A distributed neurodynamics optimization method for non-convex power resource allocation

Abstract

The application discloses a kind of distributed neural dynamics optimization methods for realizing non-convex power resource configuration, comprising: each equipment in power station is regarded as agent, constitutes multi-agent system, and constructs the energy consumption optimization model of power station;Lagrange function is constructed, and decomposition is carried out, and the multi-agent system and dynamic equation of distributed implementation are established;Different initial state is set for multi-agent system respectively, and local optimal scheduling decision and the performance of corresponding multi-agent system are obtained;Distributed average tracking mechanism is established, and group optimal scheduling decision and the average value of the performance of all multi-agent systems are obtained;Particle swarm search rule is used to reset the initial state of next round of multi-agent system;For multi-agent system, iteration is carried out, and final scheduling decision is output.The application can realize the minimization of total energy consumption of power station, and has the characteristics of distributed execution and strong convergence performance, and is suitable for large-scale power equipment collaborative control field.

Description

Technical Field

[0001] This invention relates to the intersection of next-generation information technology and power systems, specifically to a distributed neurodynamic optimization method for non-convex power resource allocation. Background Technology

[0002] With the rapid development of distributed energy systems, microgrids, and integrated energy systems, the coordinated scheduling of multiple devices, including power generation equipment, cooling / energy supply equipment, and energy storage units, has gradually become a key technical problem in energy system operation. These problems typically aim to minimize system operating costs or energy consumption while simultaneously satisfying various physical constraints such as load balancing, equipment output limits, and start-stop logic. They exhibit strong non-convexity, mixed-integer characteristics, and large-scale coupling features.

[0003] In existing research, one class of methods employs centralized or distributed neurodynamic optimization to solve energy dispatching problems. This paper proposes a distributed optimization framework based on recurrent neural networks for energy management in networked microgrids. This method achieves asymptotic convergence to the optimal solution under convex optimization conditions by constructing a continuous-time neurodynamic system and possesses some distributed computing capabilities. However, these methods typically assume that the optimization model is continuously differentiable or convex, and do not explicitly consider 0–1 decision variables such as equipment start-up and shutdown. When facing non-convex dispatching problems with discrete decisions, they are prone to getting trapped in local optima, thus limiting their applicability.

[0004] To address non-convex and combinatorial optimization problems, some studies have introduced the Collaborative Neurodynamic Optimization (CNO) framework. This framework models the scheduling of cooling and electrical loads as a global optimization problem with cardinality constraints and improves global search capabilities through parallel search using multiple neural networks combined with a metaheuristic reset mechanism. While this method alleviates the combinatorial complexity caused by cardinality constraints to some extent, its core search mechanism relies on external triggering and re-initialization strategies, resulting in a relatively complex algorithm structure. Furthermore, improvements in search speed and convergence stability primarily depend on heuristic rules, lacking further acceleration mechanisms for the continuous dynamic convergence process.

[0005] Furthermore, some existing technologies, focusing on convergence speed, have proposed distributed optimization methods with finite-time or predefined-time convergence. By constructing special nonlinear dynamic systems, they achieve consensus and convergence of the optimization objective within a preset time. However, these methods are typically designed for continuous decision variables and are difficult to directly extend to mixed-integer scheduling problems involving start and stop decisions. They are also quite sensitive to initial conditions in non-convex scenarios.

[0006] Meanwhile, the combination of deep learning and projective neural networks has also been used for multi-energy system scheduling. This method utilizes neural networks to approximate complex mapping relationships and leverages projection operators to handle constraints, achieving good optimization results in specific scenarios. However, such methods often rely on offline training or model generalization capabilities, and the stability and optimality of the algorithm are difficult to guarantee when the system scales up or the operating conditions change.

[0007] In summary, although existing technologies have made some progress in the field of energy system scheduling, they still generally have the following shortcomings: (1) Most methods are difficult to handle 0-1 decision variables such as continuous power allocation and equipment start-up and shutdown at the same time; (2) In non-convex optimization scenarios, they are prone to getting trapped in local optima or are highly sensitive to initial values; (3) Some global optimization methods have high computational complexity and are difficult to implement efficiently in large-scale distributed energy systems; (4) Existing distributed methods still have room for further improvement in terms of improving convergence speed and stability.

[0008] Therefore, there is an urgent need for an optimization method that can handle non-convex scheduling problems with cardinality constraints, has good global search capabilities, supports fully distributed implementation, and has accelerated convergence characteristics, so as to meet the needs of large-scale distributed energy systems in actual operation. Summary of the Invention

[0009] The purpose of this invention is to address the shortcomings of existing energy system scheduling methods in areas such as non-convex optimization, equipment start-up and shutdown decisions, and distributed implementation. This invention proposes a distributed neurodynamic optimization method for power plants and distribution systems to achieve non-convex power resource allocation. The core of this method is to construct a Momentum-Based Multi-Agent System (MAS) with a driving variable, and to achieve convergent solutions to non-convex constraints through a hierarchical collaborative mechanism. This method can minimize the total energy consumption of the system while satisfying global energy balance and unit start-up and shutdown constraints, and features distributed execution, strong convergence performance, and applicability to large-scale power equipment collaborative control.

[0010] To achieve the above functions, this invention designs a distributed neurodynamic optimization method for non-convex power resource allocation, executing the following steps S1-S6 to obtain the scheduling decisions for equipment in the power plant:

[0011] Step S1: For each device in the target power plant, construct a corresponding intelligent agent model, so that each intelligent agent model can solve collaboratively in the multi-agent system. Each device participates in the collaborative calculation as an intelligent agent. Establish constraints based on the local variables of each device, and construct the energy consumption optimization model of the target power plant.

