A Collaborative Grid-Connected Control Strategy for Heterogeneous Generator Groups Integrating Spatiotemporal Prediction Feedforward

Abstract

Mobile emergency generators and mobile energy storage clusters are core flexible resources for the rapid recovery of critical loads in post-disaster distribution networks and the enhancement of resilience in isolated microgrids. However, due to the strong random changes in end-load loads, heterogeneous units are prone to problems such as large transient inrush currents, unstable phase-locked loops (PLLs), and reliance on manual synchronization adjustments when connected under load. To address these issues, this paper proposes a multi-timescale smooth grid-connected control architecture that combines data-driven feedforward and physical feedback. The architecture extracts spatiotemporal load features based on a CNN-BiLSTM-Attention model to achieve capacity optimization and baseline allocation. Predicted load voltage drop is converted into feedforward compensation to construct a virtual internal potential for coarse pre-grid connection adjustment. This is then combined with a closed-loop PLL to achieve fine-tuning of phase angle and voltage errors and autonomous decoupling of transient power after grid connection. Simulation and experimental results show that the proposed method suppresses voltage overshoot from 0.3 p.u. to within 0.03 p.u., increases the minimum frequency to above 49.8 Hz, reduces inrush current, and shortens synchronization time by 15.4%, significantly improving the system’s rapid connection and recovery capabilities.

1. Introduction

In recent years, extreme weather and high-impact, low-probability natural disasters have occurred frequently, causing local or even large-scale power outages in the power distribution network, which seriously threatens social and economic operations and public safety [1,2]. Against this backdrop, improving the emergency recovery capability and system resilience of the power distribution network after disasters has become a key research direction [3]. Mobile emergency generators and mobile energy storage systems are widely used in the construction of isolated microgrids and the restoration of critical loads after disasters due to their good spatial mobility and rapid response capability [4,5]. However, due to the damage to the topology of the power distribution network after disasters and the strong random fluctuations in load, the significant heterogeneity of diesel generators (DG) and energy storage inverters on the dynamic response time scale makes them prone to problems such as inrush current and frequency drop during grid connection [6,7]. Therefore, achieving rapid synchronization and smooth grid connection of heterogeneous mobile power clusters under extreme conditions is the core issue of ensuring emergency power supply capability after disasters [8].

To address the above issues, scholars at home and abroad have conducted extensive research on load forecasting, grid pre-synchronization, and multi-source collaborative control. In load forecasting, deep learning methods have been widely used to extract the spatiotemporal characteristics of distribution network loads. The combination of convolutional neural networks and long short-term memory networks has effectively improved the prediction accuracy under complex operating conditions [9,10,11]. The introduction of attention mechanisms has further enhanced the ability to characterize load mutation features [12], providing data support for energy management and resource optimization [13,14]. In terms of grid control, droop control and phase-locked loop technology constitute the basis for the smooth switching of microgrids [15]. Related studies have effectively suppressed transient shocks in the early stage of grid connection by improving the phase-locked loop pre-synchronization strategy and adaptive droop control [16,17,18]. In terms of collaborative control, the power allocation method based on virtual synchronous generators has achieved dynamic decoupling between diesel engines and energy storage systems, thereby enhancing the system’s frequency support capability [19,20].

Although existing research has made significant progress in a single technical direction, there are still obvious shortcomings in the complex scenario of coordinated grid connection for a heterogeneous group of post-disaster power-generation vehicles. First, load forecasting primarily serves macro-dispatch, and its minute-level results are difficult to meet the millisecond-level transient control requirements at the moment of grid connection, resulting in time-scale fragmentation and insufficient information utilization [21,22]. Second, traditional control methods are mainly based on pure feedback mechanisms, relying on real-time measurement and closed-loop regulation after grid connection, which is difficult to cope with the rapid voltage drop and frequency shift caused by sudden load disturbances [23,24], thereby increasing protection malfunction and parameter adjustment costs and reducing emergency recovery efficiency [25]. Therefore, relying solely on data-driven forecasting or single feedback control is insufficient to overcome the technical bottlenecks of large impact and low synchronization efficiency in heterogeneous power-source grid connections. Furthermore, while existing hybrid predictive control frameworks balance prediction and control to some extent [26,27], they essentially rely on high-frequency online rolling optimization. Millisecond-level grid-connected transient disturbances place high demands on computing resources and real-time communication and are easily constrained by network latency and centralized distribution bottlenecks. They are difficult to adapt to the engineering requirements of decentralized access of mobile generators, rapid reconfiguration, and the coexistence of extreme disturbances in post-disaster scenarios. Thus, it can be seen that existing methods have not effectively solved the problem of mapping macroscopic prediction results to microscopic transient control quantities across time scales, and they also lack a unified approach that accounts for prior data utilization, physical-mechanism constraints, and hierarchical real-time control.

To address the aforementioned issues, this paper proposes a smooth grid-connection strategy for heterogeneous groups of generator vehicles that integrates data-driven feedforward and physical feedback. Unlike traditional MPC and centralized predictive control methods, this paper constructs a multi-timescale decoupled predictive and control collaborative mapping system, mapping 15 min load forecast results to millisecond-level control references and pre-constructing a virtual internal potential with load compensation characteristics based on line impedance parameters. Furthermore, a hierarchical implementation approach of upper-level prediction and lower-level control is adopted, deploying load forecasting at low-frequency execution on the host computer while delegating transient closed-loop regulation to the lower-level DSP for local completion, thus avoiding reliance on high-frequency online optimization and real-time control command issuance. Based on this, the proposed collaborative control mechanism achieves smooth, millisecond-level grid connection and transient, self-consistent control of heterogeneous groups of generator vehicles under extreme operating conditions.

2. Algorithm Principles and Control Models

2.1. Power Generation Vehicle Layout Process and System Architecture

Routers need to be selected based on the load conditions on the user’s side. Without load forecasting on the user side, calculations can only be made roughly based on manual experience, resulting in significant errors and wasted resources. Addressing the characteristics of strong load fluctuations and complex spatial topology at the end nodes of the distribution network, this study first constructs a hybrid deep learning prediction model based on CNN-BiLSTM-Attention. The predicted data serves as a constraint to guide the capacity optimization and spatial scheduling of heterogeneous generator clusters. Based on these predictions, a collaborative control model for mobile emergency generators, including a pre-synchronization mechanism and improved droop control, is established. This model maps load forecast information into reference commands for generator grid connection control and then, through a phase-locked loop, achieves rapid grid connection and autonomous power allocation, as shown in Figure 1.

2.2. Control Model

2.2.1. Load Forecasting and Heterogeneous Resource Baseline Allocation Model

To reduce scheduling and optimization time for mobile generators after disasters, let the hidden-layer state feature matrix extracted at time t_k be denoted by h_i. Combined with adaptive attention weight α_i, a prediction model for the active power $\widehat{P}$_L and reactive power $\widehat{Q}$_L of the target node in future time periods is established:

$${\widehat{P}}_L(t_{k+1})=W_p({\displaystyle \sum _{i=1}^T{\alpha }_i}{h}_i)+b_p$$

(1)

$${\widehat{Q}}_L(t_{k+1})=W_q({\displaystyle \sum _{i=1}^T{\alpha }_i}{h}_i)+b_q$$

(2)

In the formula, W_p and W_q are the weight matrices of the fully connected layer; b_p and b_q are the bias vectors; T is the length of the historical time window. Based on the power level and fluctuation characteristics of the predicted load, the control center rationally configures energy storage generators (ESS) and DG with different response frequency bands. Their steady-state reference output configuration satisfies the following constraint:

$$\left\{\begin{array}{l}{P}_{ref,DG}={\rho }_{DG}\cdot {\widehat{P}}_L(t_{k+1})\hfill \\ P_{ref,ESS}={\rho }_{ESS}\cdot {\widehat{P}}_L(t_{k+1})\hfill \end{array}\right.$$

(3)

In the formula, ρ_DG and ρ_ESS are the adaptive capacity allocation weights of the diesel engine and the energy storage unit based on the rated capacity ratio, respectively, satisfying ρ_DG + ρ_ESS = 1.

2.2.2. Feedforward Pre-Compensation Model Based on Predicted Data

Based on the output of the load forecasting model above, a cross-layer mapping link is established from the data domain to the physical control domain. Specifically, at time t₀, when the heterogeneous cluster arrives at the fault node and is ready to connect to the grid, the load forecast value at the moment of grid connection is extracted, and the expected voltage drop ΔV_ff and frequency offset Δω_ff are derived by combining the line impedance parameters:

$$\Delta V_{ff}(t_0)\approx {\displaystyle \frac{R_{line}{\widehat{P}}_L(t_0)+X_{line}{\widehat{Q}}_L(t_0)}{V_n}}$$

(4)

$$\Delta {\omega }_{ff}(t_0)=m_p\cdot {\widehat{P}}_L(t_0)$$

(5)

In the formula, R_line and X_line are the line resistance and reactance from the point of common coupling (PCC) to the equivalent load center; V_n is the nominal voltage; m_p is the equivalent active-frequency droop coefficient of the system. By introducing a feedforward mechanism, the expected voltage drop is injected into the inverter control loop before the physical switch operation, constructing a virtual internal potential reference value with load compensation characteristics:

$$V_{ff}^{\ast }=V_n+K_{vf}\cdot \Delta V_{ff}(t_0)$$

(6)

$${\omega }_{ff}^{\ast }={\omega }_n+K_{\omega f}\cdot \Delta {\omega }_{ff}(t_0)$$

(7)

In the formula, K_vf and K_ωf are the feedforward gain coefficients, K_vf ∈ [0.8, 1.2] and K_ωf ∈ [0.85, 1.15]. This step enables the controller to anticipate unknown loads, significantly narrowing the parameter error boundaries on both sides of the grid connection point before closing.

The output step size of the prediction model in this paper is 15 min, whereas the pre-synchronization compensation calculation for the inverter at the moment of grid-connected circuit breaker closing must be accurate to the millisecond level. To mitigate the impact of feedforward commands caused by step changes at discrete prediction points, this paper designs a time-scale mapping mechanism based on first-order ramp interpolation.

Suppose that the load prediction values output by the prediction model at two adjacent discrete times T_k and T_k+1 (ΔT = T_k+1 − T_k = 15 min) are $\widehat{P}$_L(T_k) and $\widehat{P}$_L(T_k+1), respectively. For any millisecond-level grid connection time that actually occurs within the interval t₀ ∈ [T_k, T_k+1], its mapped steady-state reference load $\widehat{P}$_L(t₀) is transformed by linear interpolation into

$${\widehat{P}}_L(t_0)={\widehat{P}}_L(T_k)+{\displaystyle \frac{{\widehat{P}}_L(T_{k+1})-{\widehat{P}}_L(T_k)}{T_{k+1}-T_k}}\cdot (t_0-T_k)$$

(8)

Similarly, the reactive load interpolation reference $\widehat{Q}$_L(t₀) at the target time can be obtained. This continuous mapping value will be directly input into the feedforward controller to calculate the expected voltage drop ΔV_ff at the moment of closing.

