TC-SOM Driven Cluster Partitioning Enables Hierarchical Bi-Level Peak-Shaving for Distributed PV Systems

Abstract

Given the urgent demand for flexible peak-shaving in power systems and underutilized distributed photovoltaic (PV) regulation potential, this paper proposes a distributed PV peak-shaving control strategy based on the temporal coupling self-organizing map (TC-SOM) neural network and a bi-level model. First, the SOM algorithm is improved for efficient feature extraction and accurate clustering of distributed PV data, realizing rational PV cluster division. On this basis, a bi-level peak-shaving model for distributed PV is constructed, forming a hierarchical peak-shaving mechanism from node demand to PV clusters to individual PVs to ensure inter- and intra-cluster coordination. This hierarchical structure embodies symmetric response logic, enabling balanced interaction between upper-layer node demand guidance and lower-layer PV execution, as well as inter-cluster coordination. Simulations on the IEEE-33 node system confirm its effectiveness: it significantly smooths the load curve, reduces peak–valley differences, and optimizes the flexible utilization of distributed PV through coordinated control, aggregation management, and curtailment regulation, providing strong support for precise PV cluster regulation and stable operation of high-proportion PV-integrated power grids.

1. Introduction

Global energy transition and decarbonization are accelerating, driving the power system toward high-proportion new energy integration while reshaping user-side load characteristics [1]. In economically active, densely populated regions, enhanced terminal electrification and large-scale distributed energy integration have spurred rapid electricity load growth and widened the load curve’s peak–valley difference [2,3]. For instance, a typical eastern China load center saw its summer peak–valley difference expand by 42% in 2024 versus 2015, while Australia’s grew by 45% in the 2022–2023 fiscal year amid soaring solar penetration and extreme heat [4]. This reflects the global challenge of intensified grid regulation and power symmetry pressure under high renewable energy integration.

The traditional coal-fired power-dominated peak-shaving system faces dual pressures globally. Domestically, beyond 40% new energy penetration, its inherent intermittency unbalances regulation resources [5,6]; coal-fired units have limited deep peak-shaving capacity, physical storage is geographically constrained, and demand-side response remains immature [7,8,9]. Internationally, the International Energy Agency highlights in its 2024 report that renewable energy integration in global power systems universally struggles with peak-shaving, as intermittent generation disrupts regulation resource balance even in mature markets [7]. Foreign studies, such as those on distributed cooperative control for microgrids [10] and hierarchical economic dispatch for hybrid energy systems [11], focus on multi-resource coordination but still fail to fully tap distributed PVs’ standalone peak-shaving potential—mirroring domestic gaps. This urges the power industry worldwide to develop new peak-shaving technologies. Distributed PV—characterized by decentralized access and large-scale deployment [12]—has become a key system component. Supported by international policies requiring “observable, measurable, adjustable, and controllable” technical foundations [13], its flexible spatiotemporal output and source–load coupling fill distribution network peak–valley gaps and reduce losses [14], playing a vital role in easing peak–valley pressures under high new energy integration. Thus, studying distributed PV clustered management and precise regulation—to boost the system’s flexible peak-shaving and stability—has become a core power sector research direction.

In recent years, research on distributed PV cluster division and partitioning has attracted extensive attention from academia and industry. Existing studies mainly realize cluster partitioning based on geographical information, electrical characteristics, and operational data, using partitioning algorithms, optimization algorithms, and deep learning assistance [15]. Reference [5] applied the mGA-PSO optimization algorithm combined with the electrical distance between nodes to realize the cluster division of the distribution network, providing useful ideas for the division method based on electrical characteristics but suffering from high computational complexity when processing high-dimensional data related to peak-shaving demands. Reference [16] used the K-means algorithm for multi-step grouping and equivalent modeling of distributed PV, and finally verified the rationality of cluster modeling but failed to integrate temporal coupling of PV output and peak-shaving-oriented evaluation indicators. Reference [17] applied the network optimization community partitioning algorithm based on SLM-RBF to distributed PV scenario partitioning, effectively handling the uneven data distribution and improving the accuracy of scenario partitioning but neglecting the comprehensive impact of electrical coupling and power balance capability on peak-shaving coordination. While existing optimization methods have respective strengths in specific scenarios, they face issues like inadequate consideration of peak-shaving demands or low efficiency in high-dimensional data processing, highlighting the necessity of our proposed strategy. On the other hand, distributed PV systems are characterized by high complexity and many variables, and traditional partitioning methods often face problems such as low computational efficiency and poor partitioning accuracy when processing high-dimensional data. Therefore, there is an urgent need for a high-performance method suitable for processing high-dimensional data to achieve accurate division and partitioning of distributed PV clusters.

Based on cluster partitioning research, distributed PV clusters can participate in grid peak-shaving as a unified cluster entity. However, existing studies have shown that the coordinated control methods for distributed PV clusters participating in grid peak-shaving have defects, such as low coordination efficiency and insufficient global optimization capability [18]. Current research on distributed PV cluster participation in grid peak-shaving control strategies mainly focuses on the coordinated peak-shaving strategies of distributed PV with multiple resources such as energy storage and conventional units [19]. Reference [11] proposed that energy storage-assisted grid peak-shaving has obvious advantages. In different time periods, the grid load varies greatly. Energy storage can be charged during low load and discharged during high load, thereby reducing the peak–valley difference of the grid to meet peak-shaving needs. Reference [10] established an “aggregation-peak-shaving-decomposition” model containing a high proportion of PV and energy storage. Studies have shown that the use of PV and energy storage resources can alleviate the peak-shaving pressure of the power system and achieve better economic benefits under the premise of ensuring peak-shaving capability. Reference [19] proposed a short-term hydro–wind–PV peak-shaving scheduling method based on approximate hydropower output characteristics, realizing multi-energy complementarity but relegating PV to a supporting role without exploring its intrinsic peak-shaving potential. However, the above studies mainly focus on the coordinated peak-shaving strategies of distributed PV with other equipment, lacking in-depth exploration of PVs’ flexible potential through optimized coordination and curtailment management. This results in distributed PV remaining in a supporting role in grid peak-shaving, with its cluster synergy value and flexible utilization potential yet to be fully tapped. For standalone PV peak-shaving control, Reference [18] proposed a distributed cooperative control method for microgrids based on communication networks, improving local coordination but struggling with global optimization in large-scale systems. At the same time, due to the geographical dispersion of distributed PV and the characteristics of grid end access, traditional peak-shaving control strategies face problems such as high communication delay, high solution dimensions, and limited control real-time performance [20]. In summary, existing issues focus on traditional algorithms’ inadequate handling of high-dimensional PV data, lack of peak-shaving metrics, high control complexity, and insufficient exploration of PVs’ standalone potential.

