This work addresses the accelerated aging of energy storage cells due to overcharging or overdischarging in photovoltaic-energy storage AC microgrids, as well as the insufficient voltage and frequency support capability of the system during load fluctuations and faults. A cooperative control strategy is proposed that considers the state of charge (SOC) characteristics of the energy storage cell. Four operating modes are designed based on the real-time power difference between generation and load, as well as the SOC of the energy storage cell. Mode switching is achieved through the cooperative control of the front-end converters of the photovoltaic system and the energy storage cell. This optimizes energy management while protecting the energy storage cell. For the back-end inverter control, a first-order transient voltage equation is introduced as the excitation controller based on the virtual synchronous generator, forming a third-order model of a synchronous machine. Additionally, dynamic damping control based on the deviation between the grid angular velocity and the virtual angular velocity is incorporated to enhance system stability and disturbance rejection capability. The effectiveness of the proposed strategy is validated through MATLAB/Simulink simulations and hardware-in-the-loop experiments.
Introduction
With the transformation of the global energy structure and the rapid development of renewable energy, photovoltaic-energy storage microgrids have attracted widespread attention. While an energy storage cell can smooth the power deviation between photovoltaic output and load, its frequent charging and discharging can lead to overcharging and overdischarging, thus affecting the lifespan of the energy storage cell. Existing research has addressed energy management considering SOC, but the increasing complexity of microgrids demands further reliability and efficiency. Furthermore, photovoltaic and energy storage converters lack the rotational inertia and damping of traditional generators, making it difficult to provide grid regulation and active support. Grid-forming inverters address this by enabling voltage and frequency support similar to synchronous machines. Current research directions focus on grid-forming control methods that consider the SOC characteristics of the energy storage cell, but challenges remain in dynamic optimization, real-time adaptation, and voltage stability. This work proposes a cooperative control strategy that integrates energy storage cell SOC management with a third-order grid-forming control to enhance system performance.
The key innovations of this work are as follows: A three-region division method based on the nonlinear terminal voltage-SOC characteristic of the energy storage cell is proposed. Mode switching is achieved through front-end converters, which fully utilizes the regulation capability of the energy storage cell while effectively avoiding overcharging and overdischarging. A third-order grid-forming control strategy is proposed by introducing a first-order transient voltage equation as the excitation controller into the virtual synchronous generator. Dynamic damping control based on the grid-virtual angular velocity deviation is incorporated to enhance disturbance rejection and voltage support capability. A collaborative optimization framework for energy storage cell lifespan, dynamic response, and grid support is constructed, achieving synchronous breakthroughs in dynamic response speed and fault ride-through capability while ensuring the health of the energy storage cell.
| Reference | Limitations |
|---|---|
| Literature [14] | Dynamic optimization of adjustment coefficients for the energy storage cell’s output power was not considered. |
| Literature [15] | The dynamic nonlinear characteristics of the energy storage cell were not considered. |
| Literature [16] | The voltage stability issue caused by active-reactive power coupling of VSG was not addressed. |
System Structure of Photovoltaic-Energy Storage AC Microgrid
The studied photovoltaic-energy storage AC microgrid consists of a photovoltaic system, an energy storage system (ESS) with at least one energy storage cell, converters, loads, and the grid. Both the photovoltaic inverter and the energy storage inverter adopt a two-stage structure connected via their respective DC/DC converters to a common DC bus. The DC power is converted to AC power through inverters and then sent to local loads and the grid via filter circuits. The front-end DC/DC converter of the photovoltaic system uses a Boost circuit to implement maximum power point tracking (MPPT) or constant power control based on the photovoltaic output, load demand, and the SOC of the energy storage cell. The energy storage system uses a bidirectional DC/DC converter connected in parallel with the photovoltaic unit, switching between Buck and Boost modes to regulate DC bus voltage and achieve power decoupling. The back-end inverter adopts a third-order grid-forming control strategy. This strategy optimizes the second-order model by introducing a first-order transient voltage equation to simulate the mechanical characteristics of a synchronous machine, thereby enhancing the active power-frequency and reactive power-voltage support capability of the system during faults.