[0012] Step S2: Construct a Lagrangian function for the energy consumption optimization model of the target power plant and decompose it. For the local variables of each device, including the continuously adjustable power variables and start-stop state variables of each device, as well as the momentum term and Lagrangian function parameters, construct an independent dynamic layer and establish dynamic equations. Based on each dynamic equation, establish a distributed multi-agent system.

[0013] Step S3: Deploy a multi-agent system, set different initial states for each multi-agent system, solve independently, and obtain local optimal scheduling decisions, including the continuously adjustable power variables and start / stop state variables of each device, as well as the performance of the corresponding multi-agent system, including the total energy consumption of each device;

[0014] Step S4: Establish a distributed average tracking mechanism to dynamically track the average performance of all multi-agent systems; each multi-agent system compares its own performance with the average performance of all multi-agent systems to obtain the optimal scheduling decision for the group.

[0015] Step S5: Based on the performance of the multi-agent system corresponding to the local optimal scheduling decision and the average performance of all multi-agent systems, the particle swarm search rule is used to reset the initial state of the multi-agent system for the next round.

[0016] Step S6: Iterate for the multi-agent system until the preset convergence condition is met or the preset maximum number of iterations is reached, then terminate the iteration and output the final optimal scheduling decision, including the continuously adjustable power variables and start / stop state variables of each device.

[0017] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0018] 1. To address the difficulty of existing methods in simultaneously handling continuous power allocation and 0–1 start-stop decisions, this invention introduces start-stop state variables and cardinality constraint modeling to naturally integrate the limit on the number of devices that can be started or stopped into the optimization framework. This enables precise characterization and satisfaction of engineering constraints such as "maximum k devices can be started", thereby effectively solving the non-convex scheduling problem that traditional continuous optimization methods struggle to handle.

[0019] 2. To address the issues of easily getting trapped in local optima and being highly sensitive to initial conditions in non-convex scheduling problems, this invention introduces a momentum mechanism in the multi-agent optimization process. By utilizing historical search information to enhance the inertia of the search direction, the system can cross shallow local minima, thereby improving convergence performance and stability in non-convex scenarios.

[0020] 3. To address the problem of insufficient global search capability of a single local search method, this invention constructs multiple sets of parallel multi-agent systems and introduces a particle swarm optimization mechanism to perform distributed reset and guidance of the initial state of each multi-agent system, thereby achieving cross-regional search and significantly improving the probability of obtaining the global optimum or near-global optimum solution.

[0021] 4. To address the problem of difficulty in obtaining global performance information under conditions without a central node, this invention introduces a distributed average tracking mechanism, enabling each multi-agent system to obtain global average performance indicators and the group's optimal search direction by relying only on local communication, thereby achieving collaborative optimization under a fully distributed architecture.

[0022] 5. This invention aims to achieve scalable and optimized scheduling of large-scale power generation systems without the need for a central controller. Through a multi-agent collaborative mechanism based on communication topology, the proposed method can be naturally extended to systems containing a large number of power generation devices, meeting the practical operational needs of distributed energy systems and large power plants.

[0023] In summary, the purpose of this invention is to provide a power generation system energy consumption optimization method that can handle non-convex scheduling problems with cardinality constraints, has good global search capabilities, fast convergence speed, and supports fully distributed implementation, so as to overcome the shortcomings of the prior art and improve the economy and reliability of energy system operation. Attached Figure Description

[0024] Figure 1 This is a flowchart of a distributed neurodynamic optimization method for non-convex power resource allocation provided by an embodiment of the present invention;

[0025] Figure 2 This is a general framework diagram of a distributed neurodynamic optimization method for non-convex power resource allocation provided by an embodiment of the present invention;

[0026] Figure 3 This is a schematic diagram of a communication network topology provided according to an embodiment of the present invention;

[0027] Figure 4 This is a graph showing the convergence result of the target value provided in an embodiment of the present invention;

[0028] Figure 5 This is a diagram illustrating the evolution of the constrained multiplier according to an embodiment of the present invention;

[0029] Figure 6 This is an iterative graph that resets the initial state based on a particle swarm search mechanism according to an embodiment of the present invention;

[0030] Figure 7This is a Monte Carlo comparison experiment diagram for different P values ​​provided according to an embodiment of the present invention. Detailed Implementation

[0031] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0032] This invention provides a distributed neurodynamic optimization method for non-convex power resource allocation, referring to... Figure 1 , Figure 2 Perform the following steps S1-S6 to obtain the scheduling decisions for the equipment in the power plant:

[0033] Step S1: For each device in the target power plant, construct a corresponding intelligent agent model, so that each intelligent agent model can solve collaboratively in the multi-agent system. Each device participates in the collaborative calculation as an intelligent agent. Establish constraints based on the local variables of each device, and construct the energy consumption optimization model of the target power plant.

[0034] The specific method for step S1 is as follows:

[0035] Step S1.1: Collect local variables for each of the N devices in the target power plant, specifically including:

[0036] Continuously adjustable power variable: This represents the continuously adjustable power variable of the i-th device. ,in , These are the minimum and maximum allowed outputs of the i-th device, respectively.

[0037] Start-stop state variables: This represents the start / stop status variable of the i-th device. , This indicates that the i-th device participates in power supply. This indicates that the i-th device does not participate in power supply;

[0038] Based on the local variables of each device, establish the overall energy consumption objective function of the target power plant:

[0039] ;

[0040] in, This represents the energy consumption function of the i-th device. This indicates the overall energy consumption of the target power plant. This represents the overall energy consumption objective function of the target power plant.

