The goal of cluster division is to achieve internal balanced autonomy and minimize the power exchange between clusters. Under the framework shown in Figure 1, the comprehensive indicators for PV cluster clustering used in this paper can be classified into three categories based on their characteristics: APSM, PSS, and NCD indicators.

APSM is utilized to quantify the aggregated adjustable power capacity of the PV cluster, providing a fundamental data basis for evaluating its potential contribution to distributed peak shaving. The PSS index assesses the temporal alignment between local PV generation and load demand. A higher PSS indicates that the load profile closely follows the PV output curve, which minimizes the net load deviation and optimizes the cluster’s self-balancing capability on a time scale. NCD index evaluates the electrical coupling strength among nodes, ensuring that the formed clusters are electrically compact and structurally suitable for coordinated voltage regulation. The specific indicators are defined as follows:

As can be seen from Figure 2, by adjusting the working voltage of the photovoltaic according to the photovoltaic characteristic curve, the output power of the photovoltaic can be changed. In order to effectively control the output of photovoltaic power, it is necessary to ensure that the leading nodes within the photovoltaic cluster have sufficient regulation capacity. In this paper, the MPPT algorithm is adopted, and there are two operating regions on its left and right. Given the reference power P r e f , there are two operating points A and B corresponding to it.

If the photovoltaic system operates on the left side of the MPPT, the photovoltaic working voltage needs to be reduced to cut down the photovoltaic output power, that is: U p v , r e f = U p v , r e f − U s t e p .

If the photovoltaic system operates on the right side of the MPPT, the photovoltaic working voltage needs to be increased to reduce the photovoltaic output power, that is: U p v , r e f = U p v , r e f − U s t e p .

The specific formula for peak shaving margin is defined as Equation 1: P r e s t = P max − P p v (1) where P max represents the upper limit of the output of the photovoltaic cluster, P p v is the current target power between P max and P r e f , and P r e s t indicates the APSM of this photovoltaic cluster.

2. PSS refers to the degree of matching between the renewable energy output power of the photovoltaic cluster as a whole and the optimized energy demand within a certain time scale, which is demonstrated through the coordinated dispatching among the nodes within the cluster.

As photovoltaic power is an uncontrollable resource, the cluster needs to establish a net load optimization model. The optimization object is all nodes within the cluster. The optimization objective is to make the optimized load curve as close as possible to the PV cluster’s power generation curve in terms of time sequence, that is, to minimize the net load within the cluster, as shown in Equations 2, 3. Δ P k t = ∑ i ∈ k P l o a d , i t − ∑ i ∈ k P p v , i t (2) f φ = min ∑ t = 1 T Δ P k t (3) where Δ P t k is the net load value of the K-th cluster after optimized scheduling at time t; P t k and P r e , k t are the load value within cluster k at time t and the total power value of renewable energy; f φ is the optimization objective of the net load optimization model; T represents the scheduling period. In order to maximize the utilization of energy within the cluster during the optimal operation stage of the distribution network and reduce cross-regional power interaction, this paper takes the net load size within the cluster after optimized dispatching as the core basis for determining the matching degree of source-load-storage resources within the cluster.

Considering that both photovoltaic output and load output have the characteristic of fluctuating over time, it is necessary to select the average value of the cluster at a specific time scale to quantify the indicators. Based on this, the functional indicators of cluster division and the peak shaving coordination indicators can be expressed as Equations 4, 5: φ P , k t = P p v , k t P k t , Δ P k t > 0 1 , Δ P k t = 0 P k t P p v k t , Δ P k t < 0 (4) φ P = 1 N C ∫ 1 N C 1 T ∫ 0 T φ P , k t   d t d k (5) where φ P , k t is the degree of coordination between PV output and load in the K-th cluster at time t, and φ P , k t ∈ (0,1]. φ P is the peak regulation coordination index of the entire distribution network, N C is the number of clusters. The more the optimized net load tends to 0, the closer the optimized load curve is to the photovoltaic output curve, indicating that the better the interaction matching degree of internal load resources in the cluster is, and the larger the value will be.