To address the above issues, this paper proposes a distributed PV cluster partitioning and flexible peak-shaving strategy based on temporal coupling SOM and bi-level model driving. The strategy aims to optimize PVs’ flexible utilization within its inherent operational constraints by improving the SOM algorithm, adopts a two-stage division structure, improves the similarity measurement method, and verifies the effectiveness of cluster division, thereby achieving efficient feature extraction and accurate partitioning of distributed PV data to realize the reasonable division of PV clusters. On this basis, a bi-level model is constructed to form a hierarchical peak-shaving mechanism from node demand to PV clusters and then to individual distributed PV. The upper model calculates the scheduling distance according to the system node load disturbance and dynamically allocates peak-shaving tasks to each cluster. The lower model controls the output of each PV unit in proportion based on the remaining output capacity of distributed PV within the cluster, ensuring effective collaboration between clusters and among distributed PV units. Finally, through case simulation and peak-shaving performance analysis of the IEEE-33 node system, the effectiveness and feasibility of the proposed method in scenarios where a high proportion of distributed PV participates in flexible peak-shaving of the power system are verified.

2. Methodology

Considering the characteristics of distributed photovoltaics such as wide distribution area, scattered locations, large quantity, and small individual capacity, directly incorporating them into the operation and control framework of the power system will lead to problems such as a significant increase in solution complexity and high dimensionality of decision variables [21]. Therefore, this paper aggregates PV resources with adjacent geographical locations and close electrical connections into cluster units through a partitioning approach, and establishes a hierarchical collaborative control architecture to realize cluster-level optimal scheduling and coordinated control of distributed PV [22]. This paper proposes a method for distributed PV cluster partitioning and flexible peak-shaving based on temporal coupling SOM and a bi-level model, whose overall framework is shown in Figure 1.

Under the above framework, the comprehensive indicators for distributed PV cluster partitioning used in this paper can be divided into three categories according to their characteristics, namely electrical coupling, power balance capability, and temporal characteristics. Electrical coupling focuses on considering the degree of electrical association between nodes within a cluster and between clusters to better evaluate the integrity and synergy of the clusters; power balance capability calculates the power balance level of each PV cluster and individual PV when participating in peak-shaving, providing a numerical basis for the next step of distributed peak-shaving; and temporal characteristics are used to measure the output variation rules and complementarity of PV clusters in different time periods, and according to the temporal characteristics of the clusters, corresponding peak-shaving tasks can be issued to each cluster.

2.1. Partition Index

The electrical coupling index is used to measure the strength of electrical association between clusters and is comprehensively evaluated using reactive power sensitivity, electrical distance, and node topological connection strength. Among them, reactive power sensitivity represents the degree of influence of load node power changes on voltage changes of other nodes, and its expression is given by Equation (1):

$$\Delta V=SQ$$

(1)

where S (kV/kW) is the sensitivity matrix, indicating the response of node voltage changes to load node power changes; electrical distance reflects the tightness of electrical connections between nodes, where $\Delta V$ is the ratio of voltage fluctuations between the node itself and related nodes when reactive power fluctuates. Detailed parameter information can be found in

Table A1. Meaning and units of each parameter.

Symbol	Definition	Unit
S	sensitivity matrix	kV/kW
E	comprehensive electrical coupling indicator
T	topological connection strength between node i and node j
$P_{PV,self} (t)$	the self-consumed output of distributed PV at time t	kW
$P_{net} (t)$	the net loads at time t	kW
$P_{load} (t)$	the system load at time t	kW
$r$	net load ramp rate	kW/h
$\lambda$	the load factor
$\rho$	output curve correlation coefficient
L	dispatch distance
d	node sensitivity coefficient
$d_j$	SOM distance set
$W_{ji }$	weight coefficient
$D$	dynamic weighted Euclidean distance
$\alpha (t)$	self-adaptive learning rate
$S_{\mathrm{dev},0}$	original deviation range	MVA
$S_{\mathrm{dev}}$	adjusted response deviation area	MVA

.

By employing the sensitivity matrix, the relationship between a node’s own voltage fluctuation and the resulting voltage fluctuations at surrounding nodes $d_{ij}$ can be obtained, from which an electrical-distance $L_{ij}$ expression is derived.

$$d_{ij}={\displaystyle \frac{S_{ij}}{S_{jj}}}$$

(2)

$$L_{ij}=\sqrt{{\left({\mathrm{d}}_{i1}-{\mathrm{d}}_{j1}\right)}^2+{\left({\mathrm{d}}_{i2}-{\mathrm{d}}_{j2}\right)}^2+\dots +{\left({\mathrm{d}}_{iN}-{\mathrm{d}}_{jN}\right)}^2}$$

(3)

Define the topological connection strength T between node i and node j as the reciprocal of the shortest path length $K_{ij}$ between the two nodes:

$$T_{ij} ={\displaystyle \frac{1}{K_{ij}}}$$

(4)

The comprehensive electrical coupling indicator E is calculated as $E=\{s,L,T\}$.

Define the net load $P_{net} (t)$ at time t as

$$P_{net} (t)=P_{load} (t)-P_{PV,self} (t)$$

(5)

where $P_{load} (t)$ is the system load at time t and $P_{PV,self} (t)$ is the self-consumed output of distributed PV at time t. Both the system load and the self-consumed output of distributed PV are in KW.

The power balance capability is measured by indicators such as the net load ramp rate and load factor. The net load ramp rate represents the rate of change of net load per unit time, reflecting the intensity of load changes, and its expression is as follows:

$$r= {\displaystyle \frac{P_{net} (t+1)-P_{net} (t)}{\Delta t}}$$

(6)

where $P_{net} (t)$ and $P_{net} (t+1)$ are the net loads at time t and t + 1 respectively, and $\Delta t$ (h) is the time interval.