2.2.3. Precise Synchronization Mechanism Based on Phase-Locked Loop Feedback

Since errors inevitably exist in the model’s predicted data and impedance parameter estimates, to ensure the final achievement of zero-transient-impact sensorless grid connection, a phase-locked loop (PLL) and a state feedback loop need to be introduced in addition to feedforward compensation to accurately eliminate the residual voltage error e_v and phase error e_θ. The three-phase grid-side voltage is collected, and the d-q-axis components are obtained via the Park transformation. Phase and voltage amplitude error functions are defined as follows:

$$e_{\theta }(t)={\theta }_{PCC}(t)-{\theta }_{inv}(t)\approx \arctan 2\left(v_{q,PCC}(t),v_{d,PCC}(t)\right)$$

(9)

$$e_v(t)=\sqrt{v_{d,PCC}^2(t)+v_{q,PCC}^2(t)}-V_{inv}(t)$$

(10)

A dual proportional–integral (PI) regulator is used to generate the final closed-loop control command for the inverter based on the pre-compensation refernce (${\omega }_{ff}^{\mathrm{*}}$, $V_{ff}^{\mathrm{*}}$):

$${\omega }_{inv}^{\ast }(t)={\omega }_{ff}^{\ast }+K_{p\theta }{e}_{\theta }(t)+K_{i\theta }{\displaystyle {\int }_0^t{e}_{\theta }}(\tau )d\tau$$

(11)

$$V_{inv}^{\ast }(t)=V_{ff}^{\ast }+K_{pv}{e}_v(t)+K_{iv}{\displaystyle {\int }_0^t{e}_v}(\tau )d\tau$$

(12)

$${\theta }_{inv}^{\ast }(t)={\displaystyle {\int }_0^t{\omega }_{inv}^{\ast }}(\tau )d\tau$$

(13)

In the formula, K_pθ, K_iθ and K_pv, K_iv are the proportional and integral coefficients of the phase-locked loop and the voltage regulator, respectively. Their values are determined with reference to the constraints on synchronization error in the IEEE Std 1547-2018 [28] grid connection standard (phase angle error < 2°, response time < 50 ms). This feedback loop can force the tiny deviations left by the open-loop prediction to converge to zero within tens of milliseconds, greatly shortening the grid connection operation time of manual trial and error.

2.2.4. Transient Decoupling Control of Heterogeneous Clusters After Grid Connection

After successful circuit closure, due to the mechanical inertia and millisecond-level hysteresis of the diesel generator set, and the extremely fast response of the energy storage unit, both are prone to transient power circulation when facing high-frequency fluctuations in the actual load. Therefore, a heterogeneous cooperative control equation with matched physical characteristics is constructed. Traditional droop control with a low-pass filter (LPF) is used for the diesel generator vehicle, allowing it to focus on handling the system’s steady-state and low-frequency load components.

$${\tau }_L{\displaystyle \frac{\mathrm{d}{\overline{P}}_{DG}(t)}{\mathrm{d}t}}+{\overline{P}}_{DG}(t)=P_{DG}(t)$$

(14)

$${\omega }_{DG}(t)={\omega }_{inv}^{\ast }-m_d\left({\overline{P}}_{DG}(t)-P_{ref,DG}\right)$$

(15)

Introducing virtual inertia and transient differential feedback compensation into the ESS vehicle enables it to quickly smooth out sudden impact loads:

$${\omega }_{ESS}(t)={\omega }_{inv}^{\ast }-m_e(P_{ESS}(t)-P_{ref,ESS})-K_{vsg}{\displaystyle \frac{d{\omega }_{PCC}}{dt}}$$

(16)

The power balance equation constraint for the entire cluster grid connection is

$$P_{L\_real}\left(t\right)=P_{DG}\left(t\right)+P_{ESS}\left(t\right)$$

(17)

In the formula, τ_L is the low-pass filter time constant; m_d and m_e are the droop coefficients of DG and ESS, respectively. The droop coefficients m_d and m_e are set based on the ratio of each unit’s rated capacity to the total system capacity, ensuring that active and reactive power are distributed proportionally under steady-state conditions. K_vsg is the virtual inertia damping coefficient of the energy storage system; P_{L_real} is the actual load that undergoes a sudden change. This strategy does not rely on high-frequency derivative commands issued by the host computer, but can achieve transient decoupling and smooth response of heterogeneous clusters by relying solely on local physical feedback. The aforementioned prediction model and control equations, along with the control mechanism, enable smooth, millisecond-level grid connection and transient, self-consistent control of heterogeneous generator-vehicle groups under extreme operating conditions. The specific process is shown in Figure 2.

2.2.5. System Small-Signal Stability and Parameter Sensitivity Analysis

To demonstrate the stability of the proposed feedforward-and-feedback coordinated control architecture under dynamic conditions, this paper investigates the effects of key control parameters using small-signal analysis. Combining Equations (6) and (12), the small-signal closed-loop transfer function of the inverter voltage inner loop can be approximately expressed as

$$\Delta V_{inv}(s)={\displaystyle \frac{K_{pv}s+K_{iv}}{s^2+K_{pv}s+K_{iv}}}\Delta V_{ref}(s)+{\displaystyle \frac{K_{vf}\cdot s}{s^2+K_{pv}s+K_{iv}}}\Delta V_{drop}(s)$$

(18)

As seen from the system characteristic equation, the traditional pure closed-loop feedback (i.e., feedforward gain K_vf = 0) requires a certain amount of time for the integral element to accumulate and eliminate errors when facing a step-type load voltage drop disturbance ΔV_drop(s), which leads to a drop in transient voltage. The data-driven feedforward term K_vf introduced in this paper effectively adds a differential lead compensation zero to the disturbance transfer function. This allows the internal potential to instantaneously follow the disturbance and perform reverse compensation at the initial moment of a load change, thereby significantly reducing the dead zone of the feedback loop. The selection of the feedforward gain K_vf directly determines the system’s disturbance rejection capability and stability margin. Theoretically, if the line impedance model is absolutely accurate, K_vf = 1 can achieve zero transient error. However, in actual operation, if the actual compensation is greater than the true voltage drop due to parameter overestimation (equivalent to overcompensation), it is very easy to push the closed-loop poles of the system to the right half of the complex plane, causing high-frequency parasitic oscillations or even system instability. Therefore, to ensure the absolute stability margin of the system, this paper conservatively sets the feedforward gain to K_vf = 0.9, that is, relying on predictive feedforward to eliminate 90% of the transient impact, while the remaining 10% of small disturbance residuals are completely eliminated by the highly stable underlying PI closed-loop feedback (K_pv, K_iv), thus achieving the optimal balance between fast response and stability.

The parameter values and their basis in the above formulas are shown in

Table 1. Values of Key Parameters and the Basis for Their Selection.

Symbols	Value	Basis for Setting	Symbols	Value	Basis for Setting
Kvf	0.9	Small-signal stability margin: GM > 6 dB, PM > 45°;	md	0.01 Hz/kW	Duty cycle 4%, rated capacity 200 kW:
Kωf	0.9	Ibid.; allowed range [0.85, 1.15]	me	0.01 Hz/kW	Ibid.
Kpθ	50 rad/(s·rad)	Bandwidth: 300 rad/s; settling time: <50 ms	Kvsg	3185 W·s/rad	Equivalent inertial time constant Hess = 5 s: 2H·Srated/ωn
Kiθ	1000 rad/s2/rad	Ibid.	τL	0.1 s	Cutoff frequency: 10 rad/s (1.6 Hz)
Kpv	40 V−1	Bandwidth: 250 rad/s, response time: <40 ms	ρDG	0.667	Tsatisfying ρDG + ρESS = 1
Kiv	800 (V·s)−1	Ibid.	ρESS	0.333	Accounting for one-third of the total capacity of 600 kW

below.

3. Simulation Analysis

3.1. Load Forecasting for Typical Nodes

The dataset used in this paper comes from a local power supply bureau. The dataset includes load data from eight nodes across four typical load areas: commercial, school, government, and residential. Data from each of the four typical nodes was collected to monitor load changes from 1 January to 31 December 2025, at 15 min intervals. For data preprocessing, a combined approach utilizing linear interpolation and historical averages from the same day was employed to handle missing data. Outliers were identified using the 3σ criterion and subsequently corrected with neighborhood medians. Timestamp deduplication and the alignment of multi-node data onto a unified timeline were also performed. Normalization was applied to map the load data into the [0, 1] interval, thereby enhancing model training stability and convergence speed. The model’s hyperparameters were determined through 5-fold cross-validation on the validation set. During training, a cosine-annealed learning-rate strategy was adopted, allowing the learning rate to decay from 0.001 to 1 × 10⁻⁵. An early stopping mechanism was triggered when the Mean Squared Error (MSE) on the validation set decreased by less than 1 × 10⁻⁵ over 15 consecutive epochs; the model ultimately converged between epochs 147 and 183. To mitigate overfitting, Batch Normalization and a Dropout layer (rate 0.2) were introduced after the BiLSTM layers. The relevant parameter configurations are included in the annotations in

Table 2. Hyperparameters of the prediction model.

Parameter	Values
Number/size of CNN convolution kernels	64/(3 × 3)
BiLSTM Hidden Layer Dimensions	128
BiLSTM layers	2
Attention dimension	64
Learning rate	0.001
Batch size	64
Training rounds	200
History window length T	96 (1440 min)
Prediction window length H	16 (240 min)

. A total of 80% of the dataset is used for training, 10% for validation, and 10% for testing to verify the model’s generalization under recent real-world conditions. The original load distribution characteristics of each node are shown in Figure 3.

This experiment, based on the TensorFlow 2.0 framework, used Python 3.13 to construct and train the CNN-BiLSTM-Attention hybrid model. The model hyperparameters are shown in Table 2. To verify the prediction and tracking performance of the proposed CNN-BiLSTM-Attention model, prediction curves for representative time windows in the test set were extracted and compared with the actual load curves, as shown in Figure 4. Simulation results show that, within the range of stable load fluctuations, the model can accurately capture the strong spatiotemporal coupling characteristics and local abrupt change trends among multi-node loads. Even under drastic load fluctuations, its prediction curves remain highly consistent with the actual load trajectory, effectively overcoming the shortcomings of traditional models, which are insufficiently sensitive to high-frequency transient features.

The aforementioned differences in tracking performance directly affect subsequent control stages: a lag in the prediction curve at inflection points leads to timing shifts in feedforward compensation commands, thereby weakening the impact-suppression effect of the pre-synchronization mechanism. Therefore, the proposed model’s accurate tracking capability under abrupt changes is a prerequisite for ensuring the control layer’s performance. Figure 5 shows the performance of the CNN-BiLSTM-Attention model in predicting data across 8 nodes. The figure demonstrates that the model achieves a minimum load prediction accuracy of 0.957 across 8 nodes, thereby shortening matching time and reducing wasted power-supply capacity in mobile generator scheduling.