3. This index is based on the modularity concept (Kumari et al., 2025), which is used to measure the structural strength of the community network. Under the given power grid topology, line parameters and reference operating point, the definition of the cluster comprehensive performance index ρ based on electrical distance and cluster comprehensive reserve degree is presented in Equation 6:

In the distribution network, the electrical distance based on which the network edge weight is determined is generally defined by the sensitivity relationship between power and voltage amplitude (Cai et al., 2020), as the changes of active and reactive power will significantly affect the voltage. The power-voltage sensitivity matrix of active and reactive power can be calculated by the power flow correction equation of Newton-Raphson method in polar coordinate form.

The Jacobian matrix is transformed to obtain the sensitivity matrix, as shown in Equation 9: Δ θ Δ V = J − 1 Δ P Δ Q = S P θ S Q θ S P V S Q V Δ P Δ Q (9) where J − 1 is the inverse of Jacobian matrix; S P θ is the active power-voltage phase Angle sensitivity matrix; S Q θ is reactive power-voltage phase Angle sensitivity matrix; S P V is the active power-voltage amplitude sensitivity matrix; S Q V is the reactive power-voltage amplitude sensitivity matrix.

The variation of voltage amplitude at any node and the variation of injected active and reactive power at all nodes are expressed as Equation 10: Δ V 1 Δ V 2 ⋮ Δ V n = S P V Δ P 1 Δ P 2 ⋮ Δ P n + S Q V Δ Q 1 Δ Q 2 ⋮ Δ Q n (10)

Thus, the electrical distances A V Q i , j and A V P i , j of nodes i and j based on re-active voltage sensitivity and active voltage sensitivity can be obtained as Equation 11: A Q V i , j = S Q V i , i − S Q V i , j − S Q V j , i + S Q V j , j A P V i , j = S P V i , i − S P V i , j − S P V j , i + S P V j , j (11) where S V Q i , i and S V P i , i are the sensitivity coefficients of injected reactive power and active power of node i to its own voltage, respectively. S V Q j , j and S V P j , j are the sensitivity coefficients of injected reactive and active power of node j to its own voltage, respectively. S V Q i , j and S V P i , j are the sensitivity coefficients of the injected reactive power and active power of node j to the voltage of node i, respectively. S V Q j , i and S V P j , i are the sensitivity coefficients of the injected reactive and active power at node i to the voltage at node j, respectively

The following can be obtained as Equation 12: A i j = 1 − A Q V i , j + A P V i , j 2 ⁡ max ⁡ A (12) where A is the electrical distance matrix composed of the electrical distance between any two nodes in the cluster.

Finally, the comprehensive cluster clustering index d = P r e s t , φ P , A i j was generated by combining the APSM index, PSS index and NCD indices.

PV cluster clustering is based on the geographical location, output characteristics, meteorological data and other multi-dimensional characteristics of PV, using clustering algorithm to extract and group its features, photovoltaic power stations with similar output patterns are divided into the same cluster, so as to achieve large-scale management and cooperative peak regulation control.

The clustering index data d = P r e s t , φ P , ρ selected above is normalized so that its mean value is 0 and its standard deviation is 1. The processed data can be expressed as Equation 13: d ′ = d − d min d max − d min (13) where d ′ is the normalized value of each clustering index data, d is the actual value of each clustering index data, d min is the minimum value of each clustering index data, and d max is the maximum value of each clustering index data.

The improved K-means clustering algorithm that optimizes the initial clustering center is simple and practical. This paper uses the clustering algorithm to divide the PV into different clusters according to the selected clustering index. Suppose that there is n distributed PV systems in the area, forming cluster Y = y 1 , y 2 , … … , y n . The optimal number of clusters is determined as K by the elbow method, where 1 < K ≤ y n :

Minimizing the squared error is expressed as Equation 14: Q pv J i , m i = ∑ i = 1 k ∑ m i ∈ J i x i − 1 J i ∑ m i ∈ J i m i 2 2 2 (14)

