Microgrid cluster low frequency load shedding method based on improved shapley value

Abstract

The micro-grid group low-frequency load shedding method based on improved Shapley value comprises the following steps: analyzing the operation characteristics of each subject in low-frequency load shedding, constructing a node contribution factor based on the importance of load, load shedding economic loss and frequency regulation effect; combining load multiplicity characteristics with Shapley value in cooperative game, calculating the marginal contribution of each node to the whole micro-grid under different indexes, and improving the contribution distribution coefficient to more reasonably allocate the load shedding capacity; constructing a load shedding model, using a model lightening method based on knowledge distillation to perform knowledge migration on the load shedding model, realizing efficient compression of the model and improvement of the solving performance, and forming a low-frequency load shedding method. The method can reasonably allocate the load shedding capacity of each node in the load shedding process, and has good frequency recovery effect.

Description

Technical Field

[0001] This invention relates to the field of microgrid low-frequency load shedding technology, specifically to a microgrid group low-frequency load shedding method based on an improved Shapley value. Background Technology

[0002] The rapid development of distributed power sources, primarily based on new energy sources, has effectively addressed the energy crisis and environmental pollution problems associated with traditional power generation. Microgrids, as an effective way to connect distributed power sources to the distribution network, are of great significance for meeting the ever-increasing electricity demand and promoting the local consumption of distributed power sources. However, distributed power generation is unstable and intermittent, potentially leading to power shortages or surpluses, posing a significant challenge to the stable operation of microgrids. When a microgrid experiences external disturbances causing a power deficit, the system frequency drops rapidly, leading to overload of electrical equipment and even system imbalance, severely impacting user experience and microgrid safety. Low-frequency load shedding, as the third line of defense for ensuring the safe and stable operation of microgrids, can effectively prevent system frequency decay and improve the reliability and security of microgrid operation. Therefore, researching efficient and reliable low-frequency load shedding strategies is crucial for ensuring the safe and stable operation of microgrids.

[0003] In existing technologies, the literature "Adaptive Low-Frequency Load Shedding Scheme Considering Transient Voltage Stability" (He Peican, Wen Buying, Wang Huaiyuan. Adaptive Low-Frequency Load Shedding Scheme Considering Transient Voltage Stability [J]. Journal of Fuzhou University (Natural Science Edition), 2019, 47(06): 765-770.) proposes a real-time identification method for system inertia based on the frequency response information of the power system, and considers the impact of active power deficit caused by voltage to obtain a method for calculating the system power deficit. At the same time, an adaptive low-frequency load shedding scheme is determined by combining the system transient voltage stability index. However, this scheme fails to fully consider the multi-dimensional characteristics of the load and is no longer applicable to new energy power generation with weak inertia.

[0004] The literature "Research on Low-Frequency Load Shedding Control Strategy of Power System Considering Wind Power Frequency Response" (Wang Yukun, Zhang Mujie, Shi Mengxuan, et al. Research on Low-Frequency Load Shedding Control Strategy of Power System Considering Wind Power Frequency Response [J]. Renewable Energy, 2023, 41(09): 1247-1254.) establishes a simplified frequency response model of the power system considering wind power participation in frequency regulation based on the virtual inertia of wind power and the primary frequency regulation control model. Secondly, it analyzes the influence of the active power response characteristics of wind power participation in frequency response on the unbalanced power of the system, and then estimates the unbalanced power used to guide low-frequency load shedding. However, it does not consider the importance of the loads being shelved, which may lead to the shelving of important loads.

[0005] The literature "Optimization Operation Strategy of Distributed Photovoltaic Community Shared Energy Storage Based on Master-Slave Game Theory and Improved Shapley Value" (Tian Xin, Chen Laijun, Li Xiaozhu, et al. Optimization Operation Strategy of Distributed Photovoltaic Community Shared Energy Storage Based on Master-Slave Game Theory and Improved Shapley Value [J]. Power System Technology, 2023, 47(06): 2252-2261.) comprehensively considers factors such as the similarity of multi-community output-alliance load waveforms, net output size, and net output correlation to improve the Shapley value, thereby achieving a reasonable allocation of additional benefits to the alliance. However, the master-slave game model based on the Shapley value is too complex for load shedding problems, making it difficult to quickly and timely calculate a reasonable load shedding allocation through optimization strategies. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a low-frequency load shedding method for microgrids based on an improved Shapley value. First, the operating characteristics of each entity in the load shedding scheme are analyzed, treating the load shedding allocation problem as a cooperative game, with the microgrid as a consortium and each node load as a sub-member of the consortium. Node contribution factors are constructed based on load importance levels, economic losses from load shedding, and frequency regulation effects. Second, combining load multiplicity characteristics with the Shapley value in the cooperative game, the marginal contribution of different indicators of each node to the entire microgrid is calculated, and the contribution allocation coefficient is improved to allocate load shedding more rationally. Finally, a load shedding model is constructed, and a knowledge distillation-based model lightweighting method is used to transfer knowledge from the model, achieving efficient model compression and improved solution performance, thus forming a low-frequency load shedding method. The method proposed in this invention can fairly and reasonably allocate the load shedding of each node during the load shedding process, exhibiting good frequency recovery performance.

[0007] The technical solution adopted in this invention is as follows:

[0008] The microgrid group low-frequency load reduction method based on improved Shapley value includes the following steps:

[0009] Step 1: Analyze the operating characteristics of each component during low-frequency load shedding, and construct a node contribution factor based on load importance, economic loss from load shedding, and frequency regulation effect;

[0010] Step 2: Combining load multiplicity characteristics with the Shapley value in cooperative game theory, calculate the marginal contribution of different indicators of each node to the entire microgrid, and improve the contribution allocation coefficient to allocate load reduction more rationally.

[0011] Step 3: Construct a load reduction model and use a knowledge distillation-based model lightweighting method to transfer knowledge from the load reduction model, thereby achieving efficient model compression and improving solution performance, forming a low-frequency load reduction method.

[0012] In step 1, low-frequency load shedding, as the third line of defense for ensuring the safe and stable operation of the microgrid, can effectively prevent system frequency decay and improve the reliability and security of microgrid operation. Its essence is to reduce the load within the system. However, the frequency recovery effect varies depending on the type of load shedding. This invention quantifies the impact of load importance, economic losses from load shedding, and frequency regulation effects on the amount of load shedding by constructing a node contribution factor.

[0013] 1.1: Load Importance Factor:

[0014] Load importance primarily refers to the significance of each node's load within a microgrid. Microgrids include industrial, commercial, and residential loads, which have an inseparable impact on the overall system operation and users' electricity experience. To specifically describe the contribution of load importance indicators to the microgrid system, loads are divided into primary, secondary, and tertiary loads, and a load importance factor I is constructed. i :

[0015]

[0016] In the formula, I i The importance of load i; P LD_i L represents the active power of load i; i χ is the reciprocal of the load level. i The degree to which users value the user experience in terms of load; P LD This represents the total power of the system's electrical load.

[0017] Load Importance Factor I i This reflects the importance of the load in the microgrid system; the higher the value, the greater the importance within the microgrid system. Therefore, when reducing load, priority should be given to removing the load based on the importance factor I. i Small load.

[0018] 1.2: Economic loss factor due to load reduction:

[0019] When an islanded microgrid implements a low-frequency load shedding strategy, regardless of the type of load, some economic loss will occur during shedding. Furthermore, for the entire microgrid, the economic loss should be minimized while completing the load shedding operation. To specifically describe the contribution of load shedding economic loss indicators to the microgrid system, economic loss is divided into load shedding loss and frequency deviation loss, and a load shedding economic loss factor E is constructed. i :

[0020]

[0021] In the formula, E i To reduce the economic loss factor; α i P is the economic loss coefficient for load i to be removed; shed_i β is the amount of resection for load i; i t is the loss coefficient for the frequency shift at node i; m is the total number of loads; t0 is the start time of frequency curve integration; t1 is the end time of frequency curve integration; Δf(t) is the frequency deviation curve at time t.

[0022] Reduced load economic loss factor E i This represents the ability of load i to assess the economic loss of the system. Due to differences in load location and type, the amount of load shedding and the resulting system frequency shift vary, leading to differences in the economic loss factor for different loads. When shedding loads, priority should be given to shedding the load shedding economic loss factor E. i Large load.

[0023] 1.3: Frequency modulation effect factor:

[0024] Frequency regulation effect refers to the ability of a microgrid system to regulate its frequency through load. To fully reflect the close relationship between system load active power and system frequency, the frequency dynamic model adopted in this invention is as follows:

[0025] P LD =a0P LDN +a1P LDN (f / f N )+…+a n P LDN (f / f N ) n ;

[0026] In the formula, P LD P represents the actual active power of the load. LDN f is the rated active power of the load; f is the actual frequency of the system; f N The system's rated frequency; a n The load weighting relative to the rated load is proportional to the nth power of the ratio of the actual system frequency to the rated frequency.

[0027] The better the frequency regulation effect of the node loads, the higher their contribution to the microgrid system. To specifically describe the contribution of this indicator to the system, the frequency regulation coefficient K is used. i As a frequency adjustment factor:

[0028]

[0029] In the formula, K i The frequency adjustment coefficient for load i; f is the per-unit value of the active power of load i; * K represents the per-unit value of the system frequency; K is the frequency adjustment coefficient of load i. i The larger the value, the greater its impact on the system frequency. That is, when the microgrid frequency decreases, the frequency regulation coefficient K is cut off. i Larger loads will further hinder frequency reduction. Therefore, when formulating low-frequency load shedding strategies, the frequency regulation factor K should be preferentially removed. i Small load.

[0030] In step 2, the load reduction allocation problem is treated as a cooperative game, with the microgrid as a consortium and each node load as a sub-member of the consortium. The marginal contribution of each node is used to quantify the correlation of sub-members in the game and their impact on the system. At the same time, the contribution allocation coefficient is improved to form the LMC-Shapley value that considers the multi-dimensional characteristics of the load, as follows:

[0031] 2.1: Node Marginal Contribution:

[0032] The Shapley value originates from cooperative game theory and is often used to measure the contribution of multiple participants to the overall coalition in a game. It is currently widely used in the power industry. Assuming a microgrid system... It contains m loads, and its set is represented as Represents a set The contribution of medium load i to the total microgrid system The contribution allocated to a participant is expressed as follows:

[0033]

[0034] Assume that the loads together form a microgrid system in a cooperative game. The probability is Its representation is shown in the following formula:

[0035]

[0036] In the formula, Indicates the remaining A load, that is, not within this size. The number of permutations in which loads in a consortium can appear in any order in other positions of the permutation; Indicates who enter the league first The number of permutations of loads.

[0037] The contribution is allocated based on the Shapley value method, and the contribution (Shapley value) assigned to load i is... As shown in the following formula:

[0038]

[0039] In the formula, The marginal contribution of load i in the alliance; Microgrid system The total contribution of the system composed of the remaining loads after removing load i; S i Let S represent the set of all possible federations containing load i; let S represent the set of all possible federations.

[0040] 2.2: Improved contribution allocation coefficient:

[0041] When the addition of load i brings an increase in the marginal contribution of the consortium, its contribution allocated based on the Shapley value method will increase. The magnitude of the marginal contribution of each load in a microgrid depends on the load's importance, the economic loss from load shedding, and the frequency regulation effect. The contributions of these three indicators to the microgrid are complex and involve numerous factors. Although the Shapley value is a fair allocation method, it may overlook the actual contributions and efficiency considerations of the participants, failing to fully reflect the diverse characteristics of the loads. This invention sets reasonable contribution allocation coefficients for the three indicators of load importance, economic loss from load shedding, and frequency regulation effect, and simultaneously determines the LMC-Shapley value by combining the Shapley values ​​of each indicator:

[0042] Contribution allocation coefficient This coefficient aims to fully reflect the complex contribution of individual loads to the microgrid system. It is assigned based on the load importance. Economic loss allocation coefficient for load reduction and frequency modulation effect allocation coefficient It consists of three parts, as shown in the following formula:

[0043]

[0044] In the formula, I i E represents the importance of load i; i To reduce the economic loss factor; K i Let ω1 be the frequency regulation coefficient of load i; m be the total number of loads; ω1, ω2, and ω3 are the weights of the load importance allocation coefficient, the load reduction economic loss allocation coefficient, and the frequency regulation effect allocation coefficient, respectively, and ω1 + ω2 + ω3 = 1.

[0045] After deriving the contribution distribution coefficient Then, combining the Shapley value obtained from load i in the cooperative game, the LMC-Shapley value is calculated:

[0046]

[0047] In the formula, Let load i be the total contribution of the microgrid system. The LMC-Shapley value assigned in the middle.

[0048] Step 3 includes:

[0049] 3.1: Load Reduction Model:

[0050] The core objective of load shedding is to enable the system to quickly recover to a stable value after being subjected to external disturbances, while maximizing the power supply rate of critical loads and minimizing overall economic losses and system frequency fluctuations. Therefore, a load shedding objective function is constructed based on the aforementioned LMC-Shapley value method:

[0051]

[0052] In the formula, Z is the comprehensive evaluation value of load reduction, and this value should be minimized as much as possible during load reduction.

[0053] In addition, node power flow constraints and bus constraints must be satisfied during load reduction:

[0054]

[0055] f min ≤f≤f max ;

[0056] In the formula, P i Q i These represent the active power and reactive power of node i, respectively; U i U j Let G be the voltage magnitudes at nodes i and j, respectively; ij B ij The conductance and susceptance of nodes i and j are respectively; θ ij f is the phase angle difference between points i and j; f is the frequency of the system bus; f max f min The maximum and minimum values ​​of the respective bus frequencies.

[0057] When a microgrid experiences a fault and disconnects from the main grid, it transitions from grid-connected mode to islanded mode. In this state, distributed generation (DG) within the microgrid adjusts its output through droop control to ensure system frequency stability. When the power deficit exceeds the maximum capacity provided by the DG, a low-frequency load shedding strategy is implemented to reduce the load. Based on the aggregation and droop characteristics of DG, the load shedding is calculated in segments. When the islanded microgrid is in segment a at frequency f... a′ The frequency f recovered to segment b b′ At that time, the required load reduction is:

[0058]

[0059] In the formula, f a+1 f is the upper limit of the frequency of segment a; a′ This indicates the frequency at which the islanded microgrid is in segment a; f b′ This indicates the frequency at which the isolated microgrid recovers to segment b.

[0060] f b This represents the lower frequency limit of segment b; △f a , △f b The frequency difference between segment a and segment b; △P a , △P b ΔP represents the active power difference corresponding to the frequency difference between segment a and segment b; i Let be the active power difference corresponding to the frequency difference of segment i, where segment i is located between segment a and segment b.

[0061] If, at any given moment, the system's power deficit exceeds the maximum range adjustable by droop control, all distributed power sources within the microgrid will adjust to operate at maximum capacity. At this point, the frequency returns to f. b′ At that time, the required load reduction is:

[0062]

[0063] In the formula, △P def This represents the system's power deficit; ΔP j f represents the active power difference corresponding to the frequency difference in segment j, where segment j lies between segment b and segment n (inclusive); b+1 Δf is the upper frequency limit of segment b; b The frequency difference of segment b; △P b This represents the active power difference corresponding to the frequency difference in segment b.

[0064] 3.2: Lightweight Model Approach Based on Knowledge Distillation

[0065] Because cooperative game theory models are highly complex, conventional optimization algorithms are slow to solve them. Furthermore, the low-frequency load shedding actions of microgrids are time-sensitive; if the solution speed is slow, the system frequency may not be restored in time, leading to system failure. Knowledge distillation, as a model compression technique, transfers knowledge from a complex teacher model to a lightweight student model, significantly reducing computational complexity while maintaining decision-making accuracy.

[0066] In this invention, the teacher model is composed of an LMC-Shapley value game model, and its output is the load reduction amount; the student model directly learns the input-output mapping relationship of the teacher model through a multilayer perceptron (MLP), transforming the game model solution process into forward propagation computation.

[0067] 1) Student Model:

[0068] The multilayer perceptron (MLP) is constructed with four hidden layers, from the input layer to the output layer, containing 56, 28, 14, and 7 neurons respectively. The first and second layers use the Tanh activation function, the third and fourth layers use the ReLU activation function, and the output layer uses the Softmax activation function. The output of the MLP constructed in this invention is:

[0069]

[0070] In the formula, and These are the outputs of neuron m in layer l+1 and neuron n in layer l, respectively; Let n be the connection weights between neuron n in layer l and neuron m in layer l+1. N represents the bias of neuron m in layer l+1; l is the total number of neurons in the l-th layer; f(·) is the activation function of the hidden layer.

[0071] The learning algorithm of a Multilayer Perceptron (MLP) is backpropagation, which updates the connection weights using the backpropagation algorithm. This algorithm first calculates the gradient of the loss function with respect to the connection weights, and then progressively updates the weight values ​​using gradient descent.

[0072] The core of backpropagation is to use the chain rule to calculate the gradient of the loss function with respect to the weights and biases of each layer:

[0073] a. The net input z of the input layer (l) With the output α of the output layer (L) Used to calculate the output layer error term δ (L) :

[0074] δ (L) =(α (L) -y mn )⊙f′(z (l) );

[0075] In the formula, y mn The label is for the current sample; ⊙ indicates element-wise multiplication.

[0076] b. Calculate the error term δ of the hidden layer from back to front. (l) :

[0077] δ (l) =(W (l+1) ) T δ (l+1) ⊙f′(z (l) );

[0078] In the formula, W (l+1) This represents the connection weights between neurons in layer l+1 and neurons in layer l.

[0079] c. Calculate the gradient of the loss function with respect to the connection weights and biases:

[0080]

[0081] In the formula, g is the loss function; c is the number of samples.

[0082] d. Finally, update the weights and biases:

[0083]

[0084] In the formula, α is the learning rate.

[0085] By repeatedly calculating the loss, backpropagating, and updating the weights, the value of the loss function is gradually reduced, allowing the prediction results of the multilayer perceptron to continuously approach the true value.

[0086] Meanwhile, in order to enable the model to fully learn the data features during training and improve the model's performance, this invention adopts the cross-entropy loss function, as shown in the following formula:

[0087]

[0088] In the formula, g loss y is the loss value; c is the number of samples; d is the number of classes; mn The label for the current sample; This is the predicted value for the current sample.

[0089] 2) Knowledge distillation:

[0090] a. The CPLEX solver is used to calculate the teacher model and generate the label knowledge probability distribution values. Details are as follows:

[0091] The output of the teacher model, i.e., the cooperative game model based on the modified Shapley value, is: the optimal load shedding for each load. Used to calculate the probability distribution value of tag knowledge:

[0092]

[0093] In the formula, This represents the probability that the load reduction is allocated to load j under the i-th fault scenario; m is the total number of loads.

[0094] The label knowledge is distilled and "heated" in the following ways:

[0095] "Heating" means adjusting the distillation temperature T to increase the output p of the teacher model. i Soft tags are generated using the Softmax function based on distillation temperature:

[0096]

[0097] In the formula, p i The output value is the teacher model based on the LMC-Shapley value; T is the distillation temperature; Soft labels generated from the teacher model output values ​​after temperature adjustment; This represents the raw values ​​output by the teacher model. First, divide by the distillation temperature T to scale the temperature, then use the exponential function exp(·) to convert the scaled value into a non-negative value.

[0098] b. Apply the generated soft-label knowledge to the student model, and adjust the distillation process inversely based on the distillation loss and the student loss;

[0099] The loss from knowledge distillation consists of two parts:

[0100] ① Distillation loss of student model and teacher soft label, i.e., probability value after distillation temperature adjustment:

[0101]

[0102] In the formula, These represent the probability distribution of the soft labels generated by the teacher model and the predicted probability distribution of the student model, respectively. This represents the KL divergence, which measures the difference between the soft label distribution of the teacher model and the predicted distribution of the student model.

[0103] ② The student loss between the student model and the true labeled student, i.e., the probability value at standard temperature:

[0104]

[0105] The total loss function can be expressed as a weighted sum of the two:

[0106] Γ=(1-δ)·Γ MSE +δ·Γ CE ;

[0107] In the formula, δ is the weighting coefficient; Γ MSE and Γ CE These are distillation losses and student losses, respectively.

[0108] Load reduction method process:

[0109] Step 1: When a fault event occurs in the microgrid, calculate the total power deficit of the microgrid.

[0110] Setp2: Construct contribution factors for each node to the microgrid based on load importance, economic losses from load shedding, and frequency regulation effects.

[0111] Step 3: Calculate the marginal contribution and contribution allocation coefficient of different indicators for each node based on the Shapley value method.

[0112] Step 4: Combine the Shapley value and contribution allocation coefficient of each node to calculate the LMC-Shapley value of the load of each node, and construct the load reduction objective function and constraints.

[0113] Step 5: Due to the high complexity of the cooperative game model, this invention uses knowledge distillation to lightweight the model: ① The CPLEX solver is used to calculate the teacher model and generate the label knowledge probability distribution value; ② The label knowledge is distilled to "heat up" the model, and the distillation process is adjusted inversely based on the distillation loss and the student loss.

[0114] Step 6: Deploy the distilled student model and output the real-time optimal load shedding strategy based on the real-time frequency state of the microgrid. This invention provides a low-frequency load shedding method for microgrid groups based on improved Shapley values, with the following technical effects:

[0115] 1) Step 1 of this invention analyzes the operating characteristics of each entity in low-frequency load shedding. Based on load importance, load shedding economic losses, and frequency regulation effects, a node contribution factor is constructed. This avoids the limitations of a single indicator while providing a quantitative basis for subsequent Shapley value correction. Specifically, the construction of the load importance factor quantifies the load priority during load shedding, avoiding the problem of reduced power supply reliability caused by blindly shedding loads and prioritizing the power supply of important loads. The construction of the load shedding economic loss factor transforms implicit economic costs into explicit indicators, directly linking the cost of load shedding to the cost of frequency disturbance. Compared with traditional load shedding strategies that focus on shedding speed, this provides a more comprehensive basis for load shedding from the perspective of economic losses. The construction of the frequency regulation effect factor allows load shedding actions to directly serve the core task of preventing frequency drops and accelerating frequency recovery, quantifying the load's ability to regulate frequency, avoiding ineffective load shedding, and adapting to the characteristics of distributed power source fluctuations in microgrids. In summary, this step, through the construction of node contribution factors, not only solves the problems of "single objective, subjective decision-making, and one-sided effect" in traditional load reduction strategies, but also provides a reliable decision-making basis for subsequent Shapley value calculation and knowledge distillation lightweighting. It is a key prerequisite for achieving optimal frequency recovery, low economic loss, and protection of important loads in the strategy presented in this paper.

[0116] 2) Step 2 of this invention calculates the marginal contribution of nodes by combining the multi-dimensional characteristics of load with the Shapley value in cooperative game theory, and improves the contribution allocation coefficient to reasonably allocate load reduction, thereby achieving objective fairness in load reduction allocation. Specifically, this step treats the microgrid as a "cooperative game alliance" and each node as a "game participant." By calculating the marginal contribution of nodes through the Shapley value, it solves the problems of subjectivity and insufficient fairness in the allocation basis of traditional strategies. It ensures that nodes with high contributions, i.e., nodes with high importance, high disconnection costs, and high frequency impact, bear less load reduction, thus comprehensively and objectively allocating load reduction and avoiding the subjective influence of expert experience weights in traditional strategies. The improved contribution allocation coefficient dynamically adapts to the operating characteristics of the microgrid, improving the accuracy of decision-making. The weights in the allocation coefficient can be adjusted according to the microgrid fault scenarios, avoiding the limitations of fixed coefficients that cannot adapt to different fault scenarios. In summary, this step, through a three-tiered design that covers all dimensions of demand with diverse load characteristics, ensures objectivity and fairness with Shapley values, and improves accuracy with improved allocation coefficients, not only solves the problems of the one-sidedness and subjectivity of traditional load reduction strategies, but also provides a reliable decision-making basis for subsequent load reduction optimization and model lightweighting.

[0117] 3) Step 3 of this invention achieves lightweighting and knowledge transfer of the load reduction model through knowledge distillation, improving compression efficiency and solution performance. This resolves the contradiction between the slow solution of complex load reduction models and the real-time requirements of microgrid load reduction. Specifically, the cooperative game-theoretic load reduction model based on modified Shapley values ​​is complex and time-consuming to solve. Knowledge distillation transfers the decision-making knowledge of the complex model to a lightweight student model based on a multilayer perceptron (MLP). Through soft-label temperature adjustment, the deep knowledge of the teacher model can be fully transferred, satisfying the need for rapid solution while avoiding the problem of reduced solution accuracy caused by parameter reduction in traditional model lightweighting methods. The student model after knowledge distillation has the advantages of being lightweight and having low computational requirements, and can be directly deployed on edge controllers without relying on high-computing-power solvers in the cloud, reducing communication latency. In summary, this step achieves the triple goals of model compression, knowledge preservation, and solution acceleration through knowledge distillation, solving the real-time bottleneck of complex load reduction models, ensuring the accuracy and scenario adaptability of load reduction decisions, and reducing deployment costs. Attached Figure Description

[0118] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0119] Figure 1 This is a flowchart of the microgrid group low-frequency load reduction method of the present invention.

[0120] Figure 2 This is a comparison chart of the degree of economic loss.

[0121] Figure 3 This is a comparison chart of frequency recovery effects. Detailed Implementation

[0122] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0123] A low-frequency load shedding method for microgrids based on improved Shapley values. First, the operational characteristics of each entity in the load shedding scheme are analyzed, treating the load shedding allocation problem as a cooperative game, with the microgrid as a consortium and each node load as a sub-member. Node contribution factors are constructed based on load importance levels, economic losses from load shedding, and frequency regulation effects. Second, combining load multiplicity characteristics with the Shapley value in the cooperative game, the marginal contribution of each node to the entire microgrid is calculated, and the contribution allocation coefficient is improved to allocate load shedding more rationally. Finally, a load shedding model is constructed, employing a knowledge distillation-based model lightweighting method to achieve efficient model compression and improved solution performance through knowledge transfer, forming a low-frequency load shedding method. The proposed method can fairly and reasonably allocate the load shedding of each node during the load shedding process, exhibiting good frequency recovery performance.

[0124] Figure 2 This is a comparison chart of the degree of economic loss. To test and verify the superiority of the load reduction strategy proposed in this invention in reducing economic losses, the load reduction strategy proposed in this invention is compared and analyzed with load reduction strategies based on the GOA optimization algorithm, adaptive load reduction strategies based on artificial neural networks, and load reduction strategies based on subjective and objective load weights. The above strategies are sequentially set as strategies A, B, C, and D, and their respective load reduction actions are executed. As shown in the figure, the economic loss caused by strategy A is 13.39% and 4.24% lower than that of strategies B and C, respectively, and the total load reduction of strategy A is 4.04% and 0.9% less than that of strategies B and C, respectively. This is because strategy B prioritizes maximizing the minimum swing frequency of the system when constructing the objective function, while strategy C prioritizes minimizing the total load reduction when determining the system's load reduction strategy based on the training results of the artificial neural network, thus making the total load reduction of strategy C lower than that of strategy B. At the same time, neither strategy considers the cost of load shedding, thus causing significant economic losses. Although Strategy D conducted both subjective and objective assessments of the economic losses from load shedding, resulting in an economic loss 0.77% lower than Strategy A, Strategy A's total load reduction was 2.52% lower than Strategy D's. Therefore, Strategy A offers superior load reduction efficiency.

[0125] Figure 3 This is a comparison chart of frequency recovery effects. To test and verify the superiority of the load reduction strategy proposed in this invention in frequency recovery, the load reduction strategy proposed in this invention is compared and analyzed with load reduction strategies based on GOA optimization algorithm, adaptive load reduction strategies based on artificial neural networks, and load reduction strategies based on subjective and objective load weights. The above strategies are sequentially set as strategies A, B, C, and D, and their respective load reduction actions are executed.

[0126] Depend on Figure 3It can be seen that the system frequency fluctuation amplitude under strategy A is the lowest, at 0.3234Hz, which is 10.39%, 22.91%, and 23.11% lower than strategies B, C, and D, respectively. Although all four strategies consider the system's frequency regulation effect, strategies C and D only use the frequency regulation coefficient as one of the reference bases for formulating load reduction strategies, while strategy B takes maximizing the system's lowest swing frequency as the primary objective for formulating load reduction strategies. Therefore, the frequency fluctuation amplitude of strategy B is smaller than that of strategies C and D. Although strategy A also only uses the frequency regulation coefficient as one of the reference bases for formulating load reduction strategies, it differs from strategy C in that it does not consider its weight and directly uses it as the input of the artificial neural network; it also differs from strategy D in that it determines its weights based on subjective and objective evaluation methods. This is because subjective evaluation methods are flexible, and if experts lack experience, it will affect the accuracy of the load evaluation results. When constructing the load reduction objective function, strategy A uses the LMC-Shapley value method to treat the microgrid as a coalition and each load as a member, determining the weights of the indicators based on their respective LMC-Shapley values, making the evaluation results more accurate. Regarding frequency recovery time, strategy A has a time of 0.3723s, which is 7.37%, 14.65%, and 3.9% lower than strategies B, C, and D, respectively. This invention, through the learning of knowledge transmitted by the teacher model by the student model, reduces model complexity and improves strategy solution efficiency while maintaining model accuracy, thus resulting in a shorter system frequency recovery time. In summary, the system frequency recovery performance under the proposed load reduction strategy A is superior.

[0127] Table 1. Comprehensive Comparison of Load Reduction Performance

[0128]

[0129] Table 1 is a comprehensive comparison table of load reduction performance. To test and verify the superiority of the load reduction strategy proposed in this invention, the proposed load reduction strategy is compared and analyzed with load reduction strategies based on GOA optimization algorithm, adaptive load reduction strategies based on artificial neural networks, and load reduction strategies based on subjective and objective load weights. The above strategies are sequentially designated as strategies A, B, C, and D, and their respective load reduction actions are executed. Based on the data in Table 1, compared with strategies B and C, strategy A proposed in this invention performs best in five aspects: Level I load shedding rate, economic loss from load reduction, total system load reduction, frequency fluctuation amplitude, and frequency recovery time. Compared with strategy D, strategy A performs better in four aspects: Level I load shedding rate, total system load reduction, frequency fluctuation amplitude, and frequency recovery time, only slightly worse than strategy D in terms of economic loss from load reduction. Therefore, considering all five load reduction performance indicators, the load reduction strategy A proposed in this invention has better load reduction benefits.

