Optimal scheduling method for power consumption of port electric equipment cluster under limited data

By constructing a total power and voltage mapping model and using a depth graph convolution method with limited data, high-precision power optimization of port electric equipment clusters was achieved, solving the scheduling deviation problem caused by insufficient data and improving the energy efficiency and allocation strategy accuracy of the port power grid.

CN119994920BActive Publication Date: 2025-11-25SHANGHAI JIAOTONG UNIV
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Patent Information

Application Number
CN202510207684.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-02-25
Publication Date
2025-11-25
Estimated Expiration
2045-02-25

AI Technical Summary

Technical Problem

Existing technologies require a large amount of node operation data for the scheduling of port electric equipment clusters. When data is limited, it is difficult to make accurate state estimates, which causes the power optimization strategy to deviate from the optimal solution. Furthermore, existing methods rely on accurate power grid models.

Method used

A total power mapping model and a voltage mapping model are constructed and trained using historical data with measurement nodes. Information on nodes without measurement nodes is compensated by a fine-grained depth map convolutional module and a filtering connection module. By combining a loss function and an optimization objective function, precise power consumption optimization of the port's electric equipment cluster is achieved.

Benefits of technology

With only a small amount of node data, high-precision power optimization of port electric equipment clusters is achieved, reducing data requirements, improving energy efficiency, adapting to the uneven distribution and sparse characteristics of port datasets, and providing the optimal allocation strategy under limited data.

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Abstract

A limited data port electric device cluster power optimization scheduling method, respectively constructs total power mapping model and voltage mapping model, and adopts training based on measured node historical measurement data, and the trained total power mapping model and voltage mapping model are used to form a measured node data driven PEE scheduling optimization model, and the corresponding PEE configuration quantity of each logistics task is obtained by solving. The application uses a few available measured values of nodes to calculate the PEE quantity allocated to the logistics task, compensates the information of unmeasured nodes by using the data from adjacent nodes with measurement, realizes accurate active / reactive power and voltage mapping.
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Description

Technical Field

[0001] This invention relates to a technology in the field of port power control, specifically a method for optimizing the power consumption scheduling of port electric equipment clusters under limited data. Background Technology

[0002] The scheduling of Port Electric Equipment Clusters (PEEs) affects the spatiotemporal distribution of port power grid load. Ignoring PEE power consumption optimization may lead to high power grid energy consumption and voltage instability. Existing technologies require a large amount of node operation data to establish a power flow model. When data is limited, it is difficult to make accurate state estimates, and the resulting PEE allocation strategy may deviate from the optimal solution. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, this invention proposes a method for optimizing power consumption scheduling of port electric equipment clusters under limited data. This method utilizes the available measurement values ​​of a few nodes to calculate the number of PEE allocated to logistics tasks and uses data from adjacent nodes with measurements to compensate for information from nodes without measurements, thereby achieving accurate mapping of active / reactive power and voltage.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a power optimization scheduling method for port electric equipment clusters under limited data. It constructs a total power mapping model and a voltage mapping model, and trains them based on historical measurement data of measurement nodes. The trained total power mapping model and voltage mapping model are combined into a measurement node data-driven PEE scheduling optimization model. The number of PEE configurations corresponding to each logistics task is obtained by solving the model.

[0006] The total power mapping model includes: a fine-grained depth map convolution module, a filtering and connection module, and a power prediction module. Specifically: the fine-grained depth map convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensating for the active and reactive power information of the unmeasured nodes, and obtaining the total power features of all nodes; the filtering and connection module performs a filtering process based on the total power features of all nodes to obtain the total power features of the measured nodes; and the power prediction module performs a mapping and fitting learning from the total power features of the measured nodes to the active power of the first node, obtaining the predicted total power consumption of the port power grid corresponding to the scheduling of the electric equipment cluster.

[0007] The voltage mapping model includes: a fine-grained depth map convolution module, a filtering and connection module, and a voltage prediction module. Specifically: the fine-grained depth map convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensating for the active and reactive power information of the unmeasured nodes, and obtaining the voltage characteristics of all nodes; the filtering and connection module performs a filtering process on the measured nodes based on the voltage characteristics of all nodes, obtaining the voltage characteristics of the measured nodes; and the power prediction module performs a mapping fitting learning from the voltage characteristics of the measured nodes to the voltage of the measured nodes, obtaining the node voltage corresponding to the scheduling of the electric equipment cluster.