The conventional K-means algorithm is inherently limited by its sensitivity to initial centroid selection and outlier data points, which often leads to suboptimal clustering outcomes. In the context of peak shaving in power systems, such limitations can significantly undermine the effectiveness of cluster-based control strategies. To over-come these challenges and ensure that the clustering results are both structurally sound and functionally aligned with peak shaving requirements, this paper introduces an enhanced K-means methodology. This approach integrates three domain-specific clustering indices-namely, the APSM, PSS, and NCD-to reformulate the clustering process as a multi-objective optimization problem. The objective is to concurrently optimize several competing criteria, thereby achieving a balanced and technically viable partition of PV clusters. This formulation provides the foundation for the multi-objective optimization model, defined as Equation 15: min   f 1 = ∑ k = 1 K ∑ i , j ∈ C k A i , j max   f 2 = ∑ k = 1 K P r e s t k min   f 3 = 1 K ∑ k = 1 K φ P k − φ P ¯ 2 s . t . ∑ k = 1 K z i k = 1 , ∀ i ∈ N ∑ i ∈ N z i k ≥ 1 , ∀ k = 1 , 2 , ⋯ , K (15)

In the formulated model, the objective function f 1 aims to maximize the electrical compactness within each cluster, thereby enhancing structural coherence; f 2 seeks to maximize the total peak-shaving capacity of the system, ensuring sufficient regulation margin across clusters; and f 3 achieves balanced distribution of peak-shaving responsibility among clusters by minimizing the standard deviation of power regulation coefficients. The set of PV nodes is denoted as N, and the predetermined number of clusters is K. The model employs binary decision variables z i k to define node-cluster assignments, constrained such that each node must belong to exactly one cluster, thereby ensuring solution feasibility and practical applicability. The complete work-flow for solving this multi-objective optimization problem is illustrated in Figure 3.

Based on the enhanced K-means clustering algorithm and integrated with a comprehensive peak shaving evaluation index-comprising the APSM, PSS, and NCD indices-the optimal partitioning scheme for each cluster is determined. Finally, the load clustering results are generated and visualized. The detailed procedure is as follows:

Data Preprocessing and Similarity Matrix Construction: First, the three key characteristic indicators for each photovoltaic (PV) node in the region are computed using the selected clustering metrics, and a dynamic time warping (DTW) distance matrix is constructed.

Over the evaluation window ( T = 1 , … , T ), the mean contribution of cluster c is calculated as Equation 17: S ¯ c = 1 T ∑ t = 1 T S c t (17)

The peak-shaving synergy coefficient between clusters m and n is defined as the Pearson correlation of their contribution time series, as shown in Equation 18: γ m n = ∑ t = 1 T S m t − S ¯ m S n t − S ¯ n ∑ t = 1 T S m t − S ¯ m 2 ∑ t = 1 T S n t − S ¯ n 2 (18) where γ m n denotes the Inter-Cluster Contribution Correlation between cluster m and cluster n, which is a scalar value ranging from −1 to 1.

6. Synergy-based Node Reallocation and Local Optimization:For any cluster pair that violates the synergy constraint, critical nodes identified as having the largest positive marginal impact on synergy improvement are reallocated. After each reallocation, the synergy coefficients are recalculated, and the process returns to Step (4) to continue the iteration until all cluster pairs satisfy the threshold or a maximum iteration/reallocation limit is reached.

In summary, this section has established a comprehensive multi-objective partitioning model for distributed PV clusters, integrating three domain-specific metrics-APSM, PSS, and NCD-to guide the clustering process. By reformulating the partitioning task as a multi-objective optimization problem and employing an improved K-means algorithm, the proposed model ensures that the resulting clusters are not only electrically compact and structurally coherent but also functionally equipped for coordinated peak shaving.

Building upon this well-structured cluster foundation, the next section will present a hierarchical multi-agent reinforcement learning framework designed to leverage these clusters as autonomous decision-making agents. The goal is to enable cooperative peak shaving through decentralized control, thereby achieving system-wide optimization in both active and reactive power dispatch while maintaining voltage stability and operational efficiency.

In machine learning, an agent collects observations from its environment and employs a policy to make decisions based on these observations. Upon executing an action, the agent influences the environment, leading to a state transition. Subsequently, the agent receives a reward determined by the new environmental state, after which it initiates the next cycle of decision-making. The definitions of the agent, observation space, action space, and reward function are detailed in references (Cao et al., 2020; Cao et al., 2022).

