With the rapid depletion of fossil fuels and increasing environmental concerns, the integration of renewable energy sources such as photovoltaic (PV) generation into the power grid has become a global priority. However, the intermittent nature of PV power and the lack of inherent inertia in inverter-based interfaces pose significant challenges to grid stability. To address these issues, we propose a coordinated control strategy that combines frequency-splitting power management with an adaptive virtual synchronous generator (VSG) scheme for a grid-connected PV hybrid battery energy storage systems. The proposed approach leverages a battery energy storage systems (BESS) and a supercapacitor to smooth power fluctuations, while the adaptive VSG provides dynamic frequency support by tuning its inertia and damping coefficients in real time. Extensive simulations under various operating conditions demonstrate that the strategy effectively suppresses frequency oscillations, enhances dynamic response, and improves the overall robustness of the system.
1. Introduction
Modern power systems are witnessing a paradigm shift towards distributed generation. Among the various renewable sources, photovoltaic systems are widely deployed due to their abundance and declining costs. Nevertheless, the high penetration of PV units reduces the system’s equivalent rotational inertia, making the grid more vulnerable to frequency disturbances. Battery energy storage systems (BESS) offer a promising solution by providing rapid power balancing and energy buffering. In many microgrid configurations, PV, battery energy storage systems, and other distributed resources are interfaced through inverters. Traditional vector control methods decouple active and reactive power but fail to emulate the inertial response of synchronous generators. The virtual synchronous generator (VSG) technique has emerged as an effective way to replicate the swing dynamics of synchronous machines, thereby improving frequency stability. However, conventional VSG controllers use fixed inertia and damping parameters, which may not be optimal under varying grid conditions. To overcome this limitation, we develop an adaptive VSG control where both the virtual inertia \(J\) and damping coefficient \(D\) are adjusted according to the system’s transient state. The adaptive law is derived from the second-order system theory and constrained by the damping ratio requirement to ensure stable operation. Furthermore, a frequency-splitting method is employed to coordinate the battery energy storage systems and the supercapacitor, reducing stress on the battery and prolonging its cycle life.
2. System Configuration and Modeling
The overall system consists of a PV array, a hybrid energy storage unit comprising a battery and a supercapacitor, a DC-DC converter for each source, and a three-phase inverter interfacing the DC bus to the AC grid. The PV array operates under maximum power point tracking (MPPT) using a variable-step incremental conductance algorithm. The DC bus voltage is regulated by the bidirectional converters of the storage units. The inverter is controlled by the proposed adaptive VSG algorithm, which generates the modulation signals for the power switches.
Figure 1 (not shown) illustrates the detailed topology of the considered PV hybrid battery energy storage systems. The battery is the primary long-term storage element, while the supercapacitor handles high-frequency power fluctuations. This hybrid configuration improves the dynamic performance and extends the operational lifetime of the battery energy storage systems. The control structure of the hybrid storage system is depicted in Table 1, which lists the key functions of each component.
| Component | Role |
|---|---|
| Battery | Low-frequency power smoothing, long-term energy balance |
| Supercapacitor | High-frequency ripple suppression, fast transient response |
| Frequency splitter | Separates power command into low and high frequency components |
| Voltage regulator | Maintains DC bus voltage within ±1% of reference (750 V) |
The power sharing between the battery and supercapacitor is achieved via a low-pass filter. The filtered component is assigned to the battery, while the residual high-frequency component is handled by the supercapacitor. This reduces the number of charge/discharge cycles of the battery energy storage systems, thereby improving its longevity.