[0008] The training described uses the following loss function. in: This represents the predicted total power consumption of the port power grid corresponding to the scheduling of electric equipment clusters, as output by the total power mapping model. This refers to the actual value of the active power at the substation node obtained by the measurement unit.

[0009] The measurement node data-driven PEE scheduling optimization model includes: an initial PEE scheduling objective function, a reconstructed PEE scheduling objective function, and PEE scheduling optimization variable constraints. Specifically: the initial PEE scheduling objective function is modeled based on the need to reduce the total electricity cost of port operations and prevent voltage exceedances, resulting in an optimized PEE scheduling objective function. The reconstructed PEE scheduling objective function, based on the initial optimization objective, represents the total power consumption of the port power grid and node voltage in the optimized objective function using a total power mapping model and a voltage mapping model, resulting in a PEE scheduling objective modeled as a convex function. The PEE scheduling optimization variable constraints are processed according to the logistics efficiency requirements that port electric equipment cluster scheduling must follow, using formulas that facilitate the solution of the optimization model, resulting in optimization variable constraints modeled as convex sets.

[0010] Technical effect

[0011] This invention utilizes limited available data for intelligent power flow perception, optimizing power consumption in port electric equipment cluster scheduling using only a small number of node measurements. It achieves optimal allocation strategies for logistics electric equipment clusters without relying on precise power grid models. Based on a fine-grained deep graph convolutional online learning method, it collects, propagates, and aggregates data from measured nodes to compensate for information from unmeasured nodes. This enables dynamic allocation of power efficiency (PEE) for logistics tasks with limited node data, improving energy efficiency. Compared to existing technologies, this invention features low data requirements and high-precision learning, allowing for accurate calculations with only 40% of node measurements, eliminating the need for measurements from all nodes. Description of the Drawings

[0012] Figure 1 is a schematic diagram of the scenario of the embodiment;

[0013] Figure 2 is a schematic diagram of the fine-grained depth map convolution block;

[0014] Figure 3 is a schematic diagram of the total power mapping model and the voltage mapping model for limited observable nodes;

[0015] Figure 4 is a flow chart of the PEE power consumption optimization scheduling under limited information;

[0016] Figure 5 is a schematic diagram of the port power grid based on the IEEE 33-node system;

[0017] Figure 6 is a schematic diagram of the convergence behavior of the total power mapping network and other deep learning networks in the embodiment;

[0018] Figure 7 is a schematic diagram of the convergence behavior of the voltage mapping network and other deep learning networks in the embodiment. Detailed Implementation Manner

[0019] As Figure 1 shown, this is the application scenario of this embodiment, that is, the port power grid, whose topological structure is graph G=(Ν, E, R, X), where: the node set Ν={1, 2,..., n} consists of substation nodes, ring main unit nodes, transformer nodes, etc., and n is the number of nodes; E is the edge set in the power grid; the resistance matrix R=[r i , mear , i , i and the reactance matrix X=[x ij where r ij and x ij are the resistance and reactance between node i and node j respectively; there is a measurement node set Ν mear ={1, 2,..., m}, m<<n, the nodes are numbered from 1 to m, and the nodes from m + 1 to n are non-measured nodes.

[0020] In the described measurement node set Ν mear node 1 is a substation node, and nodes 2 to d are the nodes connected by PEE. Nodes d + 1 to m refer to points with large power and voltage changes, which can reflect the overall load fluctuation and power quality of the network to a certain extent even though there is no PEE connection. p i q i and v i represent the active power, reactive power and voltage of the measured node i at a certain moment. The data vectors of the active power, reactive power and voltage of the nodes obtained by the PEE power consumption optimization are respectively denoted as p mear =[p1, p2,..., pd p d+1 , ..., p m ] T q mear = [q1, q2, ..., q d q d+1 , ..., q m ] T v mear = [v1, v2, ..., v d v d+1 , ..., v m ] T .

[0021] like Figure 4 As shown in the figure, this embodiment involves a power optimization scheduling method for port electric equipment clusters under limited data. A total power mapping model and a voltage mapping model are constructed respectively, and trained using historical measurement data with measurement nodes. The trained total power mapping model and voltage mapping model are combined to form a measurement node data-driven PEE scheduling optimization model. The number of PEE configurations corresponding to each logistics task is obtained by solving the model.

[0022] In this embodiment, both the total power mapping model and the voltage mapping model are implemented through a neural network comprising several graph convolutional layers, filtering connection layers, and prediction layers connected by residuals. Each graph convolutional layer compensates for the lack of information from measurement nodes by using its own and its neighboring nodes' feature data for message passing, transforming the vertex features... As the residual output of layer l, in relation to the input After addition, a new input is formed for layer l+1; the filtering connection layer traverses the vertex features of all nodes and extracts the vertex features of the measurement nodes from them; the prediction layer of the total power mapping model is implemented using a multilayer perceptron, and the prediction layer of the voltage mapping model is implemented using a multilayer perceptron.

[0023] The graph convolutional layer, through stacked L layers, enables nodes to collect feature data from their L-layer neighborhood. Specifically, the message passing rule of the L-layer fine-grained deep graph convolutional online learning method is as follows:

[0024] in: p i and q i These are the active power and reactive power at the measured node i, respectively. For the vertex features of node i in the l-th layer, Ψ (l) ReLU(·) is the activation function used to update the features of the vertices in layer l, and GraphConv(·) is the generalized graph convolution function, which passes aggregated information of features from all neighboring nodes to the current node.

[0025]

[0026]

[0027] and n i Let γ represent the set of neighboring nodes and the number of neighboring nodes of node i, respectively. For each neighbor j∈υ(i), the information is constructed by the constructor γ. (l) Applied to vertex features Neighbor characteristics Sum of edge features Constructing aggregated information p j and q j These are the active power and reactive power of the measured node j, respectively, and MLP(·) is a multilayer sensor.

[0028] like Figure 2 As shown, the filtering connection layer is located between the L-layer output and the model prediction layer, and its output is... Where: concat(·) refers to traversing the vertex features of all nodes, and then extracting the vertex features of the measurement nodes from them using the pick(·) function; L-layer fine-grained depth graph convolutional block and its message passing process. The vertex features of node i after L layers of transformation are represented as follows:

[0029] like Figure 3 As shown, the prediction layer of the total power mapping model is implemented using a multilayer perceptron, and its loss function is... Among them: the actual value of active power of substation nodes obtained by the measurement unit. F p (·) represents the functional relationship between the power of substation nodes and the power of other measurable nodes, where p1 is the active power of the substation nodes. This is the predicted value from the total power mapping model.

[0030] The prediction layer of the voltage mapping model uses a multilayer perceptron, and its loss function is:

[0031] Wherein: the actual voltage value of the measurement node F v (·) represents the functional relationship between the power and voltage of the measurement node fitted by the voltage mapping model. For the predicted values ​​of the voltage mapping model, the substation node is designated as the slack node, and its voltage v1 is given as the reference voltage and is not involved in the model training.

[0032] The PEE scheduling optimization model, established based on the trained total power mapping model and voltage mapping model, determines the optimal number of electric logistics devices to be allocated to operational tasks. The specific implementation process includes:

[0033] 1) Initial PEE scheduling objective function: The objective is to minimize the total electricity cost of port operations, while incorporating voltage constraints as a penalty term to facilitate the solution. Specifically: Where: T is the scheduling period, t∈{1,2,…,T}. λ t t is the electricity price for the time period. σ is the penalty factor for controlling the voltage to not exceed the lower limit of 0.95pu.

[0034] 2) Reconstructing the PEE scheduling objective function: Based on the trained model, we obtain:

[0035] in: F v (e t +ε t ) j This represents the j-th element in the prediction result set of the voltage mapping model. The input increment matrix ε consists of the optimization variables. t Let represent the total active power of the electric logistics equipment at node k within time period t, where k∈{2,3,…,d}. The power factor refers to the reactive power of the equipment. In this article, the power factor is taken as 0.9, i.e.

[0036] 3) PEE scheduling optimization variable constraints: Where: P LE This is the rated power of a single logistics device. When there are f logistics tasks to be processed within a scheduling cycle, skt represents the sequence number of the task receiving logistics equipment service at node k during time period t, where skt∈{1,2,…,f}. and These are the start and end times of task skt, respectively. When node k is not processing a task, the load on the logistics equipment... If the value is 0, then the constraint is as follows: Where: C skt It refers to the number of devices. The latest completion time for the task skt to ensure logistics efficiency, H skt η is the number of containers, and η is the processing efficiency of a single device. and These are the maximum and minimum device requirements for task skt, respectively, leading to: in:

[0037] 4) The PEE scheduling optimization model is solved using a multi-population genetic method. The solved optimization variables are then converted and rounded to obtain the number of PEE nodes allocated to logistics tasks. The PEE power consumption optimization scheduling process under limited information is as follows: Figure 4 As shown.

[0038] Through specific practical experiments, the performance of the method was tested on a port power grid based on the IEEE 33-node system. Nodes 1 to 13 were measured nodes, among which nodes 2 to 4 were nodes connected to the PEE (Power over Ethernet). Figure 5 As shown. The dataset contains 30,000 active power, reactive power, and voltage data points, of which 80% is the training set and 20% is the test set. In this embodiment, both the total power mapping model and the voltage mapping model contain 5 convolutional layers, each with 3 MLP layers, and each hidden layer has 20 neurons. A port scheduling cycle is set to 24 hours. The electricity price λ during peak, off-peak, and low-peak periods. t The costs are 1.094, 0.875, and 0.471 yuan / kWh, respectively. The rated power of a single PEE is 320kW, and the processing efficiency η is 35 TEU / h. The penalty coefficient σ is 0.3. The minimum and maximum equipment requirements are 2 and 5, respectively. Other parameters are shown in Table 1.

[0039] Table 1 Logistics Operation Task Parameters

[0040]

[0041] To evaluate the effectiveness of models with a limited number of observable nodes, an average relative error is introduced to describe the accuracy of the results, including the average relative error of the power mapping module. The average relative error of the voltage mapping model in: It is the i-th element of the actual voltage sequence obtained by the measurement unit, F v,i (·) represents the i-th element of the output vector of the voltage mapping model. A smaller average relative error means a more accurate learning effect.

[0042] like Figure 6 As shown, the total power mapping model based on the fine-grained deep graph convolutional online learning method significantly outperforms deep neural networks. The latter has an average relative error of around 35%, because simple data-to-data training struggles to learn complex nonlinear relationships using only a limited number of measurement nodes. In the field of graph learning, the fine-grained mapping model of this invention is compared with existing graph convolutional networks that employ mean aggregation. The average relative error of this invention is 0.628%, which is 0.96% higher than the 1.583% of the convolutional network. This demonstrates that the fine-grained deep graph convolutional online learning method can fully utilize known data and adapt to the uneven and sparse distribution of port datasets.

[0043] like Figure 7 The diagram shows the convergence behavior of the voltage mapping model, graph convolutional network, and deep neural network based on the fine-grained deep graph convolution online learning method. The average relative errors of the three are 0.362%, 0.967%, and 11.294%, respectively, further demonstrating the superiority of this invention.

[0044] A measurement node data-driven PEE scheduling optimization model was established and solved based on the trained total power mapping model and voltage mapping model. The corresponding optimized configuration scheme for logistics equipment is shown in Table 2. To demonstrate the effectiveness of this invention, it was compared with a standard method, which is based on power flow analysis, where the measurement data and topology information of all nodes are known. As shown in Table 3, the results obtained by the two methods are relatively close, confirming the reliability of the proposed method. Moreover, this invention only requires measurements from a small subset of nodes, making it applicable to situations with insufficient measurements.

[0045] Table 2 PEE Configuration Optimization Results

[0046]

[0047] Table 3 Comparison between the present invention and standard methods

[0048]

[0049] To verify the robustness of this invention to load fluctuations at unmeasured nodes, perturbations were randomly selected at these nodes to generate datasets with varying load fluctuations. A power flow mapping model was then trained on these datasets and used for PEE allocation. The accuracy of the mapping model and related scheduling results are shown in Table 4. Despite the different load fluctuations, the results remained largely consistent. Slight differences can be attributed to minor variations in the convergence of the mapping model training, which is permissible in machine learning model training, demonstrating the robustness of this invention.

[0050] Table 4 Results of the present invention under different load fluctuations

[0051]

[0052] In terms of power flow variable mapping, the total power mapping model learning accuracy of this method is greatly improved, with an average relative error of 0.628%, which is significantly better than the 35% error of deep neural networks and 0.96% higher than the 1.583% error of convolutional networks. The voltage mapping model of this method has an average relative error of 0.362%, which is better than the 11.294% error of deep neural networks and the 0.967% error of graph convolutional networks. In terms of solving the power consumption optimization scheduling strategy of port electric equipment clusters, compared with the existing technology which requires measurement data of all nodes, this method can perform accurate calculations with only the measurement values ​​of 40% of the nodes.

[0053] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A method for optimizing power consumption scheduling of port electric equipment clusters under limited data, characterized in that, A total power mapping model and a voltage mapping model are constructed respectively, and trained using historical measurement data from measurement nodes. The trained total power mapping model and voltage mapping model are combined to form a measurement node data-driven PEE scheduling optimization model. The number of PEE configurations corresponding to each logistics task is obtained by solving the model. The total power mapping model includes: a fine-grained depth map convolution module, a filtering and connection module, and a power prediction module. Specifically: the fine-grained depth map convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensating for the active and reactive power information of the unmeasured nodes, and obtaining the total power features of all nodes; the filtering and connection module performs a node-based filtering process based on the total power features of all nodes, obtaining the total power features of the measured nodes; and the power prediction module performs a mapping fitting learning from the total power features of the measured nodes to the active power of the first node, obtaining the predicted total power consumption of the port power grid corresponding to the scheduling of the electric equipment cluster. The voltage mapping model includes: a fine-grained depth map convolution module, a filtering and connection module, and a voltage prediction module. Specifically: the fine-grained depth map convolution module performs information construction, fine-grained average information aggregation, and vertex feature update processing based on the active and reactive power data of the measured nodes, compensating for the active and reactive power information of the unmeasured nodes, and obtaining the voltage characteristics of all nodes; the filtering and connection module performs a filtering process based on the voltage characteristics of all nodes to obtain the voltage characteristics of the measured nodes; and the power prediction module performs a mapping fitting learning from the voltage characteristics of the measured nodes to the voltage of the measured nodes, obtaining the node voltage corresponding to the scheduling of the electric equipment cluster. The measurement node data-driven PEE scheduling optimization model includes: an initial PEE scheduling objective function, a reconstructed PEE scheduling objective function, and PEE scheduling optimization variable constraints. Specifically: the initial PEE scheduling objective function is modeled based on the need to reduce the total electricity cost of port operations and prevent voltage exceedances, resulting in an optimized PEE scheduling objective function. The reconstructed PEE scheduling objective function, based on the initial optimization objective, represents the total power consumption of the port power grid and node voltage in the optimized objective function using a total power mapping model and a voltage mapping model, resulting in a PEE scheduling objective modeled as a convex function. The PEE scheduling optimization variable constraints are processed according to the logistics efficiency requirements that port electric equipment cluster scheduling must follow, using formulas that facilitate the solution of the optimization model, resulting in optimization variable constraints modeled as convex sets.

2. The method for optimizing power consumption scheduling of port electric equipment clusters under limited data as described in claim 1, characterized in that, The training described uses the following loss function. ,in: , This represents the predicted total power consumption of the port power grid corresponding to the scheduling of electric equipment clusters, as output by the total power mapping model. This refers to the actual value of the active power at the substation node obtained by the measurement unit.

3. The method for optimizing power consumption scheduling of port electric equipment clusters under limited data as described in claim 1, characterized in that, Both the total power mapping model and the voltage mapping model are implemented through a neural network comprising several graph convolutional layers, filtering connection layers, and prediction layers connected by residuals. Each graph convolutional layer compensates for the lack of information from measurement nodes by using its own and its neighboring nodes' feature data for message passing, thus transforming the vertex features... As the residual output of layer l, in relation to the input After addition, a new input is formed for layer l+1; the filtering connection layer traverses the vertex features of all nodes and extracts the vertex features of the measurement nodes from them; the prediction layer of the total power mapping model is implemented using a multilayer perceptron, and the prediction layer of the voltage mapping model is implemented using a multilayer perceptron.