MADDPG is a deep reinforcement learning algorithm for multi-agents in partially observable environments, which is configured with an Actor network and a Critic network for each agent. At training time, the Critic network can use the global state and the actions of all agents; However, the Actor network can only use local observation states. When executed, only the Actor network is needed and decisions are made based on local observations.

In this paper, the PV cooperative peak shaving problem is modeled as a cooperative MARL problem. Based on the clustered multi-agent environment constructed in Section 3.1, the basic components of the MADDPG algorithm are as follows. In this section, the environment state space, agent observation space, action space and reward function in MADDPG framework are formally defined, aiming to guide multiple cluster agents to coordinately control the active and reactive power output of their internal PV units according to local observation data, and finally realize the comprehensive optimization goal of global peak shaving and voltage stability in distribution network. The flowchart of the MADDPG algorithm is shown in Figure 5.

In MADDPG, The Actor network functions as a decentralized controller, mapping the local observation to a deterministic action. Following the standard notation in (Cao et al., 2020), we simplify the deep neural network representation as a parameterized policy function. For the i − t h agent, the action a i is generated as Equation 28: a t i = μ i o t i | θ i π (28) where μ i denotes the policy function parameterized by weights θ i π , and o i is the local observation vector defined in Section 3.1. The output layer employs a hyperbolic tangent (tanh) activation function to ensure the action is bounded within the feasible regulation range − 1 , 1 .

The Critic network serves as a centralized evaluator during the training phase to address the non-stationarity of the multi-agent environment. It estimates the joint action-value function by taking the global state information and joint actions as inputs. The Q-value for agent i is calculated as Equation 29: Q i = Q i o , a ; θ i Q (29) where o = o 1 , … , o N and a = a 1 , … , a N represent the set of observations and actions from all N clusters, respectively, and θ i Q represents the parameters of the Critic network. This centralized critic structure allows the agent to implicitly learn the cooperative strategies embedded in the complex power grid interactions.

Critic Network Optimization: Based on temporal difference learning, the Critic network is updated by minimizing the Bellman error, defined in Equation 30. L θ i Q   =   E o , a , r , o ′ ∼ D y i − Q i o , a | θ i Q 2 y i   =   r i + γ Q i target o ′ , a ′ | θ i Q ′ a ′   =   π 1 target o 1 ′ , … , π K target o K ′ (30)

Update the gradient parameters as per Equation 31: ∇ θ i Q L = − 2 E y i − Q i · ∇ θ i Q Q i o , a (31)

Actor Network Optimization: Based on the policy gradient theorem, the Actor network is updated in the direction of boosting Q-values, as shown in Equation 32: ∇ θ i μ J ≈ E x , a ∇ θ i μ μ i o i · ∇ a i Q i x , a 1 , … , a N | a i = μ i o i (32)

To stabilize the training, the soft update mechanism is used to synchronize the target network, as described in Equation 33: θ i Q ′ ← τ θ i Q + 1 − τ θ i Q ′ θ i π ′ ← τ θ i π + 1 − τ θ i π ′ (33) where τ ≪ 1 is the soft update coefficient.

Upon completion of the training process, the network parameters are fixed, and only the Actor components are retained for deployment. Each agent’s actuators can then make real-time decisions based on local observations. Since the augmented information is utilized exclusively by the Critic during training, agents are capable of exhibiting cooperative behavior and generating decisions that remain robust with respect to the actions of other agents, relying solely on local information. The flow of the real-time decentralized control algorithm is presented in Algorithm 1.

Algorithm 1

Multi-agent peak shaving training algorithm based on MADDPG.

1 Initialize replay buffer D , actor networks θ i π , critic networks θ i Q , and target networks θ i π ′ θ i Q ′

This section presents the specific implementation mechanism of the collaborative peak shaving strategy for PV clusters, based on the multi-agent environment and the MADDPG algorithm framework established in the previous section. By leveraging a hierarchical decision-making architecture and a real-time feedback mechanism, the strategy achieves a closed-loop control system that integrates global optimization with local execution. The detailed implementation steps of the proposed approach are illustrated in Figure 6:

Step 1: Power allocation among clusters.