[0041] To facilitate distributed structured representation, this embodiment will... Vectorization is defined as ;

[0042] Step S1.2: Establish constraints, specifically including:

[0043] Establish global coupling equality constraints to indicate that the power plant system must satisfy overall power balance constraints:

[0044] ;

[0045] in, Let be the energy conversion coefficient of the i-th device. The total power generation demand of the target power plant;

[0046] To make the global coupling equality constraints distributable, the local power balance constraints are defined as follows:

[0047] ;

[0048] ;

[0049] in, Let i represent the local power balance constraint function of the i-th device. The power generation requirement of the i-th device;

[0050] The global power balance constraints are defined as follows:

[0051] ;

[0052] in, Represents the global power balance constraint function;

[0053] The above modeling method can achieve the propagation of power balance in multi-agent networks without a central node.

[0054] The number of devices that can be operated simultaneously in a power plant system is limited, for example, the maximum number of devices that can be operated simultaneously is limited. For this device, a maximum number of devices must be enabled:

[0055] ;

[0056] in, This represents the local maximum number of devices that can be powered on, and is a constraint function. This is the maximum number of devices that the system allows to be enabled; there is an overall limit. , This represents the number of devices allowed to operate simultaneously in the target power plant; therefore, the maximum number of units that can be operated is constrained. Transform into , This is a global maximum number of devices that can be started simultaneously; it is used to limit the number of devices running at the same time in the system to a preset threshold.

[0057] To handle discrete start-stop state variables Establish nonlinear equality constraints:

[0058] ;

[0059] thereby ,in, This represents a vector consisting of discrete consistency constraint functions for all devices. This represents the discrete consistency constraint function for the start / stop state variable of the i-th device, used to characterize the deviation of the start / stop state variable from the set of discrete feasible states. The degree; due to Only or When it is established, this design can describe the value characteristics of discrete variables in a continuous space, providing a differentiable structure for subsequent continuous dynamical systems.

[0060] Step S1.3: Define the feasible region of the continuously adjustable power variable for all devices as follows: , , This represents the feasible region of the continuously adjustable power variable of the i-th device;

[0061] Step S1.4: Establish the energy consumption optimization model for the target power plant as follows:

[0062] ;

[0063] ;

[0064] in, This represents the continuously adjustable power variable of the i-th device, used to describe the output power or energy consumption of the device within the scheduling cycle; This represents a vector consisting of the continuously adjustable power variables of all devices; The dimension is The zero vector is used to describe the equilibrium conditions or initial state settings of a neurodynamic system; This represents the start / stop status variable of the i-th device. This represents a vector consisting of the start / stop status variables of all devices.

[0065] Step S2: Construct a Lagrangian function for the energy consumption optimization model of the target power plant and decompose it. For the local variables of each device, including the continuously adjustable power variables and start-stop state variables of each device, as well as the momentum term and Lagrangian function parameters, construct an independent dynamic layer and establish dynamic equations. Based on each dynamic equation, establish a distributed multi-agent system.

[0066] The specific steps of step S2 are as follows:

[0067] Step S2.1: Construct the Lagrangian function for the energy consumption optimization model of the target power plant:

[0068] ;

[0069] The KKT (Karush-Kuhn-Tucker) points of the Lagrange function are represented as:

[0070] ;

[0071] in, The dynamic estimate of the Lagrange multiplier corresponding to the global power balance constraint function is used for dynamic adjustment of the power balance constraint during the neurodynamic optimization process. The Lagrange multiplier variable represents the vector corresponding to the discrete consistency constraint functions of all devices; The dynamic estimate of the Lagrange multipliers corresponding to the global maximum number of machines started constraint function; This represents the overall energy consumption of the target power plant, used to characterize the energy consumption of each device under continuously adjustable power variables. and start / stop state variables and Energy consumption under combined effects; Indicates the feasible region The projection operator is used to restrict the update results of continuous power variables to a preset feasible range; This represents a vector consisting of continuously adjustable power variables of all devices. The gradient operator; Represents the Lagrange multiplier variables corresponding to the global power balance constraint function; This represents the Lagrange multiplier variable corresponding to the global maximum number of machines enabled constraint function; This represents a general gradient operator; The dimension is The zero vector or zero matrix is ​​used to represent the initial state; A vector representing the start / stop status variables of all devices. The gradient operator; Represent the Lagrange function; The consistency variable represents the Lagrange multiplier corresponding to the global power balance constraint function; The consistency variable represents the Lagrange multiplier corresponding to the vector composed of discrete consistency constraint functions of all devices; The consistency variable representing the Lagrange multiplier corresponding to the global maximum number of systems enabled constraint function; This represents a nonnegative projection operator used to restrict Lagrange multiplier variables to a nonnegative feasible region to satisfy the mathematical requirements of inequality constraints.

[0072] Step S2.2: Decompose the Lagrange function into five sub-problems, corresponding to:

[0073] Bounded projection optimization of continuously adjustable power variables;

[0074] Non-convex optimization of start and stop state variables;

[0075] Dynamic estimation variables of the Lagrange multipliers corresponding to the global power balance constraint function Consistent solution;

[0076] A vector consisting of discrete consistency constraint functions for all devices Lagrange update;

[0077] Global maximum number of machines to start constraint function Non-negative Lagrange update;

[0078] Independent dynamic layers are constructed for each device's local variables, momentum term, and Lagrange function parameters, including:

[0079] x-layer: A vector consisting of continuously adjustable power variables for all devices. An independent dynamic layer is constructed to be responsible for the projection update of the device's continuously adjustable power variables;

[0080] y-layer: A vector consisting of start / stop state variables for all devices. An independent dynamic layer is constructed to be responsible for the continuous search of device start-stop state variables;

[0081] -Momentum layer: for momentum terms An independent dynamic layer is constructed to accelerate the convergence of the non-convex part;

[0082] λ-layer, γ-layer, µ-layer: for Lagrange multiplier variables , , An independent dynamic layer is constructed; the λ-layer and γ-layer are used to handle global coupling constraints; the µ-layer is used to handle consistency conditions for discrete variables.

[0083] ωλ ω γ Auxiliary layer: targeting , An independently constructed dynamic layer Represents the Lagrange multiplier variables corresponding to the global power balance constraint function. The corresponding update weights, This represents the Lagrange multiplier variable corresponding to the global maximum number of machines enabled constraint function. The corresponding update weights.

[0084] Step S2.3: Since nonconvexity is mainly determined by discrete start-stop state variables Generates, introducing a momentum term into the y-layer. Its dynamic equation is:

[0085] ;

[0086] in, Indicates time, This is the momentum decay coefficient; a certain amount of momentum can help the system overcome local stagnation points in non-convex regions. This represents the first threshold parameter used to determine the convergence of a continuously adjustable power variable; This represents the second threshold parameter used to determine the convergence of start-stop state variables; This is used to form a structure of "fast momentum + slow variable" to improve convergence stability.

[0087] Step S2.4: For continuously adjustable power variables Construct the following projective neurodynamic expression to ensure that each update remains within the device's adjustable range:

[0088] ;

[0089] Step S2.5: Using the Laplace matrix right Introduce consistency constraints so that each agent can obtain the Lagrange multiplier of the global equality constraints locally:

[0090] ;

[0091] The above structure can achieve distributed solution for power balance across the entire network without a central controller.

[0092] Step S2.6: Constrain the maximum number of machines that can be started. Constructing a nonnegative projection update:

[0093] ;

[0094] make sure And they satisfy the complementary condition; among which, Represent the Lagrange function, The Lagrange multiplier variable represents the constraint function for the global maximum number of machines to be started. The gradient operator;

[0095] Step S2.7: Combining the above expressions, the dynamic equations of a multi-agent system with distributed implementation and applicable to power equipment dispatching are as follows:

[0096] ;

[0097] The component form of the dynamic equations of a multi-agent system is expressed as follows:

[0098] ;

[0099] in, Indicates time, This indicates that the i-th device has a continuously adjustable power variable. With start and stop state variables Energy consumption under action Describes the feasible region of continuously adjustable power variables for the i-th device. The projection operator; Represents the start / stop status variable of the i-th device. The corresponding momentum coefficient; The Lagrange multiplier represents the discrete consistency constraint function corresponding to the start / stop state variable of the i-th device; , Let represent the Lagrange multipliers corresponding to the local power balance constraints of the i-th and j-th devices, respectively; This represents the adjacency weight coefficient between the i-th device and the j-th device in the communication topology; and They represent the Lagrange multipliers respectively. and The corresponding updated weights; and Let these be the Lagrange multipliers corresponding to the local maximum number of devices enabled, i and j, respectively. and They represent the Lagrange multipliers respectively. and The corresponding update weights, Represents continuously adjustable power variable gradient operator, Represents start / stop state variables The gradient operator.

[0100] To address the problem of non-convex optimization easily getting trapped in local optima, this invention introduces a distributed average tracking (DAT) mechanism and a particle swarm optimization (PSO) mechanism on the basis of momentum-based multi-agent systems (MAS), constructing a hybrid multi-agent optimization system with cross-regional search capabilities. This system can achieve parallel search, information aggregation, and dynamic approximation of the global optimum across multiple multi-agent systems without a central controller.

[0101] The overall structure consists of three parts: a lower layer for local search of multi-agent systems, a middle layer for global information aggregation based on a distributed average tracking mechanism, and an upper layer for particle swarm search resetting.

[0102] Step S3: Deploy a multi-agent system, set different initial states for each multi-agent system, solve independently, and obtain local optimal scheduling decisions, including the continuously adjustable power variables and start / stop state variables of each device, as well as the performance of the corresponding multi-agent system, including the total energy consumption of each device;

[0103] The specific steps of step S3 are as follows:

[0104] Step S3.1: Deployment Groups of completely independent multi-agent systems, each group of multi-agent systems contains One agent, one device:

[0105] Step S3.2: Set different initial states for the multi-agent system, including different initial continuously adjustable power variables, initial start-stop state variables, initial momentum terms, and initial Lagrange multipliers;

[0106] Each multi-agent system runs the same continuous dynamics model, solves independently, and obtains locally optimal scheduling decisions: including , , ,in , , These represent the continuously adjustable power variable, start / stop state variable, and total energy consumption of the multi-agent system, respectively, acquired by the i-th device during distributed communication. The multi-agent systems with different initial states will converge to different local optima, thus achieving distributed multi-region parallel search.

[0107] Step S4: Establish a distributed average tracking mechanism to dynamically track the average performance of all multi-agent systems; each multi-agent system compares its own performance with the average performance of all multi-agent systems to obtain the optimal scheduling decision for the group.