3. Adaptive Virtual Synchronous Generator Control
3.1 Fundamental Principles of VSG
The VSG control mimics the swing equation of a synchronous generator. The active power-frequency relationship is given by:
$$ P_m = K_\omega (\omega_{ref} – \omega_g) + P_{ref} $$
where \(P_m\) is the mechanical power, \(P_{ref}\) the reference active power, \(\omega_{ref}\) the reference angular frequency, \(\omega_g\) the grid angular frequency, and \(K_\omega\) the droop coefficient. The rotor motion equation of the VSG is:
$$ J \frac{d\omega}{dt} = \frac{P_{ref} – P_e}{\omega_g} + D_0(\omega_g – \omega) $$
$$ \frac{d\theta}{dt} = \omega – \omega_g $$
where \(P_e\) is the electromagnetic power, \(J\) the virtual inertia, \(D_0\) the damping coefficient, and \(\theta\) the power angle. The reactive power-voltage control is expressed as:
$$ E = K_v (K_Q (Q_{ref} – Q) + U_n – U_e) $$
where \(E\) is the virtual electromotive force, \(Q_{ref}\) and \(Q\) are the reference and actual reactive power, \(K_Q\) the voltage droop coefficient, \(U_n\) the nominal voltage, and \(U_e\) the output voltage.
3.2 Power-Angle Characteristic Analysis
The transient behavior of the VSG can be studied using the power-angle curve. During a disturbance, the rotor angular frequency \(\omega\) oscillates around the synchronizing frequency \(\omega_0\). The acceleration/deceleration phases are characterized by the sign of \(\Delta\omega = \omega – \omega_0\) and its derivative \(d\omega/dt\). Table 2 summarizes the adaptive rules for \(J\) and \(D\) derived from the oscillation analysis.
| Stage | \(\Delta\omega\) | \(d\omega/dt\) | \(\Delta\omega \cdot d\omega/dt\) | \(J\) | \(D\) |
|---|---|---|---|---|---|
| 1 | >0 | >0 | >0 | Increase | Increase |
| 2 | >0 | <0 | <0 | Decrease | Increase |
| 3 | <0 | >0 | <0 | Increase | Increase |
| 4 | <0 | <0 | >0 | Decrease | Increase |
From Table 2, when the angular frequency deviation and its derivative have the same sign (stages 1 and 4), the rotor is accelerating away from the equilibrium, so increasing \(J\) helps to limit the rate of change. Conversely, when the signs differ (stages 2 and 3), decreasing \(J\) allows faster recovery. The damping coefficient should always be increased to suppress oscillations. However, independent adjustment of \(J\) and \(D\) may lead to instability; therefore, we introduce a coupling constraint based on the damping ratio \(\xi\).
3.3 Constrained Adaptive Parameter Design
The active power loop of the VSG can be represented by a second-order transfer function:
$$ G_p(s) = \frac{K_P}{J\omega_0 s^2 + D_p \omega_0 s + K_P} $$
with \(K_P \approx 3E_0 U_0 / X\). The natural frequency \(\omega_n\) and damping ratio \(\xi\) are:
$$ \omega_n = \sqrt{\frac{K_P}{J\omega_0}} $$
$$ \xi = \frac{D_p}{2} \sqrt{\frac{\omega_0}{J K_P}} $$
To achieve a satisfactory dynamic response, we require the system to be underdamped with \(0.4 < \xi < 1\) and a phase margin \(\gamma > 60^\circ\). The corresponding constraint on \(D_p\) and \(J\) is derived as:
$$ \xi = \frac{D_p}{2} \sqrt{\frac{\omega_0}{J K_P}} > 0.612 $$
Additionally, the settling time condition \(t_s = 4/(\xi \omega_n) \leq 0.4\) s leads to:
$$ \text{Re}(s_i) = -\xi \omega_n = -\frac{D_p}{2J} \leq -10 $$
Combining these constraints with the cutoff frequency limitation \(f_{cp} \leq 10\) Hz, the feasible ranges for \(J\) and \(D_p\) are obtained as \(0 < J < 0.5\) kg·m² and \(10.5 < D_p < 24.0\) N·m·s. The adaptive functions are formulated as:
$$ J = \begin{cases}
J_0, & |d\omega/dt| \leq T_j \cup \Delta\omega \cdot d\omega/dt \leq 0 \\
J_0 + K_{J1} \, |\Delta\omega \cdot d\omega/dt|, & |d\omega/dt| > T_j \cap \Delta\omega \cdot d\omega/dt > 0 \\
J_0 – K_{J2} \, |\Delta\omega \cdot d\omega/dt|, & |d\omega/dt| > T_j \cap \Delta\omega \cdot d\omega/dt \leq 0
\end{cases} $$
$$ D_p = \begin{cases}
D_0, & |\Delta\omega| \leq T_d \\
D_0 + K_D \, |\Delta\omega|, & |\Delta\omega| > T_d
\end{cases} $$
where \(J_0 = 0.2\) kg·m², \(D_0 = 10.5\) N·m·s, \(K_{J1} = 0.1\), \(K_{J2} = 0.003\), \(K_D = 5\), \(T_j = 1\), and \(T_d = 0.05\). The proposed adaptive VSG ensures that the battery energy storage systems provide frequency support while maintaining system stability under varying grid conditions.