At the system level, the power allocation among clusters is implicitly learned by the MADDPG algorithm in offline training and solidified into the policy of each agent. During the training process, the Critic network with global information guides each Actor to understand the impact of its own actions on the system as a whole and the potential reactions of other clusters. This enables each cluster to autonomously determine its share of power regulation when a system load disturbance is observed, based on its electrical distance from the disturbance node, its own peak shaving capacity, and the operating status of other clusters. The clusters with close electrical distance and strong adjustment ability will take the initiative to undertake more peak shaving tasks, otherwise, it will provide auxiliary support, so as to achieve global near-optimal power allocation without online communication and negotiation.

Step 2: Coordination of units within a cluster.

Inside the cluster, the refinement and execution of power commands are also made by the trained Actor network to achieve distributed autonomous decision-making. After the cluster agent determines the total power adjustment amount of its cluster according to its observation space, the action space output by its Actor network directly defines the active and reactive power adjustment instructions of each PV unit in the cluster. The network has learned in training how to decompose the total task into each unit according to the real-time operation point of each unit, proportion-ally or according to the principle of optimal efficiency, under the premise of meeting the inverter capacity constraints and hill climbing rate constraints.

Step 3: Closed-loop feedback and dynamic adjustment.

The execution results of each cluster will change the operation state of the distribution network, and these changes will be immediately reflected in the local observation of each agent at the next time. The agent then makes a new round of decisions, resulting in a continuous rolling optimization process. The dynamic adjustment mechanism based on real-time feedback makes the strategy automatically adapt to the uncertain factors such as light fluctuation and load change, and continuously track the optimal operating point of the system, thus ensuring the accuracy and robustness of the peak shaving effect.

To comprehensively evaluate the effectiveness and robustness of the proposed multi-objective partitioning and cooperative peak shaving strategy for PV clusters, simulations were conducted on the IEEE-33 node system (Gao et al., 2017). This system is a well-established benchmark in power distribution network studies, characterized by a radial topology consisting of 33 nodes and 32 branches. The IEEE-33 node system is particularly suited for this study due to its moderate number of nodes, clear structure, and flexibility in simulating various operational scenarios, including load fluctuations and high penetration of distributed PV systems.

In this study, a high penetration scenario was constructed by integrating 11 distributed PV systems into the IEEE-33 node system. The specific access points for these PV systems are detailed in Table 1, and the topological structure of the system is shown in Figure 7. The selection of these nodes was based on practical considerations, such as ensuring a diverse distribution of PV systems across the network to simulate real-world conditions effectively. The installed capacities of these PV systems range from 46.13 kW to 78.07 kW, reflecting a realistic distribution of PV installations in modern distribution networks.

The simulations were performed on a hardware platform equipped with an NVIDIA GTX 4050Ti GPU and an Intel Core i9-13900 KF CPU, ensuring sufficient computational power for the complex MARL algorithms employed in this study. The software environment consisted of the Windows 10 operating system, with all algorithms implemented using the PyTorch neural network framework and Python 3.10.0.

To simulate real-world load disturbances, a random disturbance factor was introduced into the IEEE-33 node system. The specific disturbance values for each hour of the day are detailed in Table 4. These disturbances were designed to mimic the random fluctuations in load that are commonly observed in power systems, providing a realistic testbed for evaluating the proposed peak shaving strategy.

By carefully configuring the test system and simulation environment, this study ensures that the results are both scientifically rigorous and practically relevant, providing valuable insights into the application of multi-objective partitioning and cooperative peak shaving strategies in modern distribution networks with high penetration of distributed PV systems.

Following the determination of the optimal cluster number (K = 4) via the elbow method, the improved K-means algorithm, guided by the comprehensive multi-objective optimization model, was leveraged to partition the distributed PV system. This advanced clustering approach moves beyond conventional methods by explicitly optimizing the defined metrics-APSM, PSS, and NCD-to ensure the resulting clusters are not only geographically and electrically coherent but also functionally prepared for cooperative control. The final partitioning scheme, which effectively delineates the network into four distinct clusters with balanced characteristics, is quantitatively summarized in Table 2. More intuitively, the spatial distribution of these clusters within the network topology is visually presented in Figure 8, clearly illustrating the physical grouping of nodes.

This rational partition provides a critical structural foundation for the subsequent MARL framework, effectively defining the autonomous decision-making agents for the cooperative peak-shaving task. The following analysis delves into the specific composition and inherent properties of each cluster.

