annealing operators will even out the effects of the target hamiltonian and the initial hamiltonian at different points in time. In other words, as annealing proceeds, the quantum system will balance between global exploration and local optimization, not too tending to focus on only the target hamiltonian or only the initial hamiltonian. The balance property enables the quantum system to escape from a local minimum value and advance towards a global optimal solution in the searching process, so that the possibility of finding the optimal solution by an algorithm is improved. By controlling the annealing scheduling function, the evolution mode of the quantum annealing operator can be dynamically adjusted between global search and local optimization so as to better balance the depth and breadth of search.
Those of ordinary skill in the art will appreciate that all or some of the steps, systems, functional modules/units in the apparatus, and methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof.
The preferred embodiments of the present disclosure have been described above with reference to the accompanying drawings, and are not thereby limiting the scope of the claims of the present disclosure. Any modifications, equivalent substitutions and improvements made by those skilled in the art without departing from the scope and spirit of the present disclosure shall fall within the scope of the claims of the present disclosure.
Claims (10)
1. The power network topology optimization method based on quantum computation is characterized by comprising the following steps of:
step 1: defining a power network topology optimization problem;
step 2: designing an initial Hamiltonian amount and a target Hamiltonian amount, and mapping an optimization target of the power network topology optimization problem to a quantum state space to form a quantum system;
step 3: setting an initial state of a quantum bit in a quantum state space, wherein the initial state is used for representing an initial state of a power network;
step 4: gradually evolving the target Hamiltonian amount by adjusting parameters of the quantum bit so as to guide the quantum system to approach an optimized target;
step 5: monitoring the change of the energy of the quantum system along with time by monitoring an expected value of the target Hamiltonian quantity; setting a convergence judgment threshold range, and executing step 6 if the change value of the energy change along with time is within the set convergence judgment threshold range; if the change value of the energy change along with time is outside the set convergence judgment threshold value range, returning to the step 4 to continue execution;
step 6: different strategies are adopted to adjust and adjust parameters of the quantum bits so as to balance rapid convergence and avoid sinking into local minimum values;
step 7: extracting a final state of the quantum system, the state corresponding to an electrical network topology; and decoding the final state of the quantum system into an optimal solution of the power network to finish the topology optimization of the power network.
2. The method for optimizing power network topology based on quantum computation according to claim 1, wherein the step 1 specifically comprises:
step 1.1: node set defining a power networkAnd connection set->Wherein each node represents a point in the power network and each connection represents a relationship between nodes;
step 1.2: construction of adjacency matrixThe adjacency matrix->Element->Representing node->And node->Connection state between (I) and (II)>Indicating connection(s)>Indicating a final connection;
step 1.3: for each connectionIntroducing a current variable->Representing by connection +.>At the same time +.>Distribution resistor->；
Step 1.4: defining a current transfer loss function as:the current transfer loss function represents the connection +.>Energy loss on the same.
3. The method for optimizing the power network topology based on quantum computing according to claim 2, wherein the step 2 specifically comprises:
step 2.1: construction of energy loss terms using the following formula：
；
wherein ,is a connection->A power transfer loss function thereon;
step 2.2: construction of node power supply and demand balance term using the following formula：
；
wherein ,is an element of the adjacency matrix representing the node +.>And node->Connection state between (I) and (II)>Is node-> andA difference in power supply and demand between them;
step 2.3: constructing a target Hamiltonian volumeThe method specifically comprises the following steps: energy loss term->And other optimization factor termsTaken together, the target Hamiltonian amount is constructed>：
；
wherein ,is a weight factor for balancing different items, and has a value ranging from 0.1 to 1.
4. The method for optimizing power network topology based on quantum computation of claim 3, wherein said step 3 specifically comprises:
step 3.1: for each power network nodeIntroducing a quantum bit to represent the quantum state of the node; the qubits are represented using a binary representation, wherein +.>Indicating that node is not connected, +.>Representing node connections;
step 3.2: setting the initial quantum state of each qubit to be a state of an equal probability distribution:
；
wherein ,is the total number of qubits, +.>Indicate->Quantum states of the individual nodes;Is an initial quantum state and is used for representing the initial state of the power network.
5. The method for optimizing power network topology based on quantum computation of claim 4, wherein said step 4 specifically comprises:
step 4,1: setting an annealing time table and scheduling evolution time: an annealing schedule is set, wherein the annealing schedule comprises a plurality of time points, which are respectively:the method comprises the steps of carrying out a first treatment on the surface of the The time point corresponds to the adjustment time of the qubit parameter in the annealing process;an upper limit for the number of set time points;
step 4.2: for each point in timeConstructing a quantum annealing algorithmSymbol->For adjusting the state of the qubit, said quantum annealing operator->The expression is used as follows:
；
wherein ,is the target hamiltonian,>is the current annealing time, +.>Is imaginary unit, ++>Takes the subscript as a positive integer and takes the value range of 0 to +.>；Is the initial hamilton amount;Scheduling a function for annealing;
step 4.3: during the annealing process, from the initial stateInitially, each quantum annealing operator is applied in turn using the following formula>Evolution is carried out:
；
over time, the state of the quantum system evolves gradually to guide the quantum system to approach the optimization objective.
6. The method for optimizing power network topology based on quantum computation of claim 5, wherein said step 5 specifically comprises:
step 5.1: at each annealing time pointCalculating the current quantum state->Corresponding target Hamiltonian quantity->Is a desired value of (2):
；
wherein ,is at the time +.>Energy expectancy of ∈ ->Is->Is a conjugate transpose of (2);
step 5.2: setting a convergence judgment threshold range, and executing step 6 if the change value of the energy change along with time is within the set convergence judgment threshold range; if the change value of the energy change along with time is outside the set convergence judgment threshold value range, returning to the step 4 to continue execution.
7. The method for optimizing power network topology based on quantum computing of claim 6, wherein said step 6 specifically comprises:
step 6.1: setting an initial temperatureAnd termination temperature->The method comprises the steps of carrying out a first treatment on the surface of the The initial temperature is higher than a set first value so as to be capable of receiving a high-energy state in an initial stage; the termination temperature->A non-zero value infinitely close to zero to converge to a low energy state at the end of annealing;
step 6.2: setting an exponentially decaying temperature decay scheme at each annealing time stepThe temperature was adjusted using the following formula:
；
wherein ,is time->Temperature at (I)>Is an attenuation factor;
step 6.3: determining whether to accept the new state by Mei Teluo wave lites criterion specifically includes: at the time ofFrom the currentState generation New State->If the energy of the new state +.>Lower, accept new state; if the energy is higher, determining whether to accept according to the set probability function, if the probability value calculated by the probability function exceeds the set acceptance threshold, accepting, otherwise, not accepting.
8. The quantum computing-based power network topology optimization method of claim 7, wherein an expression of said probability function is expressed using the following formula:
；
wherein ,for the calculated probability value.
9. The method for optimizing power network topology based on quantum computing of claim 8, wherein said step 7 specifically comprises:
step 7.1: after the annealing process is finished, the final quantum state is extracted from the quantum system；
Step 7.2: will be in the final quantum stateThe conversion to an electrical power network specifically comprises: for each qubit in the qustates, determining the connection state of the corresponding node from its state if the state of the qubit is +.>Representing the corresponding node connection; if the state is +.>Indicating that the corresponding node is not connected.
10. The quantum computing-based power network topology optimization method of claim 6, wherein said annealing schedule functionThe expression is used as follows:
；
wherein ,as hyperbolic tangent function, +.>The value range is 0.3 to 0.8 for the slope coefficient.
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