The load factor refers to the ratio of the actual output of a photovoltaic cluster to its maximum possible output, reflecting the output utilization level of the photovoltaic cluster. In the calculation, it is necessary to monitor the actual power generation of the photovoltaic cluster in real time and combine it with the maximum generating power under the meteorological conditions of the day, which reflects the output utilization level of the photovoltaic cluster. Its expression is as follows:

$$\lambda ={\displaystyle \frac{P_{actual}}{P_{max}}}$$

(7)

where $P_{actual}$ is the actual output of the photovoltaic cluster and $P_{max}$ is the maximum possible output.

The comprehensive power balance capability indicator P is calculated as $P=\{r,\lambda \}$.

The output curve correlation coefficient is calculated based on the Pearson correlation coefficient, which quantifies the linear correlation between the output sequences of two PV clusters over a continuous time period. For two PV clusters with output sequences $P_1 (t)$ and $P_2 (t)$, the covariance $Cov(P1 ,P2 )$ and standard deviations ${\sigma }_1$, ${\sigma }_2$ are first calculated:

$$Cov(P1 ,P2 )={\displaystyle \frac{1}{T-1}}{\displaystyle {\sum }_{t=1}^T [P_1 (t)-\overline{P_1}][P_2 (t)-\overline{P_2} }]$$

(8)

$${\sigma }_{P1} =\sqrt{{\displaystyle \frac{1}{T-1}}{\displaystyle \sum _{t=1}^T {[P_1 (t)-\overline{P_1} ]}^2}}$$

(9)

$${\sigma }_{P2} =\sqrt{{\displaystyle \frac{1}{T-1}}{\displaystyle \sum _{t=1}^T {[P_2 (t)-\overline{P_2} ]}^2}}$$

(10)

where $P_1$ and $P_2$ are the average outputs of the two clusters, respectively.

The output curve correlation coefficient $\rho$ is shown in Equation (11) of this paper:

$$\rho = {\displaystyle \frac{Cov(P_1 ,P_2 )}{{\sigma }_{P1} {\sigma }_{P2}}}$$

(11)

Finally, the comprehensive cluster partitioning index is generated by combining the electrical coupling, power balance capability, and temporal characteristic indicators as follows:

$$x=\{E,P,\rho \}$$

(12)

2.2. Adaptive SOM Algorithm

Distributed PV cluster partitioning leverages multidimensional features and partitioning algorithms to group PV plants with similar output patterns and close electrical connections, enabling large-scale management and coordinated peak-shaving. The self-organizing map (SOM) neural network [23]—an unsupervised learning method—excels in data dimensionality reduction, feature extraction, and visualization, making it ideal for this task [24]; its core idea is mapping high-dimensional input data to a low-dimensional topological structure via competitive learning while preserving data topological relationships. The topological structure of the traditional SOM is shown in Figure 2.

The SOM algorithm takes the aforementioned comprehensive cluster partitioning indicators of distributed photovoltaics as input and obtains a distance set by calculating the Euclidean distance between each input layer data and the competitive layer neurons, specifically as shown in Equation (13):

$$d_j={\displaystyle \sum _{i=1}^n {(x_i -W_{ji })}^2}$$

(13)

where $x_i$ is the comprehensive cluster partitioning indicator data of the i-th node and $W_{ji }$ represents the connection strength between the i-th neuron in the input layer and the j-th neuron in the competitive layer, which initially takes a small value. The minimum distance is selected from the obtained distance set, and the competitive layer neuron represented by this distance is the winning neuron. The weight vectors of the winning neuron and the neurons in its neighborhood will be updated according to the rules calculated by Equation (14) [21]:

$$W_j (t+1)=W_j (t)+\eta (t)h_{cj} (t)(x_i -W_j (t))$$

(14)

where $\eta (t)$ is the learning rate, which gradually decreases with the training time t and controls the step size of weight update; $h_{cj} (t)$ is the neighborhood function, which centers on the winning neuron and gradually reduces the neighborhood range with the training time. Its role is to make the weight vectors of the winning neuron and its surrounding neurons move towards the direction of the input vector, thereby forming a topological representation of the input photovoltaic data distribution in the competitive layer. The neighborhood function $h_{cj} (t)$ usually adopts the form of a Gaussian function:

$$h_{cj}(t)=\exp \left(-{\displaystyle \frac{\Vert r_c-r_j{\Vert }^2}{2{\sigma }^2(t)}}\right)$$

(15)

where $r_c$ and $r_j$ are the positions of the winning neuron c and the neuron j in the competitive layer respectively, and $\sigma (t)$ is the neighborhood width, which also gradually decreases with the training time t.

However, traditional SOM has notable limitations in handling distributed PVs’ complex data, failing to fully address electrical coupling, power balance capability, and temporal characteristics—key aspects for our clustering task. Thus, we propose the TC-SOM model, tailored to align with our clustering needs through a two-stage division, improved similarity measurement and cluster validation. The two-stage division includes an electrical coupling layer and a power timing layer. The TC-SOM topology is illustrated in Figure 3.

Among them, the input of the first-stage rough partitioning includes reactive power sensitivity, electrical distance, and node topological connection strength. The goal of this stage is to divide nodes with close electrical connections into the same initial cluster, using a low-dimensional mapping structure. By calculating the similarity of input indicators, nodes with high similarity are mapped to adjacent neuron positions, achieving close electrical coupling within the cluster. The second-stage fine partitioning is carried out on the basis of rough partitioning, with inputs including net load climbing rate, output curve correlation coefficient, and load rate, and a high-dimensional mapping structure is adopted. Through the analysis of these indicators, the power timing complementarity within the cluster is realized, so that the photovoltaic output within the same cluster can complement each other in time, improving the overall peak-shaving capability.

In terms of similarity measurement, dynamic weighted Euclidean distance is used to calculate the similarity between input data and neuron weights. Different weights are assigned according to the importance of different indicators in partitioning, and the weight values are dynamically adjusted based on data characteristics. For the electrical coupling layer, reactive power sensitivity, electrical distance, and node topological connection strength have larger weights; for the power timing layer, net load climbing rate, output curve correlation coefficient, and load rate have larger weights. The expression for dynamic weighted Euclidean distance is

$$D=\sqrt{{\displaystyle \sum _{i=1}^{n }{w}_i {(x_i -y_i )}^2} }$$

(16)

where $w_i$ is the weight of the i-th indicator, and $x_i$ and $y_i$ are the i-th indicator values of the input data and neuron weights, respectively.