The results show that the distributed PV nodes in the IEEE-33 node system are clustered into four clusters with significant physical significance by the improved K-means clustering algorithm. Finally, four types of clusters dominated by core indicators such as peak shaving capacity and response speed were formed. Finally, the system clustering diagram is obtained according to the final layer division results, as shown in Figure 9.

Based on the improved K-means clustering algorithm, combined with three core indicators of APSM, PSS, and NCD, the optimal number of clusters is determined to be 4, and the cluster division of PV nodes in IEEE-33 node system is completed. The results of PV cluster division will provide a clear control unit for MADDPG algorithm to construct a multi-agent environment, and will also provide key prior information for the Critic network to learn the interaction mode between clusters and the Actor network to generate the global optimal collaborative peak shaving strategy, thereby ensuring the effectiveness of algorithm training and peak shaving decisions.

To validate the physical significance of the partitioning results, a quantitative analysis of the three proposed metrics was conducted as shown in Figure 10. Regarding regulation capacity, a 40% safety margin was applied to the APSM to ensure robustness against PV output uncertainties. Under this condition, Cluster 2 retains the highest effective capacity of 1.12 MW, establishing it as a capacity-oriented unit for bulk peak shaving. In terms of PSS, Cluster 3 achieves the highest coefficient of 0.68, indicating a strong temporal alignment between source and load. Consequently, Cluster 3 should be prioritized for active power regulation due to its high self-balancing potential. Conversely, Cluster 4 exhibits a negative synergy of −0.04, reflecting a typical residential load pattern that is asynchronous with PV generation. Finally, regarding structural topology, Figure 10c shows that Cluster 4 possesses a significantly elevated NCD of 3.83, compared to the average of 1.6 in other clusters. This high NCD characterizes Cluster 4 as a voltage-sensitive cluster located at the feeder end-zone where electrical coupling is strong. Therefore, its control agent naturally focuses on voltage stability maintenance rather than large-scale power flow regulation.

It is important to note that the clustering stage serves primarily as a structural decomposition strategy to reduce the dimensionality of the control problem. The system’s overall robustness is fundamentally guaranteed by the MADDPG agents. Trained under stochastic environments, these agents act as an adaptive control layer capable of compensating for minor topological variations resulting from clustering parameter sensitivities. This hierarchical design ensures that the peak-shaving performance is not overly sensitive to the precise tuning of clustering weights, provided the partitions maintain basic electrical coherence.

To validate the effectiveness of the proposed cooperative peak-shaving strategy for PV clusters, the MADDPG algorithm was employed to train autonomous agents based on the clustering results obtained in Section 4.2. Within this framework, each cluster defined by the multi-objective partitioning process was modeled as an independent agent. Guided by centralized training, these agents performed decentralized decision-making to optimize both inter-cluster power allocation and intra-cluster unit coordination. Table 3 presents the hyperparameter settings of the MADDPG algorithm, which were carefully tuned to ensure robust performance. Specifically, the discount factor γ = 0.98 was selected to balance immediate and future rewards, allowing decision impacts to reasonably extend across the 24-h cycle while avoiding excessive emphasis on distant states that could hinder convergence. The hidden layer dimension ℎ = 256 was chosen to provide sufficient network capacity while preventing overfitting caused by overly large dimensions, thereby achieving a balance between representational power and training efficiency.

In order to verify the effectiveness of the distributed cooperative peak shaving control method based on multi-agent proposed in this paper and reflect the random fluctuation characteristics of load in the power system, this paper introduces a random disturbance factor into the IEEE-33 node system connection to simulate the peak shaving scene of the actual power grid, and the specific disturbance values are shown in Table 4.

Figure 11 shows the reward value of the agent during the training process, the blue curve in the upper left subfigure is the total reward of each training round, and the red curve is the average reward of the “10 rounds moving average”. It can be seen that with the increase of the number of training rounds, the total reward shows an overall upward trend, while the “10-round moving average” curve gradually flattens out at 120 training rounds, indicating that each node has learned the optimal strategy to reduce the network loss.

