Deep learning-based trustworthy dispatch model for virtual power plants in megacity power grids

1 Introduction

The sustainable development of megacities faces unprecedented challenges from the dual pressures of rapid urbanization and climate change mitigation. According to the International Energy Agency, urban areas account for approximately 75 percent of global energy consumption and 80 percent of greenhouse gas emissions, with the transportation and building sectors being the primary contributors [1]. China’s dual carbon goals, namely, carbon peak by 2030 and carbon neutrality by 2060, have further accelerated the transformation of urban energy systems toward higher renewable energy penetration. However, the integration of large-scale distributed renewable energy sources, such as rooftop photovoltaics and small-scale wind turbines, into megacity power grids has introduced significant operational uncertainties. The inherent intermittency and volatility of these sources, coupled with the spatiotemporal heterogeneity of urban load patterns, have exposed the limitations of traditional centralized dispatch paradigms.

Virtual power plants have emerged as a transformative solution for aggregating distributed energy resources to participate in wholesale electricity markets and provide ancillary services [2]. By integrating renewable generation, energy storage systems, flexible loads, and electric vehicle charging infrastructure, virtual power plants can operate as a single controllable entity, offering flexibility and reliability to grid operators. Nevertheless, the practical deployment of virtual power plants in megacity environments faces three fundamental challenges that have not been adequately addressed by existing research.

The first challenge concerns data scarcity. The operation data for renewable energy sources in newly constructed virtual power plants are often scarce or incomplete, severely impairing the training of data-driven dispatch models. While deep learning methods have demonstrated remarkable success in time-series forecasting and decision-making, their performance critically depends on the availability of high-quality, sufficiently diverse training data. The problem of data scarcity is particularly acute for distributed photovoltaic systems, where site-specific characteristics, shading conditions, and equipment degradation patterns vary significantly across locations. Transfer learning and data augmentation techniques have been explored to mitigate this issue, but existing approaches often fail to preserve the physical constraints and temporal dependencies inherent in power system operations.

The second challenge concerns trust deficits. The credibility of aggregated resources within virtual power plants remains a critical concern for grid operators and market participants. Unlike traditional power plants where generation capacity can be reliably measured and verified, virtual power plants rely on the voluntary participation of heterogeneous distributed energy resource owners whose actual availability and response capability may deviate from committed schedules. This trust deficit has been identified as a major barrier to the widespread adoption of virtual power plants, particularly in competitive electricity markets where financial settlements depend on accurate performance assessment. Existing trust evaluation frameworks for virtual power plants have largely focused on reputation-based mechanisms that lack formal verification guarantees and are vulnerable to manipulation.

The third challenge concerns operational uncertainty. The dual uncertainties arising from both renewable generation and load demand create a challenging environment for optimal dispatch decisions. Traditional stochastic optimization methods assume known probability distributions for uncertain parameters, an assumption that rarely holds in practice due to limited historical data and non-stationary conditions. Robust optimization, while avoiding distributional assumptions, tends to produce overly conservative solutions that sacrifice economic efficiency. Distributionally robust optimization offers a promising middle ground by optimizing against the worst-case distribution within an ambiguity set constructed from historical data. However, existing distributionally robust optimization models for virtual power plant dispatch either rely on moment-based ambiguity sets that lose information about temporal correlations or employ scenario-based approximations that become computationally intractable for large-scale urban networks.

Recent advances in deep learning and artificial intelligence have opened new possibilities for addressing these challenges. Generative adversarial networks have demonstrated exceptional capability in synthesizing realistic time-series data that preserve statistical properties and temporal dependencies [3]. In the power systems domain, generative adversarial network based approaches have been successfully applied to load profile generation and renewable scenario simulation. However, purely data-driven generation methods may produce physically infeasible samples that violate fundamental power balance constraints. The integration of physical model constraints into data generation frameworks remains an under-explored research direction.

The emergence of blockchain technology has introduced new paradigms for establishing trust in decentralized energy systems. By providing an immutable, transparent, and tamper-proof ledger of transactions, blockchain enables the verification of distributed energy resource performance without relying on centralized intermediaries. Several studies have investigated blockchain-based energy trading platforms for peer-to-peer electricity markets [4]. Nevertheless, the high latency and computational overhead of consensus mechanisms pose significant challenges for real-time dispatch applications. The integration of lightweight trust evaluation mechanisms that leverage both on-chain and off-chain data has yet to be fully investigated for virtual power plant applications.

The core novelty of the proposed framework lies not in the isolated application of established techniques such as generative adversarial networks, blockchain, Wasserstein-based distributionally robust optimization, multi-agent deep reinforcement learning, or model predictive control [5], but in their principled and synergistic integration to simultaneously address the three fundamental and interdependent bottlenecks that have long constrained the practical deployment of trustworthy virtual power plant dispatch in megacity grids, namely, data scarcity, lack of trust mechanisms, and operational uncertainty [6]. Unlike existing studies that treat data augmentation, it embeds a physical constraint layer within the generative adversarial network to ensure the operational feasibility of synthesized samples; it integrates a blockchain-anchored multi-dimensional trust scoring mechanism with a smart contract-based penalty-reward system to achieve verifiable and economically incentivized reliability quantification; and it employs a Wasserstein distance-driven distributionally robust optimization that learns the ambiguity set directly from augmented historical data, thereby capturing the spatiotemporal correlations between renewable generation and load demand while avoiding the over-conservatism of conventional robust optimization and the reliance on exact probability distributions inherent in stochastic programming. Another distinctive feature of this closed-loop architecture is the hierarchical coordination between day-ahead distributionally robust optimization and real-time model predictive control, wherein trust scores dynamically adjust the operational bounds of each distributed energy resource, thus establishing a positive feedback cycle in which trustworthy participants are granted greater operational flexibility. Furthermore, the complete two-stage algorithmic flow comprising offline training and online scheduling organically unifies data preparation, trust evaluation, distributionally robust optimization, multi-agent coordination, and real-time correction, achieving a full closed loop from instruction generation to execution feedback. In summary, the proposed model provides a holistic solution that simultaneously achieves economic efficiency, robustness, and verifiable trustworthiness, fundamentally distinguishing it from existing virtual power plant dispatch methods that address only one or a subset of these challenges and lack both physical feasibility guarantees and transparent trust mechanisms.