In order to illustrate the necessity of increasing the hierarchy to meet the different requirements of clustering, the learning rate adaptive formula for the specially added hierarchy and the multi-level domain function formula based on the traditional SOM are presented. In addition, to illustrate the necessity of increasing the hierarchy to meet diverse clustering requirements, this study presents the learning rate adaptive formula for the specially added hierarchy and the multi-level domain function formula improved based on traditional SOM, while it adopts inter-cluster tie-line power fluctuation rate, intra-cluster self-balancing rate, and climbing flexibility deficit as evaluation indicators to verify the effectiveness of cluster division.

Based on the original single SOM layer, a multi-level SOM architecture is constructed. Each layer functions as an independent SOM network, responsible for further abstraction and feature extraction of the data from the previous layer. The specific process is shown in Equation (17).

$$h_j^{(l)}={\displaystyle \frac{\exp \left(-\frac{\Vert h^{(l-1)}-w_j^{(l)}{\Vert }^2}{2{\sigma }^2}\right)}{{\displaystyle \sum _{k=1}^{m_l}\exp }\left(-\frac{\Vert h^{(l-1)}-w_k^{(l)}{\Vert }^2}{2{\sigma }^2}\right)}}$$

(17)

where $m_l$ represents the number of neurons in the l-th layer.

Meanwhile, in response to the problem of slow convergence speed and easy falling into local minima caused by the fixed learning rate in traditional SOM, the proposed improvement scheme in this paper introduces an adaptive learning rate mechanism, as shown in Equation (18). Through dynamically adjusting the learning rate based on the trend of quantization error changes during the training process, the aim is to optimize the training effect.

$$\alpha (t)={\alpha }_0\cdot \exp \left(-{\displaystyle \frac{t}{T_{\mathrm{decay}}}}\right)\cdot \left(1-{\displaystyle \frac{E(t)}{E_{\max }}}\right)$$

(18)

where ${\alpha }_0$ is the initial learning rate, $T_{\mathrm{decay}}$ is the decay period, $E(t)$ is the current quantization error, and $E_{\max }$ is the maximum quantization error. In the early stage of training, $E(t)$ is relatively large, and this term makes the learning rate larger, thus enabling rapid convergence; as the training progresses, $E(t)$ decreases, and the learning rate gradually becomes smaller, allowing for fine-tuning of weights to avoid getting stuck in local optima.

2.3. Overall Steps

Based on the abovementioned temporal coupling SOM algorithm, combined with three types of key parameters including electrical coupling, power balance capability, and temporal characteristics, the division scheme for each cluster is determined, and the specific process is shown in Figure 4. Through the two-stage division structure, hierarchical partitioning processing of data is realized, and the accuracy of cluster partitioning is improved. Finally, through the visualized partitioning results, the load cluster partitioning results are output, with the specific steps as follows:

Step 1: Establish a multidimensional evaluation index system based on three types of key parameters, namely, electrical coupling, power balance capability, and temporal characteristics. Eliminate dimensional differences through standardization to form a feature data input set.

Step 2: Perform the first-stage rough. Input reactive power sensitivity, electrical distance, and node topological connection strength into the low-dimensional mapping SOM network to realize the initial partitioning of nodes with close electrical connections.

Step 3: On the basis of the rough partitioning results, perform the second-stage fine partitioning. Input the net load climbing rate, output curve correlation coefficient, and load rate into the high-dimensional mapping SOM network, and calculate the similarity through dynamic weighted Euclidean distance to realize fine partitioning of power timing complementarity within the cluster.

Step 4: Verify the effectiveness of the division results using indicators such as inter-cluster tie-line power fluctuation rate, intra-cluster self-balancing rate, and climbing flexibility deficit. Generate a load cluster partitioning map in combination with visualization analysis tools, and finally output the cluster optimization scheme that meets the peak-shaving demand.

3. Bi-Level Model Architecture for Flexible Peak-Shaving of Distributed Photovoltaics

The bi-level control model achieves collaborative management of complex systems based on a hierarchical architecture. The upper layer focuses on global situation analysis and strategy formulation, while the lower layer specializes in localized command execution and real-time adjustment. The two form a dynamic closed loop through bidirectional information interaction. This structure not only retains the rapid response characteristics of distributed control but also enhances the overall coordination capability of the system through inter-layer collaborative optimization, ensuring the autonomy of each unit while effectively achieving global objectives.

3.1. Bi-Level Framework

The core technical novelty of the proposed bi-level model, distinct from conventional hierarchical control, lies in integrated innovative designs: the upper layer adopts a dispatch-distance-based dynamic task allocation mechanism, quantifying cluster-disturbance node electrical correlation via node sensitivity to realize differentiated peak-shaving assignments. The lower layer leverages intra-cluster resource complementarity and implements residual capacity proportional control, ensuring regulation aligns with individual PV operational potential—avoiding over-regulation risks rarely addressed in traditional models. The distributed photovoltaic peak-shaving bi-level control model proposed in this paper realizes coordinated control through a hierarchical response strategy. The upper-layer system dynamically allocates peak-shaving tasks according to load disturbances, while each photovoltaic cluster in the lower layer adjusts their output in a differentiated manner based on the degree of correlation with disturbance nodes. Between the upper and lower layers, cluster peak-shaving demands and the existing output of distributed photovoltaics serve as an interaction bridge, ultimately achieving distributed photovoltaic peak-shaving control, as shown in Figure 5.

The upper-level optimization model calculates the dispatch distance between the disturbance node and each distributed photovoltaic cluster based on system node load disturbances and determines the overall output adjustment amplitude of each cluster in response to load fluctuations according to the magnitude of the dispatch distance. The dispatch distance derived from node sensitivity is shown in Equation (17).

$$L_m^{to-node}=\sqrt{{\displaystyle \sum _{i\in m}{(d_i^{node}-{\overline{d}}_m)}^2}}$$

(19)

where $d_i^{node}$ is the sensitivity ratio from node i in cluster m to the disturbance node; ${\overline{d}}_m$ is the average sensitivity of all nodes in cluster m.

Clusters with a shorter dispatch distance respond more directly to load disturbances, so their output adjustment amplitude is relatively larger. In contrast, clusters with a longer dispatch distance adjust their output accordingly based on their relationship with the disturbance node to jointly achieve the peak-shaving effect. This process is coordinated and optimized through an optimization algorithm to ensure that the output adjustments of each cluster can effectively suppress load fluctuations, thereby achieving the goal of peak-shaving.