The top right subfigure shows the contribution of each reward component such as balance reward, regulation reward, and voltage reward in the last round of training, indicating that the agent achieved the collaborative optimization of multi-objective in the final policy. The left subgraph quantifies the actual performance of the last round strategy from the dimensions of balance deviation, total regulation, and voltage deviation, which corroborates the metric optimization logic behind the average return improvement. The right subfigure “Exploration noise attenuation curve” presents the attenuation process of exploration noise with training rounds, reflecting the strategy transition of the algorithm from “exploration oriented” to “exploitation oriented”.

Figures 12, 13 show the 24-h output of the 11 connected photovoltaics in the given example. The output of distributed PV included in the system is 0 at 0–5 and 20–24, and increases with the increase of light intensity at 5–20.

Figures 14, 15 illustrate the adjusted power output profiles for individual PV units and aggregated clusters, respectively, following the MADDPG optimization under simulated load fluctuations. As shown in Figure 14, the output of each specific PV unit is dynamically regulated based on the decision-making of its corresponding cluster agent. Furthermore, Figure 15 aggregates these responses, demonstrating how the collective adjustment of PV clusters aligns with the system’s peak-shaving requirements.

To further illustrate the collaborative behaviors of PV clusters, a typical operating day is selected from the simulation results for detailed analysis. Figure 16 shows the Controlled Power Output Ratio of each PV cluster during the peak shaving period, while Figure 17 presents the Overall Adjustment Ratio of each cluster. Together, these two figures demonstrate the coordinated decision-making mechanism and differentiated functional roles within the multi-agent system, achieved without direct communication.

Figure 16 depicts the temporal evolution of the collaboration degree among the four PV clusters over a typical operating day. During non-generation periods (01:00–05:00 and 21:00–24:00), the PV systems are inactive and do not participate in peak shaving. From 06:00 to 11:00, Cluster 3 consistently maintains the highest synergy level at approximately 0.44, followed by Clusters 2 and 1, indicating that Cluster 3 assumes the dominant regulatory role during this period. As the system transitions into the high-load period (12:00–20:00), the collaboration degrees exhibit significant fluctuations, reflecting active but unevenly distributed cooperative regulation. A notable shift occurs between 19:00 and 20:00, when Cluster 1’s synergy degree surges to 0.74 while Cluster 3’s drops sharply to 0.03, marking Cluster 1 as the primary regulator during this critical interval. Complementing the trends in Figures 16, 17 also provides the power adjustment ratios of each cluster relative to their baseline output. During the peak shaving phase, Clusters 3, 2, and 1 predominantly contribute by implementing power curtailment to maintain grid balance. In contrast, during the valley filling phase, distinct complementary behaviors emerge: Cluster 4 takes the leading role through downward regulation, while the other three clusters perform positive adjustments by increasing power injection.

The red curve in Figure 18 is the “before peak shunted” curve, showing significant fluctuation characteristics, which intuitively reflects the impact effect of load disturbance on the balance node power without PV regulation. The fluctuation of the blue curve is the “after peak adjustment” curve, which is significantly narrower, reflecting the regulation effect of the algorithm on the power balance.

The simulation results quantitatively demonstrate the performance of the pro-posed MADDPG-based control strategy in mitigating power fluctuations. The application of the strategy led to a reduction in the peak-to-valley difference from 3.3174 MW to 2.3423 MW, corresponding to an improvement of 29.39%. Concurrently, an average enhancement of 59.68% in power balance deviation was achieved. These quantitative outcomes confirm the strategy’s capability to flatten the net load curve and maintain active power balance within the distribution network, effectively alleviating the impact of load disturbances under high PV penetration.

The robustness of the proposed framework is fundamentally underpinned by the decentralized coordination mechanism established through the MARL framework. Relying on the centralized-training-decentralized-execution paradigm, MADDPG agents are trained in an environment characterized by stochastic load fluctuations and PV output uncertainties. This learning capability enables agents to develop cooperative strategies that are resilient to structural variations. Consequently, even if clustering parameters vary-leading to slight shifts in cluster boundaries-the agents can adaptively learn to adjust their policies to compensate for these changes during the training process. This mechanism allows the system to execute decisions based solely on local observations without real-time inter-cluster communication, ensuring that peak shaving performance remains robust and applicable to complex real-world scenarios regardless of precise parameter tuning.