| Unit | Function |
|---|---|
| Photovoltaic System | Main energy source; operates in MPPT or constant power mode to control power output. |
| Energy Storage System (ESS) | Contains at least one energy storage cell; provides power balance, offers inertia and damping, and maintains DC bus voltage. |
| Front-end DC/DC Converter (PV) | Boost converter for maximum power tracking or power limiting based on energy storage cell SOC. |
| Front-end DC/DC Converter (ESS) | Bidirectional converter for charging/discharging the energy storage cell and regulating DC bus voltage. |
| Back-end Inverter | Grid-forming converter using third-order synchronous machine model for voltage and frequency support. |
Energy Management Strategy Considering Energy Storage Cell SOC
Characteristics of Energy Storage Cell for Different SOC
A lithium-ion battery is chosen as the energy storage cell. A first-order RC model is used to simulate the terminal voltage of the energy storage cell. The open-circuit voltage of the energy storage cell can be expressed as a function of SOC. The terminal voltage of the energy storage cell and its SOC relationship allows for a three-region division: overcharge region, normal region, and overdischarge region. Based on these characteristics, when the photovoltaic output changes, the SOC of the energy storage cell is strictly monitored to prevent accelerated aging due to overcharging or overdischarging.
The relationship between the open-circuit voltage of the energy storage cell (Voc) and its SOC is given by:
$$ V_{oc} = K_1 + K_2 S_{SOC} + K_3 S_{SOC}^2 + K_4 S_{SOC}^3 + \frac{K_5}{S_{SOC}} + K_6 \ln S_{SOC} + K_7 \ln(1 – S_{SOC}) $$
where Ky are constants, and SSOC is the SOC of the energy storage cell. The terminal voltage Vt of the energy storage cell is:
$$ V_t = V_{oc} – V_p – V_o $$
where Vp is the polarization voltage, and Vo is the voltage drop across the internal resistance.
Energy Management Strategy for Island Mode
When the system operates in island mode, charging and discharging management of the energy storage cell is performed based on the real-time power difference and its SOC. The photovoltaic output power Ppv, the energy storage cell output power Pbat, and the inverter power reference Pm (= Pload) are monitored. The strategy defines four operating modes:
Mode I: When Ppv ≥ Pm and SOC of the energy storage cell is less than 80%, the photovoltaic DC/DC converter operates in MPPT mode, and the energy storage bidirectional DC/DC converter works in Buck mode. The surplus power charges the energy storage cell.
Mode II: When Ppv ≥ Pm and SOC of the energy storage cell is greater than or equal to 80%, the photovoltaic converter switches to constant power mode to maintain Ppv = Pm. The energy storage converter works in Boost mode but only provides power during load fluctuations for frequency regulation.
Mode III: When Ppv < Pm and SOC of the energy storage cell is greater than 20%, the photovoltaic converter operates in MPPT mode, and the energy storage converter works in Boost mode. The energy storage cell discharges to compensate for the power deficit.
Mode IV: When Ppv < Pm and SOC of the energy storage cell is less than or equal to 20%, the photovoltaic converter operates in MPPT mode, and the energy storage converter is turned off. Non-critical loads are shed to match the available power from the photovoltaic system.
| Mode | Condition (Ppv vs Pm & SOC of energy storage cell) | PV Control | ESS Control | Action |
|---|---|---|---|---|
| I | Ppv ≥ Pm and SOC < 80% | MPPT | Buck (Charge) | Surplus PV charges energy storage cell. |
| II | Ppv ≥ Pm and SOC ≥ 80% | Constant Power (Ppv = Pm) | Boost (Discharge/Standby) | PV meets load; energy storage cell provides frequency support. |
| III | Ppv < Pm and SOC > 20% | MPPT | Boost (Discharge) | Energy storage cell discharges for power balance. |
| IV | Ppv < Pm and SOC ≤ 20% | MPPT | Turned off | Load shedding to protect energy storage cell. |
Energy Management Strategy for Grid-Connected Mode
In grid-connected mode, the photovoltaic DC/DC converter always operates in MPPT mode to maximize power output. The energy storage bidirectional DC/DC converter selects Buck or Boost mode based on the real-time power difference and its SOC. When Ppv is insufficient and the energy storage cell SOC is low, the grid supplies the deficit. When Ppv exceeds the load and the energy storage cell SOC is high, the excess power flows into the grid.