On the basis of determining the total output of each cluster, each cluster allocates and controls the output of each distributed photovoltaic unit according to the remaining output capacity of each PV unit under the maximum power point tracking state, in proportion to their remaining capacities, as specifically shown in Equation (18):

$$\Delta P_m={\displaystyle \frac{1/L_m^{to-node}}{{\displaystyle \sum _{k=1}^M(1/L_m^{to-node})}}}\times \Delta P_L$$

(20)

where $\Delta P_L$ is the power variation of the load at the disturbance node; M is the total number of photovoltaic clusters; and $\Delta P_m$ is the peak-shaving power command allocated to the m-th cluster.

This control method ensures that while meeting the overall output requirements of the cluster, the actual output capabilities of each distributed photovoltaic unit are fully considered, avoiding situations where the stability and efficiency of the entire system are affected due to over-limited output of individual PV devices. Through this output control based on the proportion of remaining capacity, the lower-level control of distributed PVs is realized, enabling each PV unit to flexibly adjust its output according to its own status and capabilities, thereby improving the peak-shaving capacity and energy utilization efficiency of the entire cluster.

3.2. Upper-Level Optimization Model

The upper-level model constructs a comprehensive objective function to optimize the performance of distributed PV in power system peak-shaving. The specific implementation process is shown in Figure 6.

The core objectives of this function are to minimize the difference between peak and valley values of the post-regulation nodal load curve, maximize the utilization efficiency of PV peak regulation capacity, and enhance the response flexibility of distributed PV clusters. By optimizing the output of distributed PVs, the amplitude of nodal load fluctuations is reduced, thereby decreasing the peak–valley difference. Meanwhile, ensuring full utilization of PV peak regulation capacity improves energy efficiency, while enhancing the response flexibility of each cluster enables quicker adaptation to load changes, thus improving the stability and flexibility of the power system in the face of load fluctuations.

$$\left\{\begin{array}{c}\min F=F_1+F_2+F_3+F_4\\ F_1=\max (P_{\mathrm{load}})-\min (P_{\mathrm{load}} )\\ F_2={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N|}{P}_{\mathrm{pv},\mathrm{adjusted},\mathrm{i}} -P_{\mathrm{pv},\mathrm{original},\mathrm{i}} \mid \\ \begin{array}{l}{F}_3=1-{\displaystyle \frac{1}{N}}{\displaystyle \sum _{c=1}^N\frac{S_{\mathrm{dev}}}{S_{\mathrm{dev},0}}}\\ F_4 ={\displaystyle \sum _{t=1}^T (C_{up} P_{up,t }+C_{down} P_{down,t} )} \end{array}\end{array}\right.$$

(21)

where $\max (P_{\mathrm{load}})$ and $\min (P_{\mathrm{load}} )$, respectively, represent the maximum and minimum values of nodal load fluctuations; $F_1$ denotes the peak–valley difference; $P_{\mathrm{pv},\mathrm{adjusted},i}$ represents the photovoltaic output of the i-th cluster without peak-shaving; $P_{\mathrm{pv},\mathrm{original},\mathrm{i}}$ is the photovoltaic output of the i-th cluster after peak-shaving optimization; $F_2$ indicates the remaining value of photovoltaic peak-shaving capacity; $C_{up}$ and $C_{down}$ are the costs of increasing and decreasing photovoltaic output, respectively; $P_{up,t }$ and $P_{down,t}$ are the output increased or decreased at time t; and $F_4$ is the cost of photovoltaic peak-shaving.

Equation $F_3$ quantifies the flexible response capability of a cluster. A larger cumulative deviation area indicates better response performance, whereas a smaller cumulative deviation area indicates poorer response performance. The expression is given below:

$$S_{\mathrm{dev}}={\displaystyle {\int }_0^T(P_L(t)-P_G(t))dt}$$

(22)

$$S_{\mathrm{dev},0}={\displaystyle {\int }_0^T(P_{L0}(}t)-P_{G0}(t))dt$$

(23)

where T is the simulation period; $P_L(t)$ is the cluster’s net load at time t; $P_G(t)$ is the cluster’s actual power output at time t; $S_{\mathrm{dev}}$ is the adjusted response deviation area, representing the cumulative magnitude of the difference between the cluster’s output and its net load over the interval [0, T]; $P_{L0}(t)$ is the cluster’s initial net load; $P_{G0}(t)$ is the aggregate active-power output of all generators inside the cluster when no regulation is ap-plied; and $S_{\mathrm{dev},0}$ is the baseline response deviation area obtained in the absence of any regulation.

3.3. Lower-Level Control Model

The lower-level control focuses on the output adjustment of each distributed photovoltaic unit itself, and in actual operation, it is necessary to consider many operational constraints of the overall system. Since the power generation capacity of PV units is significantly affected by environmental factors such as illumination intensity and temperature, there exist minimum and maximum output values. Therefore, the actual output of distributed PVs must be restricted within their own adjustable range. The specific implementation process is shown in Figure 7.

Meanwhile, to avoid sharp fluctuations in the output of PV units that may impact the power grid, their ramp capability constraints also need to be considered. Specifically, the output variation amplitude of PV units at adjacent time instants must not exceed their maximum ramp rate, ensuring a smooth transition of PV output.

The output constraints of PV units are as shown in the following equation:

$$\left\{\begin{array}{l}-P_{\mathrm{down},t,\max }^m\le P_{\mathrm{PV},t,\max }^m-P_{\mathrm{PV}0,t}^m\le P_{\mathrm{up},t,\max }^m\hfill \\ |P_{\mathrm{PV},t+1}^m-P_{\mathrm{PV},t}^m|\le {\displaystyle \sum _{i\in m}\Delta }{P}_{\mathrm{PV}}^{\max ,i}\hfill \end{array}\right.$$

(24)

where $m=1,2\dots N$, and $P_{\mathrm{down},t,\max }^m$ and $P_{\mathrm{up},t,\max }^m$ are the maximum values of the reliable upward and downward regulation capacities of each photovoltaic cluster m, respectively.