To objectively quantify the prediction accuracy of this model, CNN-LSTM and CNN-BiLSTM models were constructed for comparison, both using the same data partitioning and training strategy. To analyze the prediction performance of each model, three statistical indicators were introduced: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²). The average results on the test set of distribution network nodes are shown in Figure 6. Horizontal comparison shows that the CNN-BiLSTM-Attention model has the lowest MAE and RMSE across all nodes, and its R² coefficient is stable between 0.957 and 0.965, demonstrating excellent cross-node generalization. Further statistical analysis shows that, compared with the CNN-BiLSTM model without attention weighting, the proposed method achieves an average prediction accuracy per node that is 1.7% higher, and its global weighted average accuracy reaches 96.3%.

To visually illustrate the performance differences among the models, key error metrics for each node are plotted in Figure 7. The figure provides a more intuitive view of the prediction accuracy of the CNN-BiLSTM-Attention model, which shows a significant improvement over the other two models.

Furthermore, building upon the original comparative analysis of CNN-LSTM and CNN-BiLSTM, this paper incorporates the following additional models: the Transformer–LSTM hybrid model and the TCN-Attention model, as shown in

Table 3. Comparison of Comprehensive Performance and Computational Aspects of Various Advanced Forecasting Models.

Predictive Model	MAE (kW)	RMSE (kW)	R2	Time per Inference (ms)
TCN-Attention	2.31	3.02	0.948	15.2
Transformer–LSTM	2.05	2.68	0.961	48.5
CNN-BiLSTM-Attention	2.09	2.71	0.963	18.4

Note: Inference times are based on tests conducted on a host computer with an Intel i7 processor.

.

The results indicate that although Transformer models have a theoretically high upper bound for long-sequence prediction, for the 15 min-scale ultra-short-term forecasting task addressed in this paper, their extensive self-attention matrix operations lead to a significant increase in single-inference latency (up to 48.5 ms). In contrast, the proposed CNN-BiLSTM-Attention model achieves comparable—or even slightly superior—prediction accuracy (with an R² of 0.963) while maintaining an exceptionally low inference latency of just 18.4 ms. This balance between high accuracy and low latency enables the model to transmit feedforward benchmarks to downstream controllers more quickly, thereby meeting the critical time-sensitive requirements of post-disaster emergency response.

3.2. Case Analysis of Emergency Dispatch

To verify the actual gains of the proposed spatiotemporal load prediction model on the underlying physical control, a typical high-load area sudden power outage scenario was designed as follows: At time t0, due to an extreme disaster, a critical feeder supplying power to node 3 (commercial area, peak load of 550 kW in the next 4 h) experienced a temporary failure, forcing the system into islanded operation mode. Under the traditional heuristic static configuration mode, the control center only assigns redundancy based on the historical extreme value (800 kW) over the day and relies on manual verification of the topology and unit status, resulting in a response time of approximately 7 min. Under the prediction-driven architecture proposed in this paper, the scheduling center extracts the load prediction curve for the next 4 h output by the CNN-BiLSTM-Attention model. According to the prediction results, the peak load of node 3 will reach 600 kW in the next 4 h, with the entire process taking less than 3 min. Based on this, two 200 kW DG trucks and one 200 kW ESS truck were spatially allocated to node 3, as shown in Figure 8. This saves approximately 42% of scheduling time and reduces resource redundancy by 33% compared to the traditional mode.

The grid-connection phase after the mobile generator cluster arrives at the faulty node is a core aspect in evaluating the system’s transient stability. Figure 9 shows the grid connection transient waveforms with predictive feedforward assistance (The times shown in the red boxes indicate state changes at different points in time: 2 s—grid connection; 5 s—load change; 10 s—off-grid.). At 2 s after grid connection, the node load suddenly increases by 0.1 p.u.; at 4 s, the grid disconnects and the mobile generators jointly supply power to the node load; at 5 s, the load returns to normal; at 10 s, the load increases by 0.05 p.u. and the grid resumes power supply, at which point the mobile generators disconnect from the grid. As shown in Figure 9a, in the traditional mode without predictive assistance, the maximum bus voltage fluctuation at the moment of closing exceeds 0.3 p.u., accompanied by an inrush current 1.5 times the rated value. The fundamental reason is that the phase-locked loop’s error feedback loop must wait for the bus parameters to shift after the load is connected before the diesel engine governor and excitation system can adjust. The unit’s inherent mechanical hysteresis makes this adjustment process time-consuming. After introducing a control architecture that combines data-driven feedforward and physical feedback, the system’s grid-connected transient performance was significantly improved (as shown in Figure 9b). Before the grid-connected circuit breaker closes, the controller first extracts the predicted load reference $\widehat{P}$_t+1 of the next time dimension to accurately quantify the expected voltage drop ΔV_ff, and uses it as an open-loop feedforward command to superimpose on the inverter’s excitation reference voltage V_ff* and speed reference value ω_ff* to complete the parameter coarse adjustment. Subsequently, the system relies on the phase-locked loop mechanism to quickly fine-tune the residual phase-angle error, thereby constructing a virtual internal potential that closely matches the load to be connected before physical closure.

Thanks to this multi-time-scale pre-synchronization mechanism, the bus voltage overshoot during closing transients is strictly constrained to within 0.03 p.u., and the current waveform achieves a smooth and seamless transition, thus suppressing transient disturbances in the initial stage of grid connection, as shown in Figure 10. The corresponding dynamic evolution of the power grid is shown in Figure 11. At 2 s, the mobile generator group connects to the grid, accompanied by a local sudden load jump. Since the system already has a potential compensation margin for transient loads, the bus voltage remains stable and without sudden changes at the moment of grid connection, resulting in only a weak transient inrush current with an amplitude of 0.05 p.u. All transient indicators strictly meet the IEEE Std 1547-2018 grid connection specification standard. Furthermore, at 4 s, the main grid disconnects and ceases operation, and the system seamlessly transitions to a power-supply mode in which the three heterogeneous generator groups autonomously and collaboratively support the islanded load. The complete dynamic evolution of the grid-side and generator-side electrical quantities is shown in Figure 12.

Based on the ability of load forecasting to anticipate future load change trends and enable controllers to act in advance, thus significantly reducing frequency fluctuations and adjustment time during grid connection, Figure 13 illustrates the grid connection transient process of three heterogeneous units at 2 s. The transient power allocation process of the three heterogeneous units at 2 s is shown. Facing a load step change condition, the controller of the ESS vehicle captures the maximum value of the predicted rate of change d$\widehat{P}/dt$ and instantaneously outputs high-frequency transient power to compensate for the shortfall. The two DG vehicles achieve a smooth ramp-up under their inherent inertia buffer. After the transient ends, the system achieves a proportional allocation of steady-state load according to the rated capacity ratio of each unit: the two 200 kW diesel vehicles each bear 33.3%, and the one 200 kW energy storage vehicle bears 33.3%. This process avoids violent power oscillations under traditional control and demonstrates the high-dynamic-following performance of the proposed strategy under sudden-change conditions.

As shown in Figure 14, under the traditional control mode, when faced with a load step change, the system frequency drops to a minimum of 49.0 Hz and then recovers with a relatively long time constant. This is because the DG and the ESS, due to differences in impedance characteristics and frequency-regulation bandwidths, are prone to generating transient circulating power currents without predictive coordination. Using the strategy proposed in this paper, when the predictive model output indicates a short-term load step change, the ESS, with its wider response bandwidth, rapidly increases its active power generation using the predictive derivative term to handle high-frequency transient components and provide primary frequency regulation support. The DG, buffered by this, smoothly ramps up the load, and both eventually converge autonomously to a new steady state according to their capacity ratio. The maximum dynamic frequency drop exceeds 49.8 Hz, and the adjustment time is significantly shortened.

To validate the effectiveness and accuracy of the control strategy proposed in this paper, a comparison was conducted against two existing approaches: the improved Virtual Synchronous Generator (VSG) scheme [26]—a method that introduces virtual inertia on the inverter side and currently stands as one of the mainstream solutions for suppressing grid-connected transients—and the purely data-driven Model Predictive Control (MPC) scheme [27]. The results are presented in

Table 4. Comparison of Transient Performance Metrics for Different Control Strategies Under Load Disturbances.

Control Strategy	Maximum Voltage Overshoot (p.u.)	The Frequency Drops to Its Minimum Value (Hz)	Power Oscillation Settling Time (s)	Sensitivity to Communication Latency	Computational Overhead at the Lower Levels
Traditional sag control	0.31	49.02	>4.5	Low	Low
Advanced VSG	0.18	49.45	3.2	Low	Medium
MPC	0.04	49.85	0.5	High	High
Collaborative Strategy in This Article	0.03	49.82	0.4	Low	Low

.

A comparative analysis is presented in Table 4. Although the Advanced VSG technique improves the performance of traditional droop control to some extent, its inherent nature as a post-factum adjustment mechanism (pure feedback) prevents it from avoiding initial transient shocks on a millisecond timescale. The MPC method, leveraging high-frequency receding horizon optimization, achieves excellent transient performance—comparable to that of the proposed strategy—characterized by extremely low voltage overshoot and a frequency dip limited to 49.85 Hz. However, MPC demands exceptionally high online computational power from the underlying inverters, as well as a zero-latency, high-frequency communication network operating at the microsecond level—requirements that are difficult to guarantee within the environment of a post-disaster, damaged distribution grid. The strategy proposed in this paper employs a cross-timescale mapping approach to offload computationally intensive tasks to a supervisory controller, which then dispatches commands at a low frequency; consequently, the underlying DSP is required only to execute simple feedforward compensation and phase-locked closed-loop control. By achieving robust transient shock resistance under extremely low device-level computational load and minimal reliance on communication infrastructure, the proposed method is better aligned with the practical engineering deployment constraints of distributed, heterogeneous mobile power generation units.

3.3. Analysis of System Robustness Under Prediction Errors and Measurement Uncertainties

To evaluate the impact of prediction accuracy deviation on the underlying control performance, the following control experiment was designed: Under the condition of keeping the control parameters unchanged, Gaussian white noise of different intensities was injected into the predicted load signal, so that the equivalent prediction R² gradually degraded from 0.96 (the level of the model in this paper) to 0.90 and 0.85. Changes in the extreme values of grid-connected voltage overshoot and frequency drop were observed, and the results are shown in

Table 5. Impact of Prediction Accuracy on Control Performance.

R2	Grid Voltage Overshoot (p.u.)	Frequency Drop Extreme Value (Hz)	Power Oscillation Amplitude (p.u.)
0.96 (Model in this article)	0.02	49.82	0.03
0.93	0.05	49.75	0.06
0.90	0.09	49.65	0.10
0.85	0.15	49.50	0.18
No prediction (pure feedback)	0.3	49.0	0.45

.

The results show that (1) when the predicted R² is higher than 0.90, the grid voltage overshoot and frequency drop extreme values both meet the national standard requirements (voltage deviation < 0.1 p.u., frequency deviation < 0.5 Hz), and the feedforward control strategy still has a significant transient improvement effect; (2) when R² drops to 0.85, although the control performance degrades, it is still an order of magnitude improvement compared to the pure feedback mode without prediction; (3) the derivative limiter Equation (5) effectively suppresses the amplification of prediction noise, thereby enabling the system to maintain stability even when prediction accuracy degrades. The aforementioned results validate the proposed strategy’s robustness to prediction errors and indicate that maintaining an R² value greater than 0.90 provides a practical lower bound for ensuring control performance.

