To address climate change and accelerate the green and low-carbon transition of energy systems, countries worldwide are vigorously expanding their renewable energy infrastructure. Renewable energy generation is typically integrated into power grids through power electronic devices, which inherently lack the capability to provide damping and inertial support to the grid, posing significant challenges to grid stability (Zhang et al., 2022). As the proportion of grid-connected PV systems increases, frequency-related issues in power systems have become increasingly prominent (Kurm and Agarwal, 2021; Pei et al., 2020; Chai et al., 2021). Current approaches to enable PV power plants with primary frequency regulation and inertial support capabilities include active power reserve and energy storage integration. By combining energy storage with PV systems to form PV-ESS integrated systems and adopting VSG control strategies, effective grid frequency support can be achieved during load disturbances (Nguyen et al., 2019; Shenghu et al., 2024; Chen et al., 2024).

In recent years, research on photovoltaic frequency regulation technologies has grown substantially, with the primary objective of empowering PV power plants to participate in grid frequency regulation through advanced control strategies, thereby ensuring the secure and stable operation of modern power systems. Peng et al. (2025) incorporate PV systems into conventional power system models, deriving time-domain analytical solutions for frequency dynamics, which provides a more accurate and comprehensive literature for analyzing frequency characteristics in PV-integrated grids. Zhao et al. (2024) propose an enhanced voltage-controlled, deloaded PV virtual synchronous generator frequency support method with adaptive reserve ratios, significantly improving the efficacy of PV systems in grid frequency regulation. Zhang et al. (2024) introduce a consensus-based frequency regulation strategy for PV plants utilizing the average consensus algorithm, enabling coordinated frequency control among multiple PV stations under localized communication constraints. Zhong et al. (2022) develop a hybrid control strategy integrating a deloading operation with virtual synchronous machine (VSM) control. Sun et al. (2022) incorporate generator droop characteristics into deloaded power control frameworks, endowing PV plants with active frequency oscillation suppression capabilities. Zhong et al. (2019) propose a control strategy for PV cluster participation in primary frequency regulation, which accounts for the derating factor and multiple parameters to enhance system operation stability.

The critical role of energy storage in frequency regulation lies in its ability to rapidly absorb or release energy through storage systems, compensating for grid power deficits and mitigating instantaneous imbalances between load fluctuations and generation. Ren (2024) propose embedding fast frequency regulation devices between the grid and energy storage stations to achieve rapid coordinated power dispatch. Qian et al. (2024) proposes using a flywheel energy storage system to assist in endowing pumping and power generation conditions with the same frequency regulation capability. Dang et al. (2025) develop a dual-layer power optimization framework for multi-storage plants that balances system economics with state-of-charge equilibrium, minimizing frequency regulation costs. He et al. (2024) propose a frequency-decoupled composite control strategy based on real-time battery status monitoring, improving the frequency regulation performance of energy storage batteries. Zhao et al. (2020) propose a control strategy for optimizing the dead zone of power grid energy storage frequency regulation, which enhances system stability.

The PV-ESS compensates for the volatility of the PV output by controlling the energy storage in concert with the PV power plant, using the fast power response capability of the energy storage and providing virtual inertia support and frequency regulation services for the grid. Tiecheng et al. (2023) propose the use of a supercapacitor to assist PV units for frequency regulation, which effectively enhances the frequency stability of high-occupancy PV systems. Yongxi and Jiangrong (2023) proposed an improved VSG control strategy for the problems of fixed inertial link parameters and difficult real-time adjustment in the traditional virtual synchronous machine control strategy. Jia et al. (2022) combine the variable power tracking technology with a supercapacitor to form a new coordinated control strategy for PV energy storage. Zhang et al. (2023) propose that the PV energy storage system and synchronous generator be considered to be connected through a virtual shaft system, so that the PV energy storage system can simulate the dynamic characteristics of the synchronous generator’s shaft system and provide a new method for the friendly grid connection of the PV-ESS. Ur Rehman et al. (2021) propose a method to grid-connect PV and energy storage via VSG and provide inertial support. Hongchun et al. (2025) propose a cooperative control strategy for PV-hybrid battery energy storage systems to improve the system frequency response characteristics.