The entire distribution network must satisfy real-time power balance at all times during operation. That is, the total load borne by the system equals the sum of the total output of all distributed photovoltaic clusters and the output of thermal power units. This avoids problems such as insufficient power supply caused by power shortages and energy waste caused by power surpluses, and it maintains the stable operation of the power system. The overall energy balance constraint of the system is as follows:

$$P_{\mathrm{LOAD},t}=P_{\mathrm{G},t}+\sum _{m=1}^K{P}_{\mathrm{PV},t}^m$$

(25)

where $P_{\mathrm{LOAD},t}$, $P_{\mathrm{G},t}$, and $P_{\mathrm{PV},t}^m$, respectively, represent the load, the output of thermal power units, and the total output of photovoltaic clusters.

Power grid security constraints include voltage constraints and line power constraints. Voltage constraints require that the voltage at each node must be maintained within the allowable range. Line power constraints, on the other hand, specify that the transmission power of each line must not exceed its capacity limit. Each line has a designed maximum transmission capacity to maintain the safe operation of the power grid. The system security constraints are as follows:

$$V_{\min }\le V_i\le V_{\max }$$

(26)

$$\left|P_{ij}\right|\le P_{ij}^{\max }$$

(27)

where $V_i$ and $P_{ij}$, respectively, denote the voltage at node i and the power flow from node i to node j.

Lower-level control, through the aforementioned multidimensional constraints, maximizes the tapping of PV peak-shaving potential on the premise of ensuring stable grid voltage and controllable line power. It has formed a collaborative control mechanism from individual equipment to the global system, providing underlying technical support for the engineering implementation of the bi-level model.

3.4. Implementation of the Coordinated Peak-Shaving Strategy

The coordinated peak-shaving strategy materializes the model’s technical innovations through hierarchical task decomposition and real-time bidirectional feedback: upper-layer task allocation relies on dispatch distance to ensure targeting, while lower-layer regulation is based on residual capacity proportional control. The feedback loop updates cluster dispatch distances and peak-shaving capabilities in real time, addressing the static limitation of traditional bi-level models and achieving precise matching between load disturbances and PV regulation capabilities. The specific process is shown in Figure 8.

Step 1: When the system detects a load disturbance, the upper-level model first calculates the dispatch distance between each photovoltaic cluster and the disturbance node. Based on the inverse proportion of dispatch distances, the upper-level model allocates the total peak-shaving demand of the system to each cluster. Clusters with shorter dispatch distances undertake the main peak-shaving tasks, while those with longer distances provide auxiliary support, achieving differentiation and efficiency in task allocation.

Step 2: After receiving peak-shaving commands, each cluster performs secondary allocation according to the remaining peak-shaving capacity of internal photovoltaic units. Photovoltaic units with larger remaining capacities undertake greater output adjustment amounts. This allocation method ensures that photovoltaic units respond to peak-shaving demands within their adjustable range, avoiding overload.

Step 3: The lower level feeds real-time output data back to the upper-level model, which updates the dispatch distances of each cluster and the evaluation of their peak-shaving capabilities based on the feedback information. Through the closed-loop mechanism of bi-level coordination, it adapts to the temporal and spatial output variation characteristics of distributed photovoltaics, continuously improving the accuracy and robustness of the peak-shaving strategy.

4. Case Study

4.1. Case System

To verify the feasibility and effectiveness of the proposed distributed photovoltaic cluster partitioning and coordinated peak-shaving strategy in this paper, the IEEE-33 node system is selected for simulation analysis. This system has a radial topology, consisting of 33 nodes and 32 branches [25]. It features realistic radial topology, moderate scale balancing complexity and feasibility, and mature parameters enabling effective comparison with existing research. By constructing scenarios with high penetration of distributed photovoltaics in this system, the adaptability and reliability of the proposed method under different load disturbance conditions can be comprehensively evaluated. Its specific topology is shown in Figure 9.

In the IEEE-33 node system, 11 nodes are selected as access points for distributed photovoltaics. By adding distributed photovoltaics at these nodes, a case scenario with high-penetration distributed photovoltaic integration is constructed to analyze and study the system performance under this condition. The specific access points are shown in

Table 1. Node numbers for PV integrations.

PV	Nodes	PV	Nodes
PV1	2	PV7	23
PV2	5	PV8	24
PV3	10	PV9	26
PV4	13	PV10	27
PV5	16	PV11	31
PV6	19

.

Under standard test conditions of 25 °C, 1000 W/m² irradiance, and AM1.5 solar spectrum, the grid-connected photovoltaic systems in this study have a rated capacity of 50 kW per unit, with a total installed capacity of 7.5 MW for the 11 integrated PV units. They operate at a rated frequency of 50 Hz, feature a continuously adjustable power factor between 0.95 leading and 0.95 lagging, and maintain a voltage deviation of ±5% during stable operation. As shown in Figure 10, the 24 h output of these 11 PV units presents distinct temporal characteristics: output is zero from 0 to 5 h and from 20 to 24 h, while from 5 to 20 h, the output gradually increases with rising light intensity, aligning with typical photovoltaic power generation laws.

In terms of data collection, it is simulated and set that the sampling frequency of distributed photovoltaic output and related environmental data at each node is once per hour to ensure the timeliness and accuracy of the data and provide a reliable basis for subsequent cluster partitioning. The simulation platform is built in the Python 3.9 environment, making full use of its abundant library resources. Meanwhile, combined with the Matplotlib 3.8.4 library, data visualization display is performed on the partitioning results of distributed photovoltaic clusters to more intuitively present the performance and partitioning effect of the algorithm.

4.2. Partitioning of Distributed PV Clusters

After the integration of high-proportion distributed photovoltaics, the improved SOM algorithm is adopted to conduct cluster partitioning on the parameters of this 33-node model. Based on the scheduling distance index, peak-shaving capacity index, and response sensitivity index mentioned above, cluster analysis and cluster division are performed on the data of each node in the system. After learning and screening through the multi-layer SOM neural network, the final two-layer division results obtained are shown in Figure 11.

Results show that the first-layer grid first achieves coarse partitioning based on geographical proximity via the Euclidean distance, and then determines the general affiliation of each node by integrating electrical coupling relationships. The second-layer grid strengthens the electrical coupling correlation using an adaptive learning rate and a Gaussian neighborhood function, and it accomplishes the final partitioning of the clusters by combining power temporal features. The final partitioning index ranges are shown in

Table 2. Cluster comprehensive clustering interval.