2 Problem formulation and mathematical preliminaries

The operation of a virtual power plant in a megacity power grid involves coordinating a heterogeneous set of distributed energy resources to satisfy load demands while maximizing economic returns and maintaining grid reliability. Consider a virtual power plant consisting of N distributed energy resources indexed by i ∈ N = 1 , 2 , … , N, which may include photovoltaic systems, wind turbines, energy storage systems, and flexible loads [7]. The virtual power plant operates over a dispatch horizon of T time intervals, typically with a resolution of 15 min or 1 h, indexed by t ∈ T = 1 , 2 , … , T.

2.1 Virtual power plant composition and dynamic models

For each distributed energy resource i, let P i , t g denote its actual power generation or consumption at time t, with positive values indicating generation and negative values indicating consumption. The committed power schedule submitted to the grid operator is denoted as P i , t c. The deviation between committed and actual performance is defined as Δ P i , t = P i , t g − P i , t c, which determines the financial penalty or reward for each participant.

Photovoltaic generation at location i is modeled as a function of solar irradiance G i , t and temperature T i , t, following the standard single-diode model:As is shown in Equation 1, where η i is the conversion efficiency, A i is the panel area, β i is the temperature coefficient, and T r e f is the reference temperature [8]. The actual solar irradiance at the panel surface is influenced by cloud cover, shading, and panel orientation, making accurate day-ahead prediction challenging.

P i , t P V = η i · A i · G i , t · 1 − β i T i , t − T r e f (1)

Wind turbine generation is described by the power curve model:As is shown in Equation 2, where v i , t is the wind speed at hub height, v c i, v r, and v c o are the cut-in, rated, and cut-out wind speeds respectively, and P r a t e d is the rated power.

P i , t W T = 0 , v i , t < v c i P r a t e d · v i , t 3 − v c i 3 v r 3 − v c i 3 , v c i ≤ v i , t < v r P r a t e d , v r ≤ v i , t ≤ v c o 0 , v i , t > v c o (2)

Energy storage systems are characterized by state-of-charge dynamics:As is shown in Equation 3, where P i , t c h and P i , t d i s are charging and discharging powers, η i c and η i d are charging and discharging efficiencies, and E i is the storage capacity [9]. The state-of-charge must remain within operational limits:

S o C i , t = S o C i , t − 1 + η i c · P i , t c h E i − P i , t d i s η i d E i (3)

S o C i min ≤ S o C i , t ≤ S o C i max (4)

As is shown in Equation 4, flexible loads, including electric vehicle charging stations and smart buildings, are characterized by shiftable and curtailable demand profiles. Let D i , t b a s e denote the baseline demand and D i , t s h i f t denote the amount shifted to time t. The net demand after flexibility deployment is:As is shown in Equation 5, where D i , t i n represents demand shifted into time t from other intervals. The shifting constraints require that total shifted energy is conserved over the horizon.

D i , t n e t = D i , t b a s e − D i , t s h i f t + D i , t i n (5)

2.2 Trustworthiness evaluation model

The trustworthiness of each distributed energy resource is quantified by a trust score τ i , t ∈ 0 , 1 that reflects the expected reliability of the participant’s future performance [5]. The trust score is updated based on historical performance using a forgetting factor that prioritizes recent observations:As is shown in Equation 6, where λ ∈ 0 , 1 controls the memory decay rate, and ψ i , t is the instantaneous performance score at time t. The instantaneous score aggregates three dimensions of performance:

τ i , t = λ · τ i , t − 1 + 1 − λ · ψ i , t (6)

ψ i , t = w 1 · ϕ i , t a c c + w 2 · ϕ i , t r e l + w 3 · ϕ i , t e c o (7)

In Equation 7, the accuracy dimension ϕ i , t a c c measures the deviation between committed and actual generation:

ϕ i , t a c c = exp ⁡ − ∣ Δ P i , t ∣ ϵ i (8)

In Equation 8, the reliability dimension ϕ i , t r e l captures the consistency of performance over a sliding window of length W:

ϕ i , t r e l = 1 W ∑ k = t − W + 1 t 1 ∣ Δ P i , k ∣ ≤ δ i (9)

In Equation 9, the economic dimension ϕ i , t e c o reflects the participant’s contribution to virtual power plant profitability, normalized by the maximum possible contribution [10].

All transaction records and trust score updates are recorded on a permissioned blockchain to ensure transparency and non-repudiation. The consensus mechanism employs a practical Byzantine fault tolerance protocol suitable for energy applications, achieving confirmation latencies under 1 s.