4. Simulation Results and Discussion
4.1 Simulation Setup
We built a detailed model of the PV hybrid battery energy storage systems in MATLAB/Simulink. The key parameters are listed in Table 3.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| DC bus voltage | 750 V | \(J_0\) | 0.2 kg·m² |
| Grid line voltage | 380 V | \(D_0\) | 10.5 N·m·s |
| Nominal frequency | 50 Hz | \(T_j\) | 1 |
| DC bus capacitor | 18 μF | \(T_d\) | 0.05 |
| Filter capacitor | 24 μF | \(K_{J1}\) | 0.1 |
| Filter inductor | 1.8 mH | \(K_{J2}\) | 0.003 |
| Storage inductor | 5 mH | \(K_D\) | 5 |
4.2 Scenario 1: Variable Solar Irradiance
We set the initial irradiance to 1000 W/m² at 25°C, with the VSG active power reference \(P_{ref} = 10\) kW and load 8 kW. At \(t=1\) s, irradiance steps up to 1200 W/m², and at \(t=2\) s, steps down to 600 W/m². The results show that when irradiance increases, the PV power exceeds the VSG command, and the battery energy storage systems absorb the surplus (approximately 2 kW). The battery’s state of charge (SOC) rises, indicating charging, while the supercapacitor handles the transient spikes. When irradiance drops, the battery releases energy to compensate the deficit. The DC bus voltage remains within 750 V ± 1%. The adaptive VSG adjusts its inertia and damping in real time, resulting in smoother frequency and power responses compared to fixed-parameter VSG. The battery energy storage systems effectively balance the power mismatch without excessive cycling.
4.3 Scenario 2: Power Reference and Load Changes
In the second scenario, we keep the irradiance constant at 1000 W/m². At \(t=1\) s, the VSG power reference steps from 10 kW to 12 kW, and at \(t=2\) s, the load increases by 2 kW. The hybrid battery energy storage systems immediately supply the deficit. During the first step, the battery provides 2 kW, and the supercapacitor smoothes the transient. After the load change, the battery output increases further. The adaptive VSG reduces frequency overshoot and settling time. The SOC of the battery decreases accordingly, confirming proper discharge. The frequency deviation is kept within ±0.2 Hz, meeting grid code requirements. These experiments validate that the proposed control strategy for battery energy storage systems improves dynamic performance and frequency stability under multiple disturbances.
5. Conclusion
We have developed a comprehensive control framework for grid-connected PV hybrid battery energy storage systems that integrates frequency-splitting power management with an adaptive VSG. The frequency-splitting method effectively coordinates the battery and supercapacitor, reducing stress on the battery energy storage systems and extending its lifetime. The adaptive VSG adjusts virtual inertia and damping coefficients based on the system’s instantaneous state, while respecting damping ratio constraints to ensure stability. Simulation results under varying irradiance and load conditions demonstrate that the proposed strategy significantly suppresses frequency fluctuations, enhances dynamic response, and maintains robust operation. The battery energy storage systems play a crucial role in providing the necessary power balance and inertia support. Future work will focus on experimental validation and the integration of state-of-charge limits into the adaptive law.