In the actual operational environment of post-disaster distribution networks, in addition to the inherent prediction errors of data-driven models, the system frequently encounters significant physical measurement uncertainties and real-world background disturbances. To comprehensively validate the robustness of the proposed strategy, this paper further introduces the following two extreme, non-ideal operating scenarios within a simulation platform for stress testing:

• Due to network reconfiguration and line temperature fluctuations resulting from the disaster, the line impedance parameters preset in the controller (used for calculating R_line and X_line in Equation (4)) deviate from the actual physical impedance values. This study establishes two extreme scenarios: one involving a 20% underestimation of impedance and the other involving a 20% overestimation.
• Random Gaussian white noise with a Signal-to-Noise Ratio (SNR) of 20 dB is injected into the system’s voltage and current sampling feedback loops to simulate the harsh electromagnetic interference environment typically encountered in the field.

As shown in

Table 6. Testing of System Transient Performance Metrics Under Measurement Uncertainty and Actual Disturbances.

Interference Conditions Settings	Calculating the Expected Feedforward Error	Grid-Connection Voltage Overshoot (p.u.)	Frequency Drop to Minimum (Hz)	Steady-State Determination
Uninterrupted	0%	0.02	49.82	Stable, with no static error
Underestimation of impedance (−20%)	Low 20%	0.06	49.71	Stable, with a dead time of approximately 80 ms
Overestimation of impedance (+20%)	High 20%	0.08	49.75	Stable, with a dead time of approximately 110 ms
High noise in the sampling loop (20 dB)	High-frequency jitter in instructions	0.05	49.68	Stable, with no resonant divergence

, when a 20% impedance measurement evaluation error occurs, the feedforward compensation command will produce an inherent bias. If the system relies solely on open-loop feedforward control, it will lead to continuous static voltage drops or exceeding limits. However, because the strategy in this paper integrates phase-locked loop and voltage closed-loop feedback fine-tuning mechanisms, the underlying state feedback loop can quickly identify the feedforward calculation residual ev(t) and force the steady-state error back to zero within 100 ms. Under this extreme measurement uncertainty, the grid-connected voltage overshoot only increases to a maximum of 0.08 p.u. (reverse overshoot), still strictly meeting the national standard (<0.1 p.u.) requirement, and without triggering any high-frequency oscillations. At the same time, the system still maintains good convergence under strong background noise. This fully verifies that the proposed feedforward and feedback architecture not only has tolerance for algorithm errors in the data layer, but also has strong engineering robustness against various measured interferences at the physical layer.

4. Analysis of Experimental Results

4.1. Experimental Platform Setup

To validate the engineering feasibility of the proposed scheme, this study constructed an equivalent, simplified hardware-in-the-loop co-simulation platform (as illustrated in Figure 13). On the grid side, the platform employs a Tengfei TFA2000 series three-phase programmable AC power supply (manufactured by Shandong Tengfei Power Supply Co., Ltd., Jinan, Shandong, China) to simulate main grid characteristics (maximum output power: 150 kVA). On the load side, an ETHLEY ACL-R series programmable AC electronic load (manufactured by Suzhou Jishili Electronic Power Supply Co., Ltd., Suzhou, Jiangsu, China), with a power regulation range of 100 kW and an allowable voltage range of 0–1500 V, is configured to replicate dynamic load-step conditions within a distribution network. The heterogeneous power-source side consists of two diesel generator vehicles—each with a simulated output capacity of 200 kVA—and one 200 kVA energy-storage generator vehicle; the rated grid-connection voltage for all units is uniformly set to 400 V (with experimental testing conducted at actual capacities below 20%). Within the hierarchical collaborative control architecture, the macro-scheduling layer is deployed on a high-performance computing platform (featuring an Intel i7-11800H processor and an RTX 3050Ti graphics card) and runs a CNN-BiLSTM-Attention prediction model. The extracted steady-state load prediction baseline is transmitted downward via a serial bus at a low communication frequency, providing a basis for feed-forward coarse-tuning to assist the underlying layer in constructing a virtual internal electromotive force. The underlying physical execution layer is governed by two Digital Signal Processors (DSPs), which perform real-time acquisition of electrical state variables via analog I/O interfaces. Upon receiving the feed-forward baseline, this layer relies entirely on local high-frequency feedback loops to autonomously drive the phase-locked closed-loop fine-tuning and the heterogeneous power source transient decoupling algorithms. This approach—by bypassing conventional mechanical startup and warm-up procedures—validates the robustness and smooth transition performance of the proposed hardware–software collaborative grid-connection algorithm for heterogeneous clusters. The heterogeneous generator vehicles connect to the grid at the 125 s mark, the simulated grid disconnects at 320 s, and a sudden load increase occurs at 205 s; the entire process is illustrated in Figure 15.

After receiving the feedforward benchmark, it autonomously drives the phase-locked loop fine adjustment and heterogeneous power supply transient decoupling algorithm entirely based on the local high-frequency feedback loop. This allows verification of the robustness and smooth transition performance of the heterogeneous cluster hardware–software collaborative grid connection algorithm without accounting for conventional mechanical start-up and warm-up time. The heterogeneous generator was connected to the grid at 125 s, the grid was simulated to disconnect at 320 s, and the load suddenly increased at 205 s. The whole process is shown in Figure 16.