Cluster Label	Minimum Indicator Value	Indicator Maximum Value	Indicator Range
1	−0.2156	1.1725	[−0.2156, 1.1725]
2	−1.4748	−0.2194	[−1.4748, −0.2194]
3	−2.5261	−1.3471	[−2.5261, −1.3471]
4	1.0386	2.4115	[1.0386, 2.4115]

.

To verify the partitioning performance of the TC-SOM algorithm, this study, in conjunction with the research context, selects three metrics—inter-cluster tie-line power volatility, intra-cluster self-balancing rate, and ramping flexibility deficit—for comparative analysis against the K-means algorithm. Specifically, a lower inter-cluster tie-line power volatility indicates more stable power exchange between clustered regions; a higher intra-cluster self-balancing rate signifies a better match between power supply and load within a region; and a lower ramping flexibility deficit reflects a more abundant reserve of flexible resources inside a region. The specific data comparisons are shown in Figure 12 and

Table 3. Cluster results and nodes of each cluster.

Clusters	Nodes
1	1, 18, 19, 20, 21
2	2, 3, 4, 22, 23, 24
3	5, 6, 7, 25, 26, 27, 28, 29, 30, 31, 32
4	8, 9, 10, 11, 12, 13, 14, 15, 16, 17

.

From the validation result comparison chart, the two-stage TC-SOM partitioning exhibits notable advantages across core metrics, rooted in its alignment with physical mechanisms: its first-stage electrical coupling layer groups nodes with close electrical connections, reducing inter-cluster transmission impedance and thus lowering tie-line power volatility to 38.17–15.8% lower than traditional SOM, results that are also slightly superior to K-mean. The second-stage power timing layer enhances intra-cluster output complementarity, as PV units with staggered peak outputs offset each other’s shortages, boosting the self-balancing rate to 0.8 by minimizing reliance on external grid support. Complementing these gains, TC-SOM demonstrates superior computational efficiency with a convergence time of 25.49 s for 11 PV nodes and stable scalability across different data sizes, while its parameter sensitivity analysis confirms the optimal initial learning rate that balances performance and convergence stability. Collectively, these results validate the technical rationality of TC-SOM’s two-stage design, bridging the gap between clustering accuracy, operational efficiency, and grid regulation requirements.

This paper focuses on distributed photovoltaic cluster partitioning and builds a multi-layer neural network architecture based on the adaptive SOM algorithm. By adopting an adaptive learning rate and integrating three types of indicators—scheduling distance, peak-shaving capacity, and response flexibility—it achieves efficient feature extraction and accurate classification of distributed photovoltaic data. The partitioning results are shown in Figure 13 and Table 3.

Through layer-by-layer optimization processing of the two-layer SOM network, 11 photovoltaic access points in the IEEE-33 node system are divided into four clusters with clear physical meanings. This partitioning scheme lays the foundation for the subsequent construction of a “node demand–photovoltaic cluster–single photovoltaic” bi-level peak-shaving control model. It reduces the system’s regulation dimension through clustered management, expands the channels for dynamic task logical allocation, and prepares data and architecture for the realization of hierarchical collaborative control of flexible peak-shaving for distributed photovoltaics.

4.3. Flexible Peak-Shaving of Distributed Photovoltaics

After completing the partitioning of distributed photovoltaic clusters, to verify the feasibility of the proposed collaborative peak-shaving strategy for distributed photovoltaics in this paper, load disturbances are introduced into the IEEE-33 node model. These disturbances consist of one value per hour over 24 h, which fully simulates the peak-shaving scenarios when the system experiences load disturbances. The specific disturbance values are shown in

Table 4. Twenty-four-hour values of load disturbances.

Time	Load (p.u.)	Time	Load (p.u.)
1	0.6	13	0.9
2	0.58	14	0.85
3	0.55	15	0.85
4	0.54	16	0.85
5	0.55	17	0.87
6	0.59	18	0.93
7	0.68	19	0.93
8	0.88	20	0.92
9	0.92	21	0.85
10	0.94	22	0.84
11	0.93	23	0.8
12	0.92	24	0.7

.

We introduce the abovementioned disturbances into the system, calculate the scheduling distance from each cluster to the disturbance node by virtue of the aforementioned scheduling distance index, and then allocate the peak-shaving demand for each cluster according to the calculated scheduling distance. The calculation results of the scheduling distance for each cluster are shown in

Table 5. Scheduling distance from each cluster to disturbance node.

Clusters	Central Nodes	Scheduling Distance
1	19	0.426
2	23	0.311
3	29	0
4	10	0.552

.

As shown in Table 3, Cluster 3 has a scheduling distance of 0, which, per Equation (17), indicates it is the direct load disturbance node—its nodes exhibit the highest sensitivity to local load fluctuations. To directly mitigate the load imbalance at the disturbance node and avoid aggravating power supply–demand deviation, the photovoltaics within Cluster 3 operate at full output at all times. In contrast, Clusters 1, 2, and 4 adjust their output according to the peak-shaving demand based on their respective scheduling distances to the disturbance node. The relevant photovoltaic output within the cluster is shown in Figure 14.

Since the disturbance occurs in Cluster 3, the photovoltaics within this cluster operate at full output at all times, while Clusters 1, 2, and 4 adjust their output according to the peak-shaving demand between 8:00 and 17:00. During peak load periods, the output of distributed photovoltaic clusters is effectively increased, which successfully boosts power supply and reduces the peak-shaving pressure on the power grid. Compared with the period before peak-shaving, the peak–valley difference of the power grid is significantly reduced, the maximum load is effectively cut down, and the minimum load has increased. When the load disturbance decreases, the required photovoltaic output is correspondingly reduced, and the output of the corresponding photovoltaic clusters decreases accordingly. The specific peak-shaving curve is shown in Figure 15. The hourly load variations are shown in

Table 6. Twenty-four-hour peak load data.

Time	Load (p.u.)	Time	Load (p.u.)
1	0.6	13	0.795
2	0.58	14	0.76
3	0.55	15	0.76
4	0.54	16	0.77
5	0.55	17	0.82
6	0.58	18	0.89
7	0.64	19	0.91
8	0.83	20	0.92
9	0.84	21	0.85
10	0.83	22	0.84
11	0.825	23	0.8
12	0.77	24	0.7

.