[0108] Although different multi-agent systems do not communicate directly, in actual power system deployment scenarios, it is neither possible to rely on a central node, nor is it possible for the system to automatically identify "which multi-agent system is superior." Therefore, this invention introduces a distributed average tracking mechanism to dynamically track the average performance of all multi-agent systems in the absence of a central node. The specific steps in step S4 are as follows:

[0109] Step S4.1: Let the total energy consumption of the i-th group of multi-agent systems be... As shown in the following formula:

[0110] ;

[0111] in This represents the start / stop status variable received by the i-th device from the j-th neighboring device; This indicates that the j-th device has a corresponding continuously adjustable power variable. The energy consumption function value under the following conditions;

[0112] Construct the following dynamic equations:

[0113] ;

[0114] in, This represents the third threshold parameter used to determine the termination condition; This is a local estimate of the performance of the i-th group of multi-agent systems; This represents the average performance of all multi-agent systems output by the distributed average tracking mechanism. for The components of the i-th multi-agent system; This represents the initial gain parameter in the neurodynamic system. Represents a symbolic function; express The value at the initial moment, This represents the local estimate of the performance of each group of multi-agent systems at the initial time step;

[0115] Step S4.2: Make each multi-agent system obtain the average performance of all multi-agent systems, and each multi-agent system determine whether its own performance is lower than the average performance. The scheduling decision corresponding to the multi-agent system whose own performance is lower than the average performance is taken as the group optimal scheduling decision.

[0116] Step S5: Based on the performance of the multi-agent system corresponding to the local optimal scheduling decision and the average performance of all multi-agent systems, the particle swarm search rule is used to reset the initial state of the multi-agent system for the next round.

[0117] Global quantity output by the distributed average tracking mechanism Each multi-agent system is allowed to obtain the total energy consumption level and determine whether it is below the average value, i.e. whether it is better. It is also used for the "group optimal direction" in particle swarm search updates. In addition, it can autonomously form a globally consistent evaluation under the condition of no central node.

[0118] This approach is more suitable when large-scale equipment is distributed across different factory areas or substations, there is no unified control master station, and communication can only occur within a neighborhood topology. Therefore, this invention chooses a distributed average tracking mechanism to replace centralized global optimal broadcasting.

[0119] The specific method in step S5 is as follows:

[0120] After obtaining the total energy consumption of each multi-agent system, the average performance of all multi-agent systems output by the distributed average tracking mechanism, and the current local optimum scheduling decision position, we can determine the total energy consumption of each multi-agent system. The current optimal scheduling decision position for the group Then, the particle swarm search rule is used to reset the initial decision positions of the multi-agent system for the next round:

[0121] ;

[0122] In the formula, , , This represents the weight parameters in the intelligent search mechanism of particle swarm optimization. It indicates that the i-th particle is in the... The velocity variable at the next iteration This represents the iteration count index in the swarm intelligence search process. , This represents the learning factor parameter in particle swarm optimization. It indicates that the i-th particle is in the... The decision position at the next iteration;

[0123] Among them, the current optimal scheduling decision position for the group It is obtained indirectly through a distributed average tracking mechanism, therefore the global knowledge of the particle swarm search rules does not require a central node, and the updated... As the new initial decision position for the next round of the multi-agent system, the multi-agent system will start from the new initial decision position and conduct the next round of local search using the method in step S3, so as to escape the local optimum trap.

[0124] Step S6: Iterate for the multi-agent system until the preset convergence condition is met or the preset maximum number of iterations is reached, then terminate the iteration and output the final optimal scheduling decision, including the continuously adjustable power variables and start / stop state variables of each device.

[0125] By leveraging the synergistic effect of the lower-level multi-agent system, the intermediate-level distributed average tracking mechanism, and the upper-level particle swarm search rules, this invention achieves efficient quasi-global optimal search in complex non-convex energy consumption optimization scenarios. First, the lower-level multi-agent system performs efficient local region search based on continuous dynamics. The momentum term provides the ability to overcome shallow local minima, the projection operator ensures the solution evolves within the feasible region, and the Lagrangian consistency network ensures that coupling constraints such as global power balance are always satisfied. As a result, each multi-agent system can quickly converge to the local optimum of its region.

[0126] Building upon this foundation, this invention introduces a distributed average tracking mechanism as an intermediate layer to achieve performance aggregation and cross-group evaluation among different multi-agent systems in a fully distributed network structure. Through this mechanism, each multi-agent system can dynamically acquire information such as the "global average performance" and "group optimal direction" of the entire system, thereby overcoming the limitation of global comparison being impossible in a decentralized architecture. This allows each multi-agent system to assess its own superiority or inferiority relative to other multi-agent systems in real time.

[0127] Utilizing the global information output by the distributed average tracking mechanism, the upper-level particle swarm search rule further intelligently resets the initial state of the multi-agent system, enabling cross-regional jump-style search. The particle swarm search rule performs velocity-position iteration on the current optimal solution and estimated swarm optimal direction of each multi-agent system, allowing the multi-agent system to resume local search from different starting points in the next iteration, thus effectively avoiding getting trapped in local optima. Through multiple rounds of local search by the multi-agent system and global updates of the particle swarm search rule, this invention achieves a quasi-global optimal scheduling solution process that is collaboratively advanced across multiple regions and scales.

[0128] Through the combined effect of the above three layers, the present invention can not only achieve a significant reduction in overall energy consumption, but also ensure that the non-convex constraints of equipment start-up and shutdown and the global power balance constraints are satisfied. It also has the engineering characteristics of being fully distributed, without a central node, and scalable to large-scale power generation and distribution systems, thus providing stable, reliable and near-global optimal optimization results in complex energy dispatch scenarios.