Because the virtual inertia and virtual damping coefficient are the core parameters in the VSG control technique, adjusting the VSG control parameters to improve the system dynamics and response performance has become the focus of today’s research. Jianhui et al. (2019) proposed an adaptive adjustment of virtual inertia VSG control strategy, which can effectively suppress the fluctuation of system active power. Ren et al. (2021) combined virtual impedance control with adaptive control to improve the frequency response characteristics of the system. Lu et al. (2024) derived the initial value of adaptive virtual inertia control based on an improved particle swarm algorithm, which improves the stability of the VSG grid-connected system. Fu et al. (2024) proposed the introduction of a virtual governor model, so that the primary frequency regulation under the action of delay and damping control is relatively independent, thus facilitating the completion of the control parameter design separately and effectively solving the problem of the traditional VSG control in the primary frequency regulation and damping is difficult to take into account. Ren et al. (2020) used the output angular frequency feedback control to regulate the dynamic damping of the VSG grid-connected system, which improves the performance of the system frequency regulation.

None of the above studies have deeply explored the dynamic control of parameters of the combined PV-ESS. Therefore, this article proposes an adaptive optimized strategy for the parameters of the combined photovoltaic and storage system based on GA-BP. First, the control principles of VSG active and reactive loops are introduced, and GA-BP is used for dynamic optimization of J and D in the active loop. Second, the load shedding control adopted for PV is analyzed to determine the PV load shedding control operating point. Subsequently, the ESS is introduced to use virtual inertia control. The virtual inertia control coefficients are also used in a GA-BP optimized strategy, and their dynamic changes follow the change rule of the S-type function. Finally, the effectiveness and superiority of the described adaptive optimized strategy in suppressing the frequency fluctuation of a high percentage of PV grid-connected are verified through an RT-LAB simulation as well as a hardware experimental comparison test.

GA has a strong global search ability that can avoid the defect of traditional optimization methods falling into local optimal solutions. In this article, GA and BP neural networks are deeply integrated to construct a GA-BP neural network optimization algorithm model, and through the synergistic cooperation of the two, a hybrid algorithm with better performance is obtained to optimize the parameters of the optical storage system. On the one hand, the BP is used to adjust the parameters of the PV-ESS dynamically according to the error of the desired signal and the actual signal; on the other hand, the GA is used to optimize the weight and bias of the BP globally, which significantly improves the efficiency of parameter search. The weights and biases of the BP are optimized globally with the help of GA, which significantly improves the parameter optimization efficiency. In this model, the GA dynamically optimizes the initial weights and bias parameters of the BP to break through the limitations of the traditional random initialization on the performance of the network so that the model has a faster convergence speed and a stronger generalization ability. The following are the specific steps of the algorithm implementation:

(1) The dynamic model of PV-ESS is formulated in Equation 24

The following is a specific explanation of each part of the multi-objective loss function as A: B = 1 T ∑ t = 1 T y r e f t − y t 2 (27) In Equation 27, where y _ref(t) is the literature output; y(t) is the actual output. This equation calculates the difference between the literature output y _ref(t) and the actual output y(t). C = λ 1 W 2 2 (28) In Equation 28, where λ ₁ is the weighting factor. This equation is used to prevent overfitting and make the model more generalized by increasing the penalty term of the weights. D = λ 2 ∑ t = 1 T u t 2 (29) In Equation 29, where λ ₂ is the weighting factor of the control energy consumption term. This equation reduces the energy consumption of the system by minimizing the control input. E = λ 3 ∑ t = 1 T I b a t t (30) In Equation 30, where λ ₃ is the weighting factor of the battery aging term. This equation is used to reduce the number and magnitude of charging and discharging of the battery, thus prolonging the lifetime of the battery.

(3) Chromosome code length:

For each individual k in the population, calculate its selection probability: P k = F k ∑ s = 1 N F s (33) where N is the population size.

(7) The crossover operation is defined by Equations 34, 35:

Cross-segmentation is used for the selected parents (P ₁, P ₂) for the neural network hidden layer weights w _ij part: C w i j = φ P 1 w i j + 1 − φ P 2 w i j (34) Bias the b _j part to the neural network: C b j = μ P 1 b j + 1 − μ P 2 b j (35) where φ and μ are the crossover coefficients.

(8) The mutation operation is defined by Equations 36–38:

For each locus x _i , mutate with probability p _m : x i ′ = x i + σ i · N 0 , 1 (36) where x _i ′ is the gene value after the mutation. x _i is the original gene value. σ i is the intensity of variation, which controls the magnitude of variation. N 0 , 1 is the standard normal distribution, which represents the random perturbation.