As illustrated above, photovoltaic output is intrinsically governed by solar irradiance, resulting in a daily power profile marked by pronounced peaks and troughs: steep ramps on clear-sky days, abrupt fluctuations under scattered clouds, and a complete collapse to zero at night. Pooling data across the entire 24 h span would inject lengthy pre-sunrise and post-sunset zero-output segments—along with their low-irradiance “tails”—as a large share of invalid points. These artifacts dilute the prominence of peak-to-valley variations, inflate the mean, and suppress the variance, thereby obscuring the true variability. Accordingly, after filtering out such low-irradiance disturbances, only the effective generation window is retained for subsequent analysis to ensure both credibility and comparability of the results. To exclude the low-irradiance disturbances noted above, the analysis confines itself to the 05:00–18:00 window of reliable insolation, and the resulting peak-shaving curve is presented in Figure 16.

The figure above systematically presents the changes in four key load-balancing metrics before and after the implementation of the peak-shaving strategy. First, the load imbalance index drops sharply from its original value of 0.3443 to 0.1280, a 21.64% improvement, demonstrating that the optimization is highly effective in peak clipping and valley filling, directly reducing the supply–demand deviation. Second, the peak–valley difference is compressed from 0.8893 to 0.6, an 11.72% reduction, confirming that restricting the analysis to the high-irradiance window successfully mitigates intra-day power swings. Third, the standard deviation falls from 0.0975 to nearly 0, a 14.36% decrease, indicating a markedly narrower dispersion of the power sequence and a smoother operational profile. Finally, load stability also improves by 2.55%, further lowering the risk of frequency disturbances. Overall, the optimized peak-shaving strategy not only enhances all balancing indicators across the board but also provides a solid basis for the stable operation of power systems with high photovoltaic penetration. The specific reduction of the peak–valley difference is shown in Figure 17.

Meanwhile, to verify the differences between the traditional unclustered load-shift peak-shaving method [26] and the bi-level model proposed in this paper, a comparative analysis was conducted. The traditional method directly adjusts individual PV output based on global load-shift demand without cluster partitioning or considering electrical correlation between PV units and disturbance node, uniformly allocating peak-shaving tasks to offset load fluctuations. The comparative results are shown in Figure 18.

To clearly demonstrate the advantages of the clustering-based control method, we conducted a comparative experiment between the proposed clustering-based control method and the standalone photovoltaic control method. The standalone photovoltaic control, without performing clustering, directly assigns the peak-shaving tasks to each photovoltaic unit based on the load disturbance. The optimization objective and constraints adopted by this method are the same as those of the proposed method. By comparing in 33-node and 123-node scenarios, we analyzed the differences in load power fluctuation coefficient, unit optimization time regulation accuracy, and total computing time. The specific results are shown in

Table 7. Indicators related to cluster control and single control among the 33 nodes.

Indicator Name	Cluster Regulation	Individual Regulation
Load Power Fluctuation Coefficient	0.8345	0.8432
Optimization of Unit Time Control Accuracy	0.0006	0.0005
Total Calculation Time	25.0853 s	28.2204 s

and

Table 8. Indicators related to cluster control and single control among the 123 nodes.

Indicator Name	Cluster Regulation	Individual Regulation
Load Power Fluctuation Coefficient	0.951251	0.958149
Optimization of Unit Time Control Accuracy	0.0232	0.0041
Total Calculation Time	59.3888 s	333.6868 s

.

As shown in Table 4 and Table 5, when the system size is small, there is little difference between the two. However, when it comes to multi-node system operations, compared with the individual photovoltaic control, the cluster-based control reduces the average computing time per control cycle by 80%. Moreover, under power fluctuation conditions, the two systems do not differ much. This confirms that the cluster control can effectively reduce the peak regulation computing time of the system while also ensuring high peak regulation accuracy. It proves the necessity and superiority of its performance in balancing efficiency and regulation capability.

In summary, the proposed model outperforms traditional unclustered methods due to intrinsic physical and operational alignments: first, TC-SOM’s two-stage division enhances intra-cluster electrical coupling and temporal complementarity, reducing inter-cluster power exchange losses and improving self-balance—this explains the 21% peak–valley difference reduction. Second, the bi-level model’s dispatch-distance-based task allocation targets load disturbances directly, minimizing unnecessary PV output adjustments and reducing grid fluctuation risks. Third, cluster-level residual capacity proportional control aligns with PVs’ actual adjustable potential, avoiding over-regulation and maintaining stable operation during large-scale data processing.

5. Conclusions

This paper proposes a distributed photovoltaic cluster partitioning and flexible peak-shaving strategy based on an improved adaptive SOM algorithm and a bi-level model, which significantly enhances the feature extraction and partitioning accuracy of distributed PV data. It effectively coordinates the output of distributed PVs both between clusters and within clusters, achieving hierarchical peak-shaving control from node demand to individual PVs. The simulation results on the IEEE-33 node system strongly demonstrate the significant effects of this strategy in smoothing the load curve, reducing the peak–valley difference, and optimizing PVs’ flexible potential through coordinated control and curtailment management, verifying the effectiveness and feasibility of the method.

(1)

The improved SOM model achieves significant optimization of the network structure by incorporating a multi-layer neuron structure and an adaptive learning rate adjustment strategy into the neuron learning rule, thereby greatly enhancing the model’s partitioning ability. The quantization error converges to below 0.003, effectively capturing the complex characteristics of PV output fluctuations, such as solving the problem of inaccurate division by traditional partitioning methods, and realizing the precise division of PV clusters into clusters with clear physical meanings.

(2)

Compared with traditional peak-shaving methods, the two-layer optimization model proposed in this paper shows significant technical advantages and engineering applicability in peak-shaving control. In the case example, compared with the traditional unclustered load-shift peak-shaving method, the load peak–valley difference is reduced by 0.074 MW with a reduction rate of 21%, fully demonstrating the proposed model’s superior peak-shaving performance. Under the high-proportion access scenario with a PV penetration rate of 33%, the peak-shaving efficiency is 12% higher than that of traditional methods, which significantly smooths the load curve and fully exploits the peak-shaving potential of distributed PVs.

(3)

This strategy offers a scalable technical roadmap for large-scale distributed PV integration, with long-term engineering value in supporting the stable operation of high-proportion renewable energy power grids; future work will focus on extending the framework to multi-energy coupling scenarios and optimizing partitioning adaptability under extreme weather conditions.