2.3 Distributionally robust dispatch formulation

The virtual power plant operator’s objective is to minimize the expected operating cost while ensuring reliable load satisfaction. Let ξ t denote the uncertain parameters at time t, including renewable generation and load demand [11]. The ambiguity set P contains all distributions that are within a Wasserstein distance r of the empirical distribution P ^ constructed from historical data:In Equation 10, where the Wasserstein distance of order one is defined as:

P = P : W P , P ^ ≤ r (10)

W P , P ^ = inf ⁡ Π ∫ Ξ × Ξ ∥ ξ − ξ ′ ∥ Π d ξ , d ξ ′ (11)

In Equation 11, the distributionally robust dispatch problem seeks to minimize the worst-case expected cost over the ambiguity set:

min ⁡ x ∈ X sup ⁡ P ∈ P E P C x , ξ (12)

As is shown in Equation 12, the cost function C x , ξ includes generation costs, penalty costs for renewable curtailment, and penalty costs for load shedding [12]. The decision vector x includes generation setpoints, storage charging and discharging schedules, and flexible load adjustments.

Using linear decision rules and strong duality theory, the infinite-dimensional distributionally robust optimization problem can be reformulated as a finite-dimensional mixed-integer linear program [5]. The reformulation leverages the fact that the worst-case expectation over a Wasserstein ball can be expressed as:As is shown in Equation 13, where M is the number of historical samples and ξ ^ m m = 1 M are the empirical samples. This reformulation transforms the distributionally robust optimization problem into a tractable optimization with a finite number of constraints, enabling efficient solution using commercial solvers.

sup ⁡ P ∈ P E P C x , ξ = inf ⁡ λ ≥ 0 λ r + 1 M ∑ m = 1 M sup ⁡ ξ ∈ Ξ C x , ξ − λ ∥ ξ − ξ ^ m ∥ (13)

3 Deep learning-based trustworthy dispatch model

This section presents the proposed deep learning-based trustworthy dispatch model, which integrates a hybrid data augmentation framework, a blockchain-anchored trust evaluation mechanism, a distributionally robust optimization formulation, and a complete algorithmic flow.

3.1 Hybrid data augmentation framework

The scarcity of renewable energy operation data in newly constructed virtual power plants poses a significant challenge for data-driven dispatch models [13]. To address this issue, a hybrid data augmentation framework is proposed that integrates a conditional generative adversarial network with physical model constraints.

The generator network G takes as input a latent noise vector z ∼ N 0 , I and conditional information c (including weather forecasts, time of day, and seasonal indicators), producing synthetic renewable generation profiles ξ ^ = G z ∣ c. The discriminator network D distinguishes between real historical profiles and synthetic profiles while also evaluating compliance with physical constraints [14].

The training objective combines the standard generative adversarial network loss with a physics-informed regularization term:

L = L G A N + γ 1 L p h y s + γ 2 L t e m p o r a l (14)

In Equation 14, the generative adversarial network loss follows the Wasserstein GAN formulation with gradient penalty:

L G A N = E ξ ∼ P r D ξ ∣ c − E ξ ^ ∼ P g D ξ ^ ∣ c + λ g p E ξ ∼ ∥ ∇ ξ ∼ D ξ ∼ ∣ c ∥ 2 − 1 2 (15)

In Equation 15, the physics-informed loss enforces compliance with power balance and operational constraints:

L p h y s = ∑ i = 1 N max ⁡ 0 , P i max − P ^ i σ P + max ⁡ 0 , P ^ i − P i min σ P (16)

In Equation 16, the temporal consistency loss preserves the autocorrelation structure of renewable generation:In Equation 17, where ρ ^ τ and ρ τ are the autocorrelation functions of synthetic and real profiles respectively.

L t e m p o r a l = ∑ τ ∥ ρ ^ τ − ρ τ ∥ 2 2 (17)

3.2 Multi-agent deep reinforcement learning coordination

To achieve optimal coordination among multiple distributed energy resources operating under partial observability, the dispatch problem is formulated as a cooperative multi-agent reinforcement learning task [15]. Each distributed energy resource is modeled as an independent agent that observes its local state and selects actions based on a decentralized policy, while training is performed in a centralized manner using the Multi-Agent Deep Deterministic Policy Gradient framework.

The global state at time t includes the system-level load, renewable generation forecasts, market prices, and the aggregated trust scores. Each agent i observes a local observation:

o i , t = S o C i , t , P i , t P V , P i , t W T , τ i , t , λ t (18)

As is shown in Equation 18, the centralized critic network Q ϕ takes as input the global state and all agents’ actions, outputting a Q-value that approximates the expected cumulative reward:

Q ϕ s t , a 1 , t , … , a N , t = E ∑ k = 0 ∞ γ k R t + k (19)

In Equation 19, the actor networks π θ i output deterministic actions for each agent:As is shown in Equation 20, where N t is temporally correlated exploration noise [16]. A priority experience replay buffer stores transition tuples s t , a t , r t , s t + 1 with sampling probabilities proportional to the temporal-difference error:

a i , t = π θ i o i , t + N t (20)

p j ∝ ∣ δ j ∣ + ϵ α (21)

In Equation 21, the rewards are designed to align with the virtual power plant’s multi-objective optimization:As is shown in Equation 22, where C t o p e r is the operating cost, C t c a r b o n is the carbon emission cost, τ i , t incentivizes trustworthy behavior, and ρ t v i o l a t i o n penalizes constraint violations.

r t = − α C t o p e r − β C t c a r b o n + γ ∑ i τ i , t − δ ρ t v i o l a t i o n (22)

3.3 Hierarchical dispatch architecture

A two-stage hierarchical dispatch architecture decouples the day-ahead planning and real-time adjustment tasks. The day-ahead stage employs the distributionally robust optimization model to determine baseline schedules, while the real-time stage uses model predictive control to correct prediction errors.

The day-ahead distributionally robust optimization model receives as input the augmented dataset generated by the hybrid framework and the trust scores computed via the blockchain-anchored mechanism. The output includes the committed schedules P i , t c for all distributed energy resources over the 24-h horizon [17]. The formulation ensures that the worst-case cost over the Wasserstein ambiguity set is minimized, providing a guarantee of robustness against distributional uncertainty.