[0129] The following is an application example of the present invention:

[0130] Assume the power plant system consists of It consists of several power generation units, each corresponding to an intelligent agent. The output power of each power generation unit is Its energy consumption function is expressed in cubic polynomial form as follows:

[0131] ;

[0132] in, Let i be the energy consumption model for the i-th power generation unit. , , , These are the energy consumption model parameters corresponding to the i-th power generation unit, used to characterize the nonlinear energy consumption characteristics of different power generation units under different load levels. Start-stop state variables are introduced. , used to indicate whether the i-th power generation unit participates in operation. Then, the total energy consumption optimization model for the target power plant is defined as:

[0133] ;

[0134] in, This represents the total energy consumption of the target power plant. Let represent the total energy consumption objective function of the target power plant; the total energy consumption objective function describes the problem of minimizing the total energy consumption of the power plant under the combined effect of start-up and shutdown decisions and power allocation.

[0135] The constraints and parameter settings for the power plant are as follows:

[0136] Global power generation demand constraints: ,in This represents the system's total power generation demand;

[0137] Single generator unit power constraints: ; , These are the maximum and minimum allowable outputs of the i-th power generation unit, respectively;

[0138] Start-stop state variable constraints: ;

[0139] Maximum number of machines to be started: ;

[0140] In the embodiments, reference is made to Figure 3 Consider a system containing 8 power generation units ( Energy consumption function parameters of each power generation unit. , , , The rated power limit is taken from the operating data of typical power generation equipment. The rated power limit for all power generation units is set to the same level to ensure the representativeness of the simulation. In addition, the total power generation demand of the system is set to... The minimum and maximum power output of each power generation unit are set as follows: The model parameters and rated power limits for each power generation unit are shown in Table 1 below:

[0141] Table 1. Rated Power and Parameter Settings

[0142]

[0143] Communication Topology and Distributed Setup: In a distributed solution environment, each power generation unit interacts with other units only through local communication, and its communication structure is modeled as a connected undirected graph. Each agent exchanges only necessary state information with its neighboring nodes to achieve power balance consistency and distributed average tracking, without the need for a central controller.

[0144] The convergence process and the optimal solution results are as follows:

[0145] Under the above parameter settings, the method of this invention is used for solving. Simulation results show that the... Output power of each power generation unit With start and stop state variables The system gradually converges over time and eventually reaches a steady state. After convergence, the optimal power generation allocation is obtained as follows: The corresponding start / stop state variables for the power generation unit are: It can be seen that the system ultimately only activates a portion of the power generation units to participate in operation, and the number of activated units strictly meets the preset maximum activation limit. The remaining power generation units remain in the off state. (Refer to...) Figure 4 Under this scheduling scheme, the minimum total energy consumption of the system is: The result indicates that, with reference to Figure 5 Under the premise of meeting power generation requirements and start-up / shutdown constraints, the method of the present invention can effectively reduce the overall energy consumption of the system and automatically select the optimal combination of power generation units and power allocation scheme.

[0146] Numerical experiments verify that the proposed method achieves stable convergence in non-convex start-stop scheduling problems, and the obtained solution satisfies power balance constraints, start-stop constraints, and cardinality constraints. Introducing a momentum term improves the system's initial convergence speed and effectively avoids getting trapped in local optima. Combining distributed average tracking and particle swarm optimization rules, the system possesses cross-regional search capabilities. (See [link to relevant documentation]). Figure 6 This further increases the probability of obtaining the global optimal solution.

[0147] To further verify the effectiveness of the technical solution of this invention, under the same system parameters and load requirements, the method of this invention was compared and analyzed with the following comparative method: a method using a global search mechanism with different numbers of groups. This method only uses multi-agent systems with different numbers of groups for local optimization, introducing parallel search of multiple multi-agent systems and a particle swarm reset mechanism.

[0148] The comparative results show that, under the same system parameters and load requirements, Monte Carlo comparative experiments were conducted on different numbers of multi-agent methods that introduced a global search mechanism. (See attached document.) Figure 7 Specifically, for each type of parallel multi-agent system with a set number P, multiple sets of different initial states were randomly generated, and the system was subjected to multiple independent simulations. The distribution of the optimal objective function value obtained after final convergence was then statistically analyzed. Experimental results show that when only a single multi-agent system is used for local optimization (i.e., P=1), the system is highly sensitive to initial conditions, and the convergence results are extremely dispersed. Although some simulation results can converge to a relatively good solution, a considerable proportion of the results remain at significantly poor local optima, and even the objective function value is significantly larger than expected. This indicates that in non-convex start-stop scheduling problems, a single local search mechanism is insufficient to guarantee a stable and high-quality solution.

[0149] As the number of parallel multi-agent systems gradually increases (P=2, P=4, and P=8), and the initial states of each multi-agent system are reset in a distributed manner using particle swarm optimization, the dispersion of the final convergence result of the system is significantly reduced, and the optimal value distribution gradually concentrates near the global optimum. Especially at a large parallel scale, the probability of obtaining the global optimum or near-global optimum in multiple random experiments is significantly increased, and extreme poor solutions are basically eliminated.

[0150] Monte Carlo experiments clearly demonstrate that, in the absence of global search and cross-regional jump mechanisms, multi-agent systems are easily affected by initial conditions and fall into local optima. This invention introduces an appropriate number of parallel search structures for multi-agent systems and uses particle swarm optimization rules to intelligently reset the initial state, enabling the system to effectively explore multiple potential solution regions. This significantly improves the stability and reliability of obtaining globally optimal or near-global optimal solutions in non-convex scheduling problems, while balancing computational complexity.

[0151] Comprehensive comparative analysis shows that the present invention not only has a faster convergence speed in non-convex start-stop scheduling problems, but also outperforms the above-mentioned comparative methods in terms of energy consumption level and stability of scheduling results, fully demonstrating the technical advantages of momentum mechanism and hybrid multi-agent optimization structure in complex power generation system scheduling.