4.2. Results Analysis

Furthermore, total harmonic distortion (THD) analysis was performed on the voltage and current during steady-state grid connection, load surge, and disconnection processes, as shown in Figure 17. During grid connection and disconnection, the THD of both types of emergency generators remained at 1.25%, but jumped to 2.5% during load surges, as shown in Figure 17a. The distortion differences between the different types of emergency generators were mainly concentrated at the moment of disconnection. Due to the mechanical inertial delay of the internal combustion engine’s physical speed regulation, both DGs exhibited significant transient current distortion during disconnection, with THD increasing to approximately 4%. Conversely, the ESS, with its millisecond-level instantaneous power discharge capability, effectively mitigated the transient current impact caused by load shedding, significantly reducing the current THD to 1.25%, as shown in Figure 17b. This is because the rapid power buffering of the energy storage unit effectively compensated for the DG’s transient response lag. Combined with the low THD index throughout the period and stable load changes, the system’s overall power supply quality fully meets the grid connection standards. This not only reflects the advantages of the synergistic complementarity of the “energy storage + diesel” heterogeneous power sources, but also fully demonstrates the effectiveness of the proposed predictive feedforward control mechanism in suppressing transient distortion and improving the system’s dynamic robustness.

As shown in Figure 18a, the frequency fluctuations under the proposed strategy are all within ±0.2 Hz, achieving seamless grid connection. During the grid connection process for the traditional model, the frequency at its lowest point exceeded the national grid connection standard by ±0.2 Hz, reaching a minimum deviation of 0.24 Hz, resulting in grid connection failure and increasing manual operation time. The grid disconnection process is shown in Figure 18b, where the proposed strategy is also evident to be significantly advantageous. Figure 18c shows the frequency changes during the complete experimental process, with fluctuations ranging from 49.9 to 50.1 Hz.

Figure 19 quantitatively verifies the transient response characteristics of the three emergency power supplies under grid-connected, load-surge, and disconnection conditions. The experiment shows that during complex mode switching, the system’s B-phase output voltage remains a smooth, continuous sinusoidal waveform, with only minor fluctuations of ±1 to 2 V due to the inherent physical characteristics of the generators. Regarding the current response, the system exhibits rapid dynamic adjustment capability: the current stabilizes at 12.5 A during grid connection and disconnection, and the current amplitude responds quickly under load surge conditions. Furthermore, the voltages of the three units stabilize at the rated voltage of 311 V, confirming the system’s synchronous control and power-sharing (current-sharing) capabilities under the proposed strategy.

To quantify the improvement in on-site operation and maintenance efficiency achieved by the proposed strategy, this experiment statistically analyzed the unit reset time under 10 different load-change conditions, as shown in

Table 7. Statistics on manual debugging time.

Experiment Number	1	2	3	4	…	8	9	10	Mean ± Standard Deviation
Traditional control	258	270	249	283	…	290	253	269	265 ± 18
This article’s strategy	218	232	210	240	…	245	215	217	224 ± 15

. Under the traditional control mode, the generator car employs a standard PLL-based grid connection with fixed-parameter droop control, without load-prediction feedforward. On-site operators need to manually adjust the secondary frequency regulation command, droop intercept, and excitation reference value according to the frequency and voltage over-limit indicators. The manual intervention process after each load change includes (1) observing the over-limit alarm (about 30 s); (2) judging the adjustment direction and amplitude (about 60 s); (3) manually issuing the adjustment command (about 30 s); (4) waiting for the system to stabilize and confirm (about 145 s), with an average intervention time of about 265 s. Under the prediction feedforward and adaptive transient decoupling mechanism in this paper, the system realizes autonomous power coordination, and steps (2) and (3) are greatly simplified to status confirmation. The average manual intervention time for a single-change condition is reduced to 224 s, a 15.4% reduction overall.

5. Conclusions

This paper addresses the challenges of resource mismatch and transient instability in the emergency recovery of distribution networks during extreme disasters. It proposes a multi-timescale, heterogeneous generator group active collaborative control strategy based on data-driven feedforward and physical feedback.

(1)

The constructed CNN-BiLSTM-Attention prediction model extracts the spatiotemporal features of complex loads at multiple end nodes. In tests on typical heterogeneous nodes, the model’s coefficient of determination (R²) ranges from 0.957 to 0.965, and the attention mechanism improves the average prediction accuracy by 1.7% over the baseline model.

(2)

A collaborative mechanism of expected voltage drop feedforward coarse adjustment and phase-locked loop fine adjustment is proposed. This mechanism reduces the voltage overshoot at the moment of load closing from 0.30 p.u. to within 0.03 p.u. and strictly constrains frequency fluctuations to ±0.2 Hz under multiple load-change conditions, achieving smooth and seamless grid connection.

(3)

Energy storage and DG sets absorb transient impacts and steady-state base loads, respectively, based on their inherent frequency band differences, significantly improving the frequency drop extreme value from 49.0 Hz to above 49.8 Hz. At the same time, feedforward optimization replaces the cumbersome manual trial-and-error process, reducing on-site commissioning synchronization time by 15.4% and improving the microgrid’s emergency recovery response speed.

Although this paper validates the effectiveness of the proposed strategy using a scaled hardware-in-the-loop platform, disparities remain between this platform and an actual mobile power generation vehicle system—specifically regarding power ratings, mechanical dynamics, communication conditions, and environmental disturbances. Consequently, the engineering generalizability of the conclusions drawn herein requires further verification. It should be noted, however, that the research platform employed in this study adheres to the principle of power-scaled equivalence, maintaining consistent critical control time constants and effectively capturing the dynamic characteristics of the proposed control method. Furthermore, the core algorithms—including feedforward compensation, PLL fine-tuning, and frequency band allocation—are primarily software-implemented, thereby ensuring their transferability. Future research will leverage medium-capacity diesel generator sets, hardware-in-the-loop platforms, and real-world field trials to conduct in-depth investigations into the applicability and robustness of the proposed method under high-power conditions, complex communication environments, and severe disturbances.