4. The method for optimizing power consumption scheduling of port electric equipment clusters under limited data as described in claim 3, characterized in that, The graph convolutional layer, through stacked L layers, enables nodes to collect feature data from their L-layer neighborhood. Specifically, the message passing rule of the L-layer fine-grained deep graph convolutional online learning method is as follows: ,in: p i and q i These are the active power and reactive power at the measured node i, respectively. Let i be the vertex feature of node i in the l-th layer. ReLU(·) is the activation function used to update the features of the vertices in layer l, and GraphConv(·) is the generalized graph convolution function, which passes aggregated information of features from all neighboring nodes to the current node. , , , , υ(i) and n i Let represent the set of neighboring nodes and the number of neighboring nodes of node i, respectively. For each neighbor j∈υ(i), the information is constructed using the constructor. Applied to vertex features Neighbor characteristics Sum of edge features Constructing aggregated information , and These are the active power and reactive power of the measured node j, respectively, and MLP(·) is a multilayer sensor.

5. The method for optimizing power consumption scheduling of port electric equipment clusters under limited data as described in claim 4, characterized in that, The filter connection layer is located between the L-layer output and the model prediction layer, and its output is... Where: concat(·) refers to traversing the vertex features of all nodes, and then extracting the vertex features of the measurement nodes from them using the pick(·) function; L-layer fine-grained depth map convolutional blocks and their message passing process. The vertex features of node i after L layers of transformation are represented as follows: .

6. The method for optimizing power consumption scheduling of port electric equipment clusters under limited data as described in claim 5, characterized in that, The prediction layer of the total power mapping model is implemented using a multilayer perceptron, and its loss function is... Among them: the actual value of active power of substation nodes obtained by the measurement unit. F p (·) represents the functional relationship between the power of the substation node and the power of other measurable nodes, p1 represents the active power of the substation node, and yprep represents the predicted value of the total power mapping model.

7. The method for optimizing power consumption scheduling of port electric equipment clusters under limited data as described in claim 6, characterized in that, The prediction layer of the voltage mapping model uses a multilayer perceptron, and its loss function is: Wherein: the actual voltage value of the measurement node F v (·) represents the functional relationship between the power and voltage of the measurement node fitted by the voltage mapping model. For the predicted values ​​of the voltage mapping model, the substation node is designated as the slack node, and its voltage v1 is given as the reference voltage and is not involved in the model training.

8. The method for optimizing power consumption scheduling of port electric equipment clusters under limited data as described in claim 7, characterized in that, The PEE scheduling optimization model, established based on the trained total power mapping model and voltage mapping model, determines the optimal number of electric logistics devices to be allocated to operational tasks. The specific implementation process includes: 1) Initial PEE scheduling objective function: The objective is to minimize the total electricity cost of port operations, while incorporating voltage constraints as a penalty term to facilitate the solution. Specifically: Where: T is the scheduling period, t∈{1,2,…,T}, It is the electricity price for time period t. It is a penalty factor that controls the voltage to not exceed the lower limit of 0.95 pu; 2) Reconstructing the PEE scheduling objective function: Based on the trained model, we obtain: ,in: , , The j-th element in the prediction result set of the voltage mapping model represents the input increment matrix consisting of the optimization variables. This represents the total active power of the electric logistics equipment at node k during time period t, where k∈{2,3,…,d}. The meaning is the reactive power of the equipment; 3) PEE scheduling optimization variable constraints: , where: P LE This refers to the rated power of a single logistics device. When there are f logistics tasks to process within a scheduling cycle, skt represents the sequence number of the task receiving logistics device service at node k during time period t, where skt ∈ {1, 2, ..., f}. tstartskt and tfinishskt are the start and end times of task skt, respectively. When node k is not processing tasks, the logistics device load εtk is 0. The specific constraints are as follows: , where: C skt It refers to the number of devices. tlatestskt is the latest completion time of the task skt to ensure logistics efficiency. H skt η is the number of containers, η is the processing efficiency of a single device, and Cmaxskt and Cminskt are the maximum and minimum device requirements for task skt, respectively. Therefore, we obtain: ,in: ; 4) Solve the PEE scheduling optimization model based on the multi-population genetic method. The optimized variables after the solution are converted and rounded to obtain the number of PEE allocated to logistics tasks by each node.

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