[0152] Experimental results show that the present invention can not only minimize the energy consumption of the power generation system under a distributed architecture, but also achieve coordinated optimization of the number of power generation units to start and stop and the power allocation without the need for a central controller. It is suitable for engineering applications of large-scale power plants and distributed energy systems.

[0153] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A distributed neuromanifold optimization method for non-convex power resource placement, characterized in that, Perform the following steps S1-S6 to obtain the scheduling decisions for the equipment in the power plant: Step S1: For each device in the target power plant, construct a corresponding intelligent agent model, so that each intelligent agent model can solve collaboratively in the multi-agent system. Each device participates in the collaborative calculation as an intelligent agent. Establish constraints based on the local variables of each device, and construct the energy consumption optimization model of the target power plant. Step S2: Construct a Lagrangian function for the energy consumption optimization model of the target power plant and decompose it. For the local variables of each device, including the continuously adjustable power variables and start-stop state variables of each device, as well as the momentum term and Lagrangian function parameters, construct an independent dynamic layer and establish dynamic equations. Based on each dynamic equation, establish a distributed multi-agent system. Step S3: Deploy a multi-agent system, set different initial states for each multi-agent system, solve independently, and obtain local optimal scheduling decisions, including the continuously adjustable power variables and start / stop state variables of each device, as well as the performance of the corresponding multi-agent system, including the total energy consumption of each device; Step S4: Establish a distributed average tracking mechanism to dynamically track the average performance of all multi-agent systems; each multi-agent system compares its own performance with the average performance of all multi-agent systems to obtain the optimal scheduling decision for the group. The specific steps in step S4 are as follows: Step S4.1: Let the total energy consumption of the i-th group of multi-agent systems be... As shown in the following formula: ； in This represents the start / stop status variable received by the i-th device from the j-th neighboring device; This indicates that the j-th device has a corresponding continuously adjustable power variable. The energy consumption function value under the following conditions; Construct the following dynamic equations: ； in, This represents the third threshold parameter used to determine the termination condition; This is a local estimate of the performance of the i-th group of multi-agent systems; This represents the average performance of all multi-agent systems output by the distributed average tracking mechanism. for The components of the i-th multi-agent system; This represents the initial gain parameter in the neurodynamic system. Represents a symbolic function; express The value at the initial moment, This represents the local estimate of the performance of each group of multi-agent systems at the initial time step; Step S4.2: Make each multi-agent system obtain the average performance of all multi-agent systems, and each multi-agent system determine whether its own performance is lower than the average performance. The scheduling decision corresponding to the multi-agent system whose own performance is lower than the average performance is taken as the group optimal scheduling decision. Step S5: Based on the performance of the multi-agent system corresponding to the local optimal scheduling decision and the average performance of all multi-agent systems, the particle swarm search rule is used to reset the initial state of the multi-agent system for the next round. Step S6: Iterate for the multi-agent system until the preset convergence condition is met or the preset maximum number of iterations is reached, then terminate the iteration and output the final optimal scheduling decision, including the continuously adjustable power variables and start / stop state variables of each device.

2. The distributed neurodynamic optimization method for non-convex power resource allocation according to claim 1, characterized in that, The specific method for step S1 is as follows: Step S1.1: Collect local variables for each of the N devices in the target power plant, specifically including: Continuously adjustable power variable: This represents the continuously adjustable power variable of the i-th device. ,in , These are the minimum and maximum allowed outputs of the i-th device, respectively. Start-stop state variables: This represents the start / stop status variable of the i-th device. , This indicates that the i-th device participates in power supply. This indicates that the i-th device does not participate in power supply; Based on the local variables of each device, establish the total energy consumption objective function of the target power plant: ； in, This represents the energy consumption function of the i-th device. This represents the total energy consumption of the target power plant. This represents the objective function for the total energy consumption of the target power plant. Step S1.2: Establish constraints, specifically including: Global coupling equality constraints: ； in, Let be the energy conversion coefficient of the i-th device. The total power generation demand of the target power plant; The local power balance constraints are defined as follows: ； ； in, Let i represent the local power balance constraint function of the i-th device. The power generation requirement of the i-th device; The global power balance constraints are defined as follows: ； in, Represents the global power balance constraint function; Maximum number of machines to be started: ； in, This represents the local maximum number of devices that can be powered on, and is a constraint function. This is the maximum number of devices that the system allows to be enabled; there is an overall limit. , This represents the number of devices allowed to operate simultaneously in the target power plant; therefore, the maximum number of units that can be operated is constrained. Transform into , This is the global maximum number of systems enabled constraint function; Nonlinear equality constraints: ； thereby ,in, This represents a vector consisting of discrete consistency constraint functions for all devices. The discrete consistency constraint function represents the start / stop state variable of the i-th device; Step S1.3: Define the feasible region of the continuously adjustable power variable for all devices as follows: , , This represents the feasible region of the continuously adjustable power variable of the i-th device; Step S1.4: Establish the total energy consumption optimization model for the target power plant as follows: ； ； in, This represents the continuously adjustable power variable of the i-th device; This represents a vector consisting of the continuously adjustable power variables of all devices; The dimension is The zero vector; This represents the start / stop status variable of the i-th device. This represents a vector consisting of the start / stop status variables of all devices.