Claims

1. A low-frequency load shedding method for microgrid groups based on improved Shapley values, characterized in that... Includes the following steps: Step 1: Analyze the operating characteristics of each component during low-frequency load shedding, and construct a node contribution factor based on load importance, economic loss from load shedding, and frequency regulation effect; Step 2: Combining the multi-dimensional characteristics of loads with the Shapley value in cooperative game theory, calculate the marginal contribution of different indicators of each node to the entire microgrid, and improve the contribution allocation coefficient to allocate load reduction more rationally. Step 3: Construct a load reduction model and use a knowledge distillation-based model lightweighting method to perform knowledge transfer on the load reduction model; In step 1, the impact of load importance, load reduction economic loss, and frequency regulation effect on load reduction is quantified by constructing a node contribution factor. 1.1: Load Importance Factor: To represent the contribution of load importance indicators to the microgrid system, loads are divided into primary, secondary, and tertiary loads, and a load importance factor is constructed. : ； In the formula, For load The degree of importance; For load The active power; It is the reciprocal of the load level; For users to load The degree of importance attached to the experience; This represents the total power of the system's electrical load. Load importance factor This reflects the importance of the load in the microgrid system; the higher the value, the greater the importance in the microgrid system. Therefore, when reducing load, priority should be given to removing loads based on their importance. Small load; 1.2: Economic loss factor due to load reduction: To describe the contribution of load shedding economic loss indicators to microgrid systems, economic losses are divided into load shedding losses and frequency deviation losses, and a load shedding economic loss factor is constructed. : ； In the formula, To reduce the economic loss factor; For load The economic loss coefficient of resection; For load The amount of resection; For load The loss coefficient due to the shift in node frequency at that location; The total number of loads; The starting time for integrating the frequency curve; The end time of the integral of the frequency curve; for Frequency deviation curve at any given time; Reduced load economic loss factor Represents load The ability to assess system economic losses; when reducing load, prioritizing the removal of load reduction economic loss factors. Large load; 1.3: Frequency modulation effect factor: To reflect the close relationship between system load active power and system frequency, the following frequency dynamic model is adopted: ； In the formula, This represents the actual active power of the load. This is the rated active power of the load; This refers to the actual frequency of the system. The system's rated frequency; It is proportional to the ratio of the system's actual frequency to its rated frequency. The weight of the load to the rated load is the power of the load. The better the frequency regulation effect of the node load, the higher its contribution to the microgrid system; to specifically describe the contribution of this indicator to the system, the frequency regulation coefficient is... As a frequency adjustment factor: ； In the formula, For load The frequency adjustment coefficient; For load Per-unit value of active power; The per-unit value of the system frequency; load Frequency adjustment coefficient The larger the value, the greater its impact on the system frequency; that is, when the microgrid frequency decreases, the frequency regulation coefficient is cut off. Larger loads will further hinder frequency reduction; therefore, when formulating low-frequency load shedding strategies, the frequency regulation coefficient should be removed first. Small load.

2. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 1, characterized in that: In step 2, the load reduction allocation problem is regarded as a cooperative game, the microgrid is the alliance, and the load of each node is the alliance sub-member. The marginal contribution of the nodes is used to quantify the correlation of the sub-members in the game and their impact on the system. At the same time, the contribution allocation coefficient is improved to form the LMC-Shapley value that considers the multi-dimensional characteristics of the load.

3. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 2, characterized in that: The Shapley value originates from cooperative games in game theory and is used to measure the contribution of multiple participants to the entire alliance in a game. Set up a microgrid system Includes A load, whose set is represented as , Represents a set medium load In the total contribution of microgrid systems The contribution allocated to a participant is expressed as follows: ； Assume that the loads together form a microgrid system in a cooperative game. The probability is Its representation is shown in the following formula: ； In the formula, Indicates the remaining A load, that is, not within this size. The number of permutations in which loads in a consortium can appear in any order in other positions of the permutation; Indicates who enter the league first The number of permutations of loads; The contribution is allocated based on the Shapley value method, and the load... The allocated contribution (Shapley value) As shown in the following formula: ； In the formula, For load Marginal contribution within the alliance; Microgrid system Remove load Finally, the total contribution of the system composed of the remaining load; Indicates that the load is included. The set of all possible alliances; It represents the set of all possible alliances.

4. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 3, characterized in that: Contribution allocation coefficients are set for three indicators: load importance, load reduction economic loss, and frequency regulation effect. At the same time, the LMC-Shapley value is determined by combining the Shapley values ​​of each indicator. Contribution allocation coefficient The aim is to fully reflect the complex contribution of a single load to the microgrid system; This coefficient is allocated based on the importance of the load. Economic loss allocation coefficient for load reduction and frequency modulation effect allocation coefficient It consists of three parts, as shown in the following formula: ， ， ； ； In the formula, For load The degree of importance; To reduce the economic loss factor; For load The frequency adjustment coefficient; The total number of loads; These are the weights of the load importance allocation coefficient, the load reduction economic loss allocation coefficient, and the frequency regulation effect allocation coefficient, respectively. ; After deriving the contribution distribution coefficient Then, combined with load From the Shapley value obtained in the cooperative game, the LMC-Shapley value is calculated: ； In the formula, For load In the total contribution of microgrid systems The LMC-Shapley value assigned in the middle.

5. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 4, characterized in that: In step 3, the load reduction objective function is constructed based on the LMC-Shapley value method: ； In the formula, This is the comprehensive evaluation value for load reduction; the load should be reduced to the smallest possible value. In addition, node power flow constraints and bus constraints must be satisfied during load reduction: ； ； In the formula, , They are nodes Active power and reactive power; , They are nodes and The voltage amplitude; , They are nodes and Conductivity and susceptance; For point and The phase angle difference; The frequency of the system bus; , These represent the maximum and minimum bus frequencies, respectively.

6. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 5, characterized in that: When a microgrid fails and disconnects from the main grid, it will switch from grid-connected mode to islanded mode. At this time, the distributed power sources in the microgrid will adjust their respective outputs through droop control to ensure system frequency stability. When the power deficit in the system exceeds the upper limit that the distributed power sources can provide, a low-frequency load shedding strategy needs to be implemented to reduce the load to a certain extent. Based on the aggregation droop characteristics of distributed generation, the load shedding is calculated in segments when the islanded microgrid is in the first stage. frequency of the segment Restore to the first frequency of the segment At that time, the required load reduction is: ； In the formula, For the first The upper limit of the frequency of the segment; This indicates that the islanded microgrid is in the first stage. The frequency of the segment; This indicates that the isolated microgrid has recovered to the first level. The frequency of the segment; For the first The lower limit of the segment's frequency; , For the first Section and the Frequency difference of segments; , For the first Section and the The active power difference corresponding to the frequency difference; For the first The active power difference corresponding to the frequency difference, the first The segment is located in the first Section and the Between paragraphs; If, at any given moment, the system's power deficit exceeds the maximum range that droop control can adjust, all distributed power sources within the microgrid will adjust to operate at maximum capacity; at this time, the frequency will return to normal. At that time, the required load reduction is: ； In the formula, This is the system's power deficit; For the first The active power difference corresponding to the frequency difference; For the first The upper limit of the frequency of the segment; For the first Frequency difference of segments; For the first The difference in active power corresponding to the frequency difference.

7. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 6, characterized in that: The lightweight model simplification method based on knowledge distillation is as follows: Knowledge distillation transfers knowledge from a complex teacher model to a lightweight student model, significantly reducing computational complexity while maintaining decision-making accuracy. The teacher model consists of an LMC-Shapley value game model, whose output is the load reduction. The student model directly learns the input-output mapping relationship of the teacher model through a multilayer perceptron (MLP), transforming the game model solution process into forward propagation computation. 1) Student Model: The multilayer perceptron (MLP) is constructed with four hidden layers, from the input layer to the output layer, containing 56, 28, 14, and 7 neurons respectively. The first and second layers use the Tanh activation function, the third and fourth layers use the ReLU activation function, and the output layer uses the Softmax activation function. The output of the constructed MLP is: ； In the formula, and Neuron In the Layer output and neurons In the Layer output; For the first neurons in the layer and the neurons in the layer The connection weights; For neurons In the Layer bias; For the first Total number of neurons in the layer; The activation function for the hidden layer; The learning algorithm of the Multilayer Perceptron (MLP) is backpropagation, which updates the connection weights by using the backpropagation algorithm. The algorithm first calculates the gradient of the loss function with respect to the connection weights, and then updates the weight values ​​step by step according to the gradient descent method. The cross-entropy loss function is used, as shown in the following equation: ； In the formula, This is the loss value; The number of samples; Number of categories; The label for the current sample; This is the predicted value for the current sample.

8. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 7, characterized in that: Knowledge distillation specifically includes: using the CPLEX solver to calculate the teacher model and generate the label knowledge probability distribution values; as detailed below: The optimal load shedding for each load is determined by the output of the teacher model, i.e., the cooperative game model based on modified Shapley values. Used to calculate the probability distribution value of tag knowledge: ； In the formula, Indicates the first In this fault scenario, the load reduction is allocated to the load. The probability of; The total number of loads; The label knowledge is distilled and heated, as follows: Increasing the temperature means adjusting the distillation temperature. The output of the teacher model Soft tags are generated using the Softmax function based on distillation temperature: ； In the formula, Output values ​​for the teacher model based on LMC-Shapley values; This refers to the distillation temperature; Soft labels generated from the teacher model output values ​​after temperature adjustment; This represents the raw values ​​output by the teacher model. First divide by the distillation temperature Perform temperature scaling, then apply the exponential function exp( Convert the scaled value to a non-negative number.

9. The microgrid group low-frequency load reduction method based on improved Shapley value according to claim 8, characterized in that: The generated soft-label knowledge is used in the student model, and the distillation process is adjusted inversely based on the distillation loss and the student loss. The loss from knowledge distillation consists of two parts. composition: ① Distillation loss of student model and teacher soft label, i.e., probability value after distillation temperature adjustment: ； In the formula, , These represent the probability distribution of the soft labels generated by the teacher model and the predicted probability distribution of the student model, respectively. This represents the KL divergence, which measures the difference between the soft label distribution of the teacher model and the predicted distribution of the student model. ② The student loss between the student model and the true labeled student, i.e., the probability value at standard temperature: ； The total loss function is expressed as a weighted sum of the two: ； In the formula, These are the weighting coefficients; and These are distillation losses and student losses, respectively.

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