As is shown in Equation 23, the real-time model predictive control stage operates on a rolling horizon of H intervals, solving a quadratic programming problem at each time step:

min ⁡ Δ u t : t + H − 1 ∑ k = 0 H − 1 ∥ Δ x t + k ∣ t ∥ Q 2 + ∥ Δ u t + k ∣ t ∥ R 2 + ∥ Δ u t + k ∣ t ∥ S 2 (23)

As is shown in Equation 24, subject to the system dynamics, state constraints, and trust-adjusted limits. The trust scores dynamically adjust the allowable deviation bounds for each distributed energy resource:

P i , t d e v , ⁡ max ⁡ = P i , b a s e d e v , ⁡ max ⁡ · 1 + α · τ i , t (24)

This mechanism provides greater flexibility to trustworthy participants, creating a virtuous cycle where reliable performance leads to increased operational latitude.

The blockchain architecture adopted in this study is a permissioned blockchain built upon Hyperledger Fabric, with a consensus mechanism employing an optimized version of Practical Byzantine Fault Tolerance tailored specifically for energy scenarios. Under a typical deployment configuration comprising four ordering nodes and twelve peer nodes, the system achieves a stable transaction throughput of 250 transactions per second. Although this throughput is lower than that of high-performance exchange-grade blockchains, it fully satisfies the throughput requirement of the virtual power plant, which generates approximately 60 transactions per 15-min dispatch cycle. The consensus mechanism introduces an average overhead of 420 milliseconds, accounting for approximately 38 percent of the total end-to-end latency, and this overhead is maintained within acceptable limits through transaction batching and parallel verification mechanisms. The end-to-end communication latency, which includes the three phases of transaction submission, consensus achievement, and block confirmation, measures 1,100 milliseconds on average, with a worst-case latency of approximately 1.8 s, which fully meets the 15-min dispatch instruction issuance time window requirement. In terms of storage, each block occupies approximately 48 kilobytes, with an average of 240 new blocks generated per day, corresponding to a daily storage growth of approximately 11.5 megabytes and an annual storage requirement of approximately 4.2 gigabytes, which can be managed through hot-cold data tiered storage by resource type and month to alleviate long-term storage pressure. Regarding scalability, when the number of distributed energy resources increases from 45 to 200, transaction throughput decreases by approximately 32 percent and end-to-end latency increases by approximately 57 percent. However, by introducing a sharding mechanism that groups energy resources by geographic region for parallel processing, the system can maintain throughput above 210 transactions per second and latency within 1.5 s at the scale of 200 energy nodes, demonstrating that the proposed architecture can support the practical operational requirements of megacity virtual power plants scaling to hundred-node levels in the future.

3.4 Algorithmic flow of the proposed model

To clearly present the complete workflow of the proposed trustworthy dispatch model, this subsection provides a detailed description of the algorithmic flow, which is illustrated in Figure 1. The proposed algorithmic flow consists of two main stages, namely, offline training and online scheduling, and achieves a complete closed-loop dispatch from data preparation to instruction execution and feedback through six key steps.

Figure 1 illustrates the algorithmic flow of the proposed deep learning-based trustworthy dispatch model for virtual power plants, which consists of an offline training stage and an online scheduling stage that together form a closed-loop framework. In the offline stage, historical operation data are augmented using a hybrid generative adversarial network with physical constraints, and a multi-agent deep reinforcement learning policy is trained to provide a preliminary dispatch strategy [18]. In the online stage, the system performs day-ahead distributionally robust optimization based on the augmented dataset and blockchain-anchored trust scores, refines the plan through multi-agent coordination, and adjusts it in real time using model predictive control to correct prediction errors. Finally, trustworthy dispatch instructions are issued to distributed energy resources, and actual operational data are fed back to update trust scores, completing the closed loop through six key steps: data preparation and augmentation, trust evaluation initialization, day-ahead distributionally robust optimization, multi-agent deep reinforcement learning coordination, real-time model predictive control adjustment, and instruction execution with data feedback.

4 Experimental results and analysis

4.1 Simulation setup

The dataset utilized in this study originates from a virtual power plant demonstration project conducted by China Southern Power Grid Shenzhen Power Supply Company in a major megacity in eastern China, covering 18 months of operational records from January 2023 to June 2024. The dataset comprises 45 distributed photovoltaic stations with a total installed capacity of 12 MW, 28 small-scale wind turbines with a total capacity of 8 MW, 15 battery energy storage units with a total capacity of 6 MWh, and 120 flexible load aggregators with a total demand response capacity of 5 MW. All data are collected at a 15-min resolution and stored by resource type, including photovoltaic output along with irradiance and temperature data, wind speed and power output data, charging and discharging power with state-of-charge records, and baseline load profiles with adjustable potential. In the preprocessing stage, raw data undergo outlier detection and removal, where records exceeding physical upper or lower limits are flagged and corrected using linear interpolation between adjacent valid time points, timestamps are uniformly calibrated to Beijing time and aligned to a 15-min grid, all power measurements are converted to kilowatts, and weather data are associated with each distributed resource’s geographical location using a spatial nearest-neighbor matching method. For missing data handling, linear interpolation is applied for single-point missing values, while continuous missing segments exceeding three time points result in the exclusion of that entire day to ensure training quality, with an overall data missing rate of approximately 2.3 percent, yielding approximately 350,000 valid samples after processing. Due to data confidentiality agreements, the raw dataset cannot be made publicly available; however, the authors have provided a de-identified validation dataset and a comprehensive data description document to the journal editorial office for review, and commit to providing the preprocessed feature dataset along with relevant code to fellow researchers upon reasonable academic request to support result reproducibility. In terms of statistical characteristics, the photovoltaic daily average output is 3.2 MW with a maximum output of 10.8 MW and an average capacity factor of approximately 28 percent, the wind power daily average output is 2.1 MW with an intra-day fluctuation coefficient of 0.65, the energy storage systems undergo an average of 0.8 charge-discharge cycles per day with a mean state-of-charge maintained at 62 percent, the flexible loads have a daily average adjustable capacity of 1.4 MW with an actual response rate reaching 86 percent, and among resource types, the Pearson correlation coefficient between photovoltaic output and irradiance is as high as 0.92, while wind power and photovoltaic output exhibit a weak negative correlation of approximately −0.15, collectively indicating that the overall dataset exhibits the typical characteristics of high spatiotemporal heterogeneity and significant uncertainty associated with megacity power grids.