3. The distributed neurodynamic optimization method for non-convex power resource allocation according to claim 2, characterized in that, The specific steps of step S2 are as follows: Step S2.1: Construct the Lagrangian function for the total energy consumption optimization model of the target power plant: ； The KKT points of the Lagrange function are represented as: ； in, The dynamic estimation variables of the Lagrange multipliers corresponding to the global power balance constraint function; The Lagrange multiplier variable represents the vector corresponding to the discrete consistency constraint functions of all devices; The dynamic estimate of the Lagrange multipliers corresponding to the global maximum number of machines started constraint function; This represents the total energy consumption of the target power plant; Indicates the feasible region The projection operator; This represents a vector consisting of continuously adjustable power variables of all devices. The gradient operator; Represents the Lagrange multiplier variables corresponding to the global power balance constraint function; This represents the Lagrange multiplier variable corresponding to the global maximum number of machines enabled constraint function; This represents a general gradient operator; The dimension is The zero vector or zero matrix; A vector representing the start / stop status variables of all devices. The gradient operator; Represent the Lagrange function; The consistency variable represents the Lagrange multiplier corresponding to the global power balance constraint function; The consistency variable represents the Lagrange multiplier corresponding to the vector composed of discrete consistency constraint functions of all devices; The consistency variable representing the Lagrange multiplier corresponding to the global maximum number of systems enabled constraint function; Represents the nonnegative projection operator; Step S2.2: Construct independent dynamic layers for each device's local variables, momentum term, and Lagrange function parameters, including: x-layer, y-layer, -Momentum layer, λ-layer, γ-layer, µ-layer, ω-layer λ ω γ Auxiliary layer, where: The x-layer is a vector consisting of continuously adjustable power variables for all devices. An independent dynamic layer is constructed; the y-layer is a vector composed of start / stop state variables of all devices. An independently constructed dynamic layer; - The momentum layer is for momentum terms. Constructed independent dynamic layers; the λ-layer, γ-layer, and µ-layer are respectively designed for Lagrange multiplier variables. , , An independently constructed dynamic layer; ω λ ω γ The auxiliary layer is for , An independently constructed dynamic layer Represents the Lagrange multiplier variables corresponding to the global power balance constraint function. The corresponding update weights, This represents the Lagrange multiplier variable corresponding to the global maximum number of machines enabled constraint function. The corresponding update weights; Step S2.3: Introduce a momentum term into the y-layer Its dynamic equation is: ； in, Indicates time, The momentum decay coefficient; This represents the first threshold parameter used to determine the convergence of a continuously adjustable power variable; This represents the second threshold parameter used to determine the convergence of start-stop state variables; Step S2.4: For the vector composed of continuously adjustable power variables of all devices... Construct the following projective neurodynamic expression: ； Step S2.5: Using the Laplace matrix right Introduce consistency constraints: ； Step S2.6: Constrain the maximum number of machines that can be started. Constructing a nonnegative projection update: ； in, Represent the Lagrange function, The Lagrange multiplier variable represents the constraint function for the global maximum number of machines to be started. The gradient operator; Step S2.7: Construct the dynamic equations of the multi-agent system as follows: ； The component form of the dynamic equations of a multi-agent system is expressed as follows: ； in, Indicates time, This indicates that the i-th device has a continuously adjustable power variable. With start and stop state variables Energy consumption under action Describes the feasible region of continuously adjustable power variables for the i-th device. The projection operator; Represents the start / stop status variable of the i-th device. The corresponding momentum coefficient; The Lagrange multiplier represents the discrete consistency constraint function corresponding to the start / stop state variable of the i-th device; , Let represent the Lagrange multipliers corresponding to the local power balance constraints of the i-th and j-th devices, respectively; This represents the adjacency weight coefficient between the i-th device and the j-th device in the communication topology; and They represent the Lagrange multipliers respectively. and The corresponding update weights; and Let these be the Lagrange multipliers corresponding to the local maximum number of devices enabled, i and j, respectively. and They represent the Lagrange multipliers respectively. and The corresponding update weights, Represents continuously adjustable power variable gradient operator, Represents start / stop state variables The gradient operator.

4. The distributed neurodynamic optimization method for non-convex power resource allocation according to claim 3, characterized in that, The specific steps of step S3 are as follows: Step S3.1: Deployment Groups of completely independent multi-agent systems, each group of multi-agent systems contains One agent, one device: Step S3.2: Set different initial states for the multi-agent system, including different initial continuously adjustable power variables, initial start-stop state variables, initial momentum terms, and initial Lagrange multipliers; Each multi-agent system runs the same continuous dynamics model, solves independently, and obtains locally optimal scheduling decisions: including , , ,in , , These represent the continuously adjustable power variable, start / stop state variable, and total energy consumption of the multi-agent system obtained by the i-th device during distributed communication.

5. The distributed neurodynamic optimization method for non-convex power resource allocation according to claim 4, characterized in that, The specific method in step S5 is as follows: After obtaining the total energy consumption of each multi-agent system, the average performance of all multi-agent systems output by the distributed average tracking mechanism, and the current local optimum scheduling decision position, we can determine the total energy consumption of each multi-agent system. The current optimal scheduling decision position for the group Then, the particle swarm search rule is used to reset the initial state of the multi-agent system for the next round: ； in, , , This represents the weight parameters in the intelligent search mechanism of particle swarm optimization. It indicates that the i-th particle is in the... The velocity variable at the next iteration This represents the iteration count index in the swarm intelligence search process. , This represents the learning factor parameter in particle swarm optimization. It indicates that the i-th particle is in the... The decision position at the next iteration; Updated As the new initial decision position for the next round of the multi-agent system, the multi-agent system will start from the new initial decision position and conduct the next round of local search using the method in step S3.

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