Calculate the intensity of variation σ i , σ i = σ max · 1 − t T max 2 max (37) where σ max is the maximum variation intensity; t is the current iteration number; T _max is the maximum iteration number.

Projective corrections are applied to the mutated parameters: x i ′ = x i min , x i ′ < x i min x i max , x i ′ > x i max x i ′ , e l s e (38)

(9) The BP neural network design is formally expressed in Equations 39–43:

Step 1. Import the input variables. The ith neuron in the input layer is X _i ;

Step 2. Calculate the input value h j i n and the output value h j o u t of the jth neuron h _j in the hidden layer; h j i n = ∑ i = 1 3 w i j i n X i + b j (39) h j o u t = f i n h j i n (40)

The activation function of the hidden layer uses the sigmoid function: f i n x = 1 1 + e − x (41)

Step 3. Calculate the input and output quantities of the output layer. The input y i i n of the ith neuron of the output layer is y i i n = ∑ j = 1 n W i j h j + B j (42)

The output of neuron i in the output layer, y i o u t , is J = y i o u t = f o u t y i i n , i = 1 D = y i o u t = f o u t y i i n , i = 2 K = y i o u t = f o u t y i i n , i = 3 (43)

where the activation function of the output layer is also chosen to use the sigmoid function.

The above GA-BP is applied to the optimization process of the VSG control parameters J and D of the optical storage system, as well as the virtual inertia coefficient K of the energy storage dynamics. The flowchart of the GA-BP shown in Figure 8 is obtained. First, the GA is used to find the optimal weights and bias values in the BP; then the optimal weights and bias values are inputted into the BP; then the BP dynamically outputs the control parameters such as K, J, and D according to the inputs as well as the optimal weights and bias values, and the parameters are returned to Equations 2, 18 after the adaptive adjustments to realize the adaptive closed-loop control of K, J, and D. Closed-loop control can be realized by returning the adaptively adjusted parameters to Equations 2, 18.

In this study, a digital twin model of an optical storage, multi-source cooperative control system is constructed based on the RT-LAB platform, and the proposed cooperative control strategy is verified through comparative simulation. As shown in Figure 9, the real-time simulation system adopts a heterogeneous computing architecture, integrating multi-core CPUs, field-programmable gate array (FPGA) hardware acceleration units, and development hosts, in which the CPU cluster undertakes the numerical solving tasks of the electromagnetic transient model of the new energy station cluster and the dynamic model of the three-machine, nine-node system and realizes multi-protocol communication, such as CAN and IEC61850. The FPGA module performs the microsecond-level step execution of the power electronics converter. The FPGA module performs accurate power electronic converter modeling and SFP + fiber optic communication protocol processing in microsecond steps and realizes nanosecond data interaction with the main computing unit via PCIe Gen4 ×16 bus, constructing a deterministic simulation environment with a fixed step size of 50 ms for the whole system.

The installed capacity of the PV array is 4 MW. The parameters of the PV array are set according to the model of SunPower SPR-200-WHT-U, and 20 strings and 20 parallels are set as a group; there are a total of 50 groups under the standard ambient temperature and irradiance conditions. The output power of this PV array is maximally 4 MW. PV strings are connected to the converter through a convergence box and then connected to the DC bus after boosting. The DC side voltage is 600 V, and the AC side voltage is 380 V. After two boosts, the PV string is connected to the 35-kV main grid. The installed capacity of the energy storage system is 1 MW, and the rated load shedding rate of PV is K _f = 0.9. The parameter of the energy storage system is SOC _initial = 0.8. The simulation results are based on the standardized value, and the power literature value is 5 MW.

This article proposes a GA-BP-based adaptive parameter adjustment method to dynamically optimize the virtual inertia J, damping coefficient D, and droop coefficient K in real time. A GA-BP driven adaptive optimization strategy for PV-ESS is developed to suppress frequency oscillations, shorten regulation time, and enhance system stability. The main conclusions are as follows:

(1) Compared to fixed-parameter control strategies for K, J, and D, the proposed GA-BP-based parameter adaptive dynamic adjustment strategy significantly improves frequency stability and dynamic response performance. The frequency nadir deviation is reduced by 14.81%, the overshoot amplitude is suppressed by 62.5%, and the steady-state recovery time is shortened by 44.44%, demonstrating the effectiveness of the proposed strategy in enhancing transient stability and mitigating power oscillations.