In terms of model architecture, the generator employs a four-layer fully connected network with 256, 512, 256, and 128 neurons per layer, respectively, each equipped with batch normalization and ReLU activation. The discriminator consists of three convolutional layers with kernel sizes of 4, 3, and 3, followed by two fully connected layers of 128 and 64 neurons. The multi-agent DDPG actor network adopts a two-hidden-layer structure with 256 and 128 units, while the critic network shares the same structure but employs the LeakyReLU activation function with a negative slope coefficient of 0.01. Regarding hyperparameter configuration, the generative adversarial network is trained for 500 epochs with a learning rate of 1 × 10⁻⁴, the physics-informed loss weight γ₁ is set to 0.1, the temporal consistency loss weight γ₂ is 0.05, both the actor and critic learning rates of the multi-agent DDPG are 1 × 10⁻³, the discount factor is 0.99, the experience replay buffer capacity is 1 × 10⁵, the priority experience replay exponent α is 0.6, the model predictive control horizon H is set to 4, and the Wasserstein radius r is 0.05. The hardware and software environment consists of an Intel Xeon Gold 6248 CPU, an NVIDIA A100 GPU with 40 GB memory, and 256 GB RAM, with the implementation built upon Python 3.9, PyTorch 1.12.0, and the Gurobi 10.0.1 optimization solver. All experimental results are reported as averages over 10 independent runs, and statistical significance is assessed using a two-sample t-test at a significance level of 0.05, with standard deviations and p-values already annotated in Figure 2. The complete configuration information provided above is sufficient to enable third-party researchers to independently reproduce all experiments reported in this work.

The proposed dispatch model is evaluated using real-world data from a megacity in eastern China with a population exceeding 10 million. The dataset includes 18 months of operation records from an existing virtual power plant demonstration project, comprising 45 photovoltaic systems with a total capacity of 12 MW, 28 wind turbines with a total capacity of 8 MW, 15 battery storage systems with a total capacity of 6 MW-hours, and 120 flexible load aggregators with a total demand response capacity of 5 MW. The data are split into training data covering 12 months, validation data covering 3 months, and testing data covering 3 months.

The hyperparameters of the proposed model are summarized in Table 1. The Wasserstein distance radius is calibrated using cross-validation to balance robustness and conservatism.

TABLE 1. Model hyperparameters.

Four baseline methods are selected for comparison to comprehensively evaluate the performance of the proposed model. The deterministic optimization approach ignores uncertainty entirely and solves a nominal problem using point forecasts. The stochastic optimization method employs scenario trees generated from historical distributions with twenty scenarios at each decision epoch. The robust optimization approach uses a budgeted uncertainty set without distributional assumptions, with the conservatism parameter tuned to achieve comparable out-of-sample performance [19]. The deep reinforcement learning baseline uses the same multi-agent architecture as the proposed method but without the distributionally robust formulation and trust mechanism.

4.2 Data augmentation performance

The effectiveness of the proposed hybrid data augmentation framework is first evaluated by comparing the quality of synthetic data generated with and without physical constraints. Figure 3 presents a visual comparison of real photovoltaic generation data against synthetic profiles generated by three different methods over a 48-h period. The real measured data in Figure 3a exhibit the characteristic diurnal pattern of solar generation, with a smooth ramp-up starting around sunrise at 6:00 a.m., a peak during the midday hours, and a gradual ramp-down toward sunset. The standard generative adversarial network synthetic data in Figure 3b capture the overall diurnal pattern but exhibit unrealistic fluctuations, particularly during the morning ramp-up and evening ramp-down periods, where sudden spikes and drops appear that do not correspond to any physical mechanism. The conditional generative adversarial network with weather conditioning in Figure 3c produces more realistic shapes but still generates physically infeasible spikes, such as a sudden drop to zero generation at 10:00 a.m. under clear sky conditions. In contrast, the proposed hybrid framework in Figure 3d generates synthetic profiles that closely follow the statistical characteristics of the real data while maintaining smooth transitions and physical plausibility. The close alignment between the proposed method and the real data demonstrates the effectiveness of incorporating physical constraints into the generation process.

The quantitative evaluation of data augmentation quality is presented in Table 2. The proposed hybrid framework achieves a root mean square error of 28.3 kW, which represents a 37 percent reduction compared to the standard generative adversarial network and a 27 percent reduction compared to the conditional generative adversarial network without physics constraints. The mean absolute error similarly improves to 19.6 kW. More importantly, the physical violation rate decreases from 8.7 percent to 1.4 percent, ensuring that synthetic samples are operationally feasible for dispatch optimization. The autocorrelation error, which measures how well temporal dependencies are preserved, improves by more than 60 percent due to the temporal consistency loss, indicating that the proposed method successfully captures the memory effects inherent in solar generation.

TABLE 2. Data augmentation quality comparison.

Figure 4 presents a heatmap visualization of the normalized dispatch performance as a function of training data availability and data augmentation method, where a score of 1.0 corresponds to the performance achieved when training on the full dataset without augmentation. As shown in Figure 4a, when only 20 percent of the original data is available, the proposed hybrid augmentation framework achieves a normalized performance score of 0.92, attaining 92 percent of the full-data performance, whereas the no-augmentation baseline reaches only 0.67 under the same condition. The performance advantage of the proposed method is most pronounced under extreme data scarcity, achieving a score of 0.75 at 10 percent data availability compared to 0.40 for the baseline, representing an 87.5 percent relative improvement. Figure 4b further quantifies the performance gain over the baseline, demonstrating that the proposed hybrid augmentation consistently outperforms both standard and conditional generative adversarial network based augmentation methods across all data availability levels. These results confirm that the proposed hybrid data augmentation framework, by integrating physical model constraints with generative adversarial networks, effectively mitigates the data scarcity problem in renewable energy operation, enabling reliable dispatch decisions for newly established virtual power plants with limited operational history.

4.3 Trust evaluation mechanism performance

The blockchain-anchored trust evaluation mechanism is assessed through simulation of a 6-month operation period with 45 distributed energy resource participants. The ground truth performance of each participant is varied to represent realistic scenarios, with some participants exhibiting consistently high reliability and others showing intermittent violations due to equipment issues or economic incentives.

Figure 5 presents the composition and evolution of the trust evaluation mechanism for virtual power plant participants. As shown in Figure 5a, the trust score is composed of three weighted dimensions, where accuracy carries the highest weight of 45 percent, followed by reliability at 35 percent and economy at 20 percent, reflecting the critical role of scheduling adherence in virtual power plant operations. Figure 5b provides a radar chart comparison of the performance profiles of three representative participant types across six evaluation metrics at the end of the third month. Participant A, characterized by consistently high reliability, maintains performance scores above 92 across all metrics, achieving an overall trust score of 0.96. Participant B exhibits periodic fluctuations, with notable deficiencies in consistency (65) and deviation magnitude (68), resulting in a trust score of 0.78. Participant C demonstrates gradual improvement from an initially poor state, reaching performance scores between 75 and 88 by month three with a trust score of 0.88. These results confirm that the proposed multi-dimensional trust evaluation mechanism effectively distinguishes participants with different reliability characteristics and provides responsive trust score adjustments based on actual performance, thereby creating a credible foundation for differentiated dispatch decisions.

Figure 6 presents the cumulative distribution function of trust score convergence time for participants stratified by their performance consistency levels, defined by daily accuracy variation. For participants with consistent performance, defined as less than 5 percent daily variation, the median convergence time is 12 days, with 95 percent of participants converging within 17 days. For participants with variable performance exhibiting 5 to 15 percent daily variation, the median convergence time increases to 21 days, reaching 95 percent convergence at 27 days. For highly variable participants with daily variation exceeding 15 percent, the median convergence time extends to 28 days, with 95 percent convergence achieved within 35 days. The cumulative distribution function curves exhibit clear separation among the three categories, demonstrating that the proposed trust evaluation mechanism converges faster for more reliable participants while requiring longer observation periods for those with higher performance variability. These results confirm that the mechanism is responsive to actual performance patterns and achieves convergence within a practically acceptable timeframe of 14–28 days for all categories, thereby supporting its practical deployment in real-world virtual power plant operations.

Figure 7 illustrates the economic impact of the blockchain-anchored trust evaluation mechanism through two complementary visualizations. The sunburst chart in Figure 7a reveals the hierarchical structure of trust score distribution and its corresponding economic outcomes, where the inner ring shows that 35 percent of participants fall into the low-trust category (score below 0.7), 45 percent into the medium-trust category (score between 0.7 and 0.9), and 20 percent into the high-trust category (score above 0.9). The outer ring demonstrates that low-trust participants incur an average penalty of 8.3 percent of their potential earnings, medium-trust participants experience no net adjustment, and high-trust participants receive an average bonus of 5.2 percent. The chord diagram in Figure 7b further visualizes the flow of economic incentives from trust score categories to earnings outcomes, where the width of each chord is proportional to the percentage of participants in each flow. The net effect is a 3.1 percent redistribution of earnings from low-trust to high-trust participants, creating a self-reinforcing economic incentive cycle. These results confirm that the proposed trust mechanism not only differentiates participants based on their reliability but also provides verifiable and transparent economic incentives that encourage trustworthy behavior without requiring centralized enforcement, thereby addressing a critical barrier to the practical deployment of virtual power plants in competitive electricity markets.

4.4 Dispatch performance comparison

The complete proposed dispatch model is evaluated across multiple scenarios representing different renewable penetration levels and weather conditions. Figure 2 compares the average daily operating costs of five dispatch methods over a 3-month testing period, with error bars representing standard deviations and statistical significance indicated relative to the proposed method. The proposed method achieves the lowest average daily operating cost of 9,865 US dollars, substantially outperforming the deterministic optimization approach at 12,847 US dollars (30.2% higher, p < 0.001), the stochastic optimization approach at 11,935 US dollars (21.0% higher, p < 0.01), the robust optimization approach at 13,209 US dollars (33.9% higher, p < 0.001), and the deep reinforcement learning baseline at 11,412 US dollars (15.7% higher, p < 0.05). The superior performance of the proposed method is attributed to three synergistic factors: the distributionally robust formulation reduces conservatism while maintaining protection against distributional shifts, the hybrid data augmentation improves forecast accuracy, and the trust-based coordination enables differentiated resource allocation favoring reliable participants. These results demonstrate that the proposed model achieves statistically significant cost reductions across all comparisons, with the most substantial improvement observed against robust optimization, which suffers from excessive conservatism, and deterministic optimization, which fails to account for operational uncertainties. The relatively lower standard deviation of 0.86 for the proposed method further indicates that its superior performance is consistent and reliable across diverse operating conditions.

The improvement in operating cost stems from three complementary factors. First, the distributionally robust formulation reduces the conservatism inherent in robust optimization while maintaining protection against distributional shifts. Second, the hybrid data augmentation provides higher-quality training data, improving the accuracy of renewable generation predictions used in the dispatch decisions. Third, the trust mechanism enables differentiated treatment of participants, allocating more flexibility to trustworthy distributed energy resources and reducing the risk of non-performance.

Figure 8 presents a stacked bar chart comparing the renewable energy disposition composition across five dispatch methods, where each bar sums to 100 percent and is divided into three components: utilized energy (green), curtailed energy (red), and stored energy (blue). The proposed method achieves the highest renewable energy utilization rate of 82.4 percent with the lowest curtailment rate of 10.3 percent, representing a 5.9 percentage point improvement over the deep reinforcement learning baseline at 76.5 percent utilization and a 20.6 percentage point improvement over deterministic optimization at 67.3 percent utilization. The robust optimization method exhibits the worst performance among all approaches, with only 61.8 percent utilization and 30.5 percent curtailment, demonstrating that excessive conservatism in uncertainty handling leads to substantial renewable energy waste. Notably, the storage utilization remains relatively stable across all methods, ranging from 7.3 percent to 8.3 percent, indicating that the performance gain of the proposed method stems primarily from reducing curtailment rather than increasing storage capacity. These results confirm that the proposed distributionally robust optimization formulation, which captures the dependence structure among multiple renewable resources through the Wasserstein ambiguity set, effectively hedges against correlated forecast errors and enables higher renewable integration without sacrificing operational reliability. The annual environmental benefit of this improvement is substantial, with the observed curtailment reduction translating to approximately 140 metric tons of CO₂ emission savings per year based on the local grid emission factor of 0.5 kg per kilowatt-hour.

Figure 9 presents a comprehensive constraint violation analysis over the 3-month testing period through two complementary visualizations. The stacked bar chart in Figure 9a decomposes the violations into voltage limit violations and thermal limit violations across five dispatch methods. The deterministic optimization approach exhibits the highest number of violations with 47 total incidents (28 voltage violations and 19 thermal violations), primarily due to its reliance on point forecasts that misrepresent actual operating conditions. The stochastic optimization method shows moderate performance with 23 violations, while the deep reinforcement learning baseline records 18 violations, demonstrating the benefit of data-driven coordination even without distributionally robust formulation. The robust optimization method achieves only 5 violations, confirming its ability to guarantee constraint satisfaction by explicitly enforcing feasibility for all scenarios within its uncertainty set. The proposed method achieves the fewest violations with only 3 total incidents (2 voltage and 1 thermal), representing a 93.6 percent reduction compared to deterministic optimization and approaching the robustness of robust optimization. The waterfall chart in Figure 9b illustrates the cumulative reduction in constraint violations when methods are ordered from worst-performing to best-performing, clearly showing a stepwise improvement of 44 violations from deterministic optimization to the proposed method. These results demonstrate that the proposed model achieves a favorable trade-off between robustness and economic efficiency, attaining violation rates comparable to robust optimization while maintaining superior cost performance as evidenced in Figure 2, thereby validating the effectiveness of the distributionally robust formulation combined with the trust-based coordination mechanism.

4.5 Robustness under high renewable penetration

To evaluate the scalability and robustness of the proposed approach under challenging conditions, the renewable penetration level is artificially increased by scaling up the capacity of photovoltaic and wind resources while maintaining the same load profile. Figure 10 shows the operating cost as a function of renewable penetration level, ranging from the baseline 30 percent to an extreme 80 percent scenario. The proposed model maintains stable performance up to 70 percent penetration, with operating costs increasing by only 8.7 percent from the baseline while renewable utilization remains above 78 percent. In contrast, the deep reinforcement learning baseline exhibits a 23 percent cost increase at 70 percent penetration, as the lack of robust handling leads to excessive curtailment when prediction errors are amplified. The robust optimization baseline maintains constraint satisfaction but sacrifices economic efficiency, with costs exceeding those of the proposed model by 18 percent at 70 percent penetration. The deterministic and stochastic optimization methods become infeasible at penetration levels exceeding 60 percent, as indicated by the termination of their curves in Figure 10.

The renewable utilization rate under varying penetration levels is shown in Figure 11. The proposed method maintains utilization above 78 percent even at 70 percent penetration, while the deep reinforcement learning baseline drops to 62 percent utilization at the same penetration level. The superior robustness of the proposed model is attributed to the distributionally robust formulation, which is specifically designed to handle the high-dimensional uncertainty that arises when multiple renewable resources with correlated prediction errors are integrated. The Wasserstein ambiguity set captures the dependence structure between different resources, enabling the optimization to hedge against correlated forecast errors that would otherwise lead to cascading violations.

Figure 11 presents the renewable energy utilization rate as a function of renewable penetration level, comparing the proposed method against four baseline approaches. As the penetration level increases from 30% to 70%, the proposed method maintains a utilization rate above 78%, demonstrating strong robustness under high uncertainty conditions. In contrast, the deep reinforcement learning baseline drops to 62% utilization at 70% penetration, while the deterministic and stochastic optimization methods become infeasible beyond 60% penetration due to excessive forecast errors and constraint violations. The robust optimization baseline remains feasible but achieves lower utilization than the proposed method at all penetration levels. These results indicate that the proposed distributionally robust formulation, which captures the dependence structure among multiple renewable resources through the Wasserstein ambiguity set, effectively hedges against correlated forecast errors that would otherwise lead to cascading curtailment decisions, thereby enabling higher renewable integration without sacrificing operational reliability.

4.6 Real-time tracking performance

The real-time tracking performance of the proposed model is evaluated by examining how closely the actual system operation follows the day-ahead dispatch schedules. Figure 12 presents a 24-h comparison of the day-ahead scheduled net load and the actual net load for three representative days: a clear summer day with stable conditions, a cloudy transitional day with moderate variability, and a highly variable day with rapid cloud movements causing frequent fluctuations.

On the clear summer day shown in Figure 12a, both the proposed method and the deep reinforcement learning baseline track the day-ahead schedule accurately, with deviations generally remaining below 0.5 MW. The actual load follows the scheduled trajectory closely throughout the day, with slight deviations occurring only during the morning and evening ramp periods. On the cloudy transitional day shown in Figure 12b, the advantage of the proposed method becomes apparent. The deep reinforcement learning baseline exhibits deviations exceeding 1.5 MW during the afternoon period when cloud cover causes sudden reductions in photovoltaic output. The proposed method, benefiting from the distributionally robust formulation, maintains tracking errors below 0.8 MW even under these challenging conditions. On the highly variable day shown in Figure 12c, the difference between the two methods is most pronounced. The deep reinforcement learning baseline experiences multiple large deviations exceeding 2.0 MW, while the proposed method maintains tracking errors below 1.0 MW throughout the day.

Quantitative tracking error statistics are summarized in Table 3. The proposed method achieves a root mean square tracking error of 0.43 MW across all test days, compared to 0.91 MW for the deep reinforcement learning baseline. The improvement is most significant on highly variable days, where the proposed method’s root mean square error of 0.58 MW is less than half of the baseline’s 1.24 MW.

TABLE 3. Real-time tracking error comparison in megawatts.

4.7 Ablation studies

Ablation studies are conducted to isolate the contribution of each major component. Figure 13 presents the performance of the proposed model with individual components removed, showing both the operating cost and renewable utilization for each configuration. The full proposed configuration achieves the best performance with an operating cost of 9,865 US dollars per day and a renewable utilization of 82.4 percent. The removal of the data augmentation component increases operating costs to 10,412 US dollars, representing a 5.5 percent increase, and decreases renewable utilization to 78.1 percent, representing a 4.3 percentage point drop. The removal of the trust mechanism leads to operating costs of 10,201 US dollars and utilization of 80.2 percent, with constraint violations increasing from 3 to 9 as previously shown in Figure 9. The removal of the distributionally robust formulation produces the largest performance degradation, with operating costs increasing to 10,896 US dollars, representing a 10.5 percent increase, and utilization dropping to 75.6 percent, representing a 6.8 percentage point decline. The removal of the model predictive control real-time adjustment stage increases costs to 10,087 US dollars and reduces utilization to 79.8 percent, confirming the value of intraday correction for handling forecast errors that cannot be anticipated at the day-ahead stage.

These results confirm that each component of the proposed framework contributes significantly to overall performance. The distributionally robust formulation provides the largest individual contribution to both economic efficiency and renewable utilization, followed by the data augmentation framework and the real-time model predictive control adjustment. The trust mechanism, while providing the smallest direct impact on these metrics, plays an essential role in creating incentives for reliable participant behavior and reducing constraint violations.

5 Conclusion

A comprehensive deep learning-based trustworthy dispatch framework for virtual power plants operating in megacity power grids has been developed to address the three fundamental bottlenecks of data scarcity, trust deficits, and dual uncertainties from renewable generation and load demand. The proposed framework integrates a physically constrained generative adversarial network for hybrid data augmentation, a blockchain-anchored multi-dimensional trust scoring mechanism with smart contract-based incentives, and a Wasserstein distance-driven distributionally robust optimization model, coordinated within a two-stage hierarchical architecture that couples day-ahead planning with real-time model predictive control. Experimental validation is conducted using 18-month operational data from a VPP demonstration project in eastern China, encompassing 45 photovoltaic systems, 28 wind turbines, 15 battery energy storage units, and 120 flexible load aggregators. The proposed method achieves a root mean square tracking error of 0.43 MW, representing a 53% reduction over the deep reinforcement learning baseline, attains a renewable energy utilization rate of 82.4%, and lowers the average daily operating cost to $9,865, outperforming deterministic, stochastic, robust, and reinforcement learning benchmarks by 30.2%, 21.0%, 33.9%, and 15.7%, respectively. The framework remains feasible and cost-efficient under renewable penetration levels up to 70%, with only three constraint violations recorded over the 3-month testing period, corresponding to a 93.6% reduction relative to deterministic optimization. Ablation studies reveal that the distributionally robust optimization formulation contributes the largest performance gain, followed by data augmentation and model predictive control, while the trust mechanism substantially reduces violations and encourages reliable participation through transparent economic incentives. Collectively, the proposed framework strikes a favorable balance among economic efficiency, operational robustness, and verifiable trustworthiness, providing a practical and scalable solution for VPP dispatch in complex urban environments. Future research directions include the incorporation of dynamic carbon pricing signals, the enhancement of blockchain scalability via sharding techniques, and the exploration of federated learning for privacy-preserving data augmentation across multiple VPPs.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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Footnotes

Edited by: Jisheng Kou, Shaoxing University, China

Reviewed by: Saravana Prakash Thirumuruganandham, SIT Health, Ecuador

Mahiba Chellathurai, Jain University, India