Control Strategy for Each Converter
Control of Energy Storage Bidirectional DC/DC Converter
The bidirectional DC/DC converter for the energy storage cell maintains the DC bus voltage constant. It operates in Buck mode when the inverter power command is less than the photovoltaic output, allowing the energy storage cell to absorb excess energy. It operates in Boost mode when the inverter power command is greater than the photovoltaic output, causing the energy storage cell to discharge. A constant voltage control loop compares the measured DC bus voltage with its reference, and the output is used to control the converter switches.
Control of Photovoltaic DC/DC Converter
The photovoltaic converter uses a Boost circuit to increase voltage to the DC bus level. It switches between MPPT mode and constant power mode based on the SOC of the energy storage cell. When the energy storage cell SOC is below 80%, MPPT mode is active. When the SOC is at or above 80% and photovoltaic output exceeds the inverter command, the converter switches to constant power mode to prevent overcharging the energy storage cell.
Grid-Forming Control Based on Third-Order Synchronous Machine Model
The back-end inverter control is based on a third-order model of a synchronous machine. This model includes power-frequency control, dynamic damping, and a virtual excitation control system.
Power-Frequency Control with Additional Dynamic Damping
The rotor motion equation for VSG is used as the basis for power-frequency control. To improve response speed and stability, an additional dynamic damping term is introduced. This term uses the deviation between the grid angular velocity and the virtual angular velocity of the rotor. The modified equation is:
$$ 2H \frac{d\omega}{dt} = P_m – P_e – D\Delta\omega – K_\omega (\omega – \omega_g) $$
where H is the virtual inertia, ω is the actual angular velocity, ωg is the grid angular velocity, D is the damping coefficient, and Kω is the frequency regulation parameter. This adaptive damping mechanism effectively suppresses frequency fluctuations during disturbances.
Virtual Excitation Control Based on Transient Voltage Equation
Traditional VSG uses a linear reactive power-voltage droop control, which may be insufficient during faults or large voltage deviations. To address this, a first-order transient voltage equation is introduced as the excitation controller. The virtual excitation control adjusts the excitation voltage based on the deviation between the reference voltage and the actual voltage at the point of common coupling. The relationship is expressed as:
$$ \frac{U_0 – U_{ref}}{K_e / (1 + sT_e)} = \Delta u_f $$
where Δuf is the excitation voltage deviation, U0 and Uref are the actual and reference voltages, Ke is the proportional coefficient, and Te is the time constant. The forced no-load electromotive force Eqe is related to the excitation voltage uf by Eqe = xad / rf * uf. This formulation allows for dynamic adjustment of reactive power output, providing stronger transient voltage support. The transient electromotive force equation is:
$$ T’_{d0} \frac{dE’_q}{dt} = E_{qe} – E’_q – i_d (x_d – x’_d) $$
where E’q is the transient electromotive force, T′d0 is the time constant of the excitation winding, id is the d-axis current, xd is the d-axis synchronous reactance, and x′d is the d-axis transient reactance. This virtual excitation loop more accurately simulates a synchronous generator’s automatic voltage regulator, ensuring stable voltage control during transient processes.
| Feature | Traditional VSG (Second-Order) | Proposed Third-Order Grid-Forming |
|---|---|---|
| Power-Frequency Control | Fixed damping coefficient D. | Dynamic damping with grid-virtual angular velocity deviation. |
| Voltage-Reactive Power Control | Linear droop control (U-Q). | First-order transient voltage equation as virtual excitation. |
| Dynamic Response (Load Change) | Slower recovery, potential oscillations. | Faster recovery, reduced overshoot, improved damping. |
| Fault Ride-Through Capability | Limited voltage support, risk of voltage collapse. | Stronger voltage support, stable voltage, controlled fault current. |
Simulation and Experimental Validation
Simulation Results
Simulations were conducted in MATLAB/Simulink to validate the proposed control strategy. The simulation parameters correspond to a typical low-voltage microgrid.
Island Mode Energy Management
The energy management strategy in island mode effectively switches between the four operating modes based on instantaneous power balance and the SOC of the energy storage cell.
In Mode I, when photovoltaic power exceeds the load, the surplus power charges the energy storage cell. When the photovoltaic power drops below the load demand, the system transitions to Mode III, where the energy storage cell discharges to compensate for the deficit. In Mode II, when the energy storage cell SOC reaches 80%, the photovoltaic system shifts from MPPT to constant power mode to prevent overcharging. In Mode IV, when the energy storage cell SOC drops to 20%, the energy storage cell is disconnected and non-critical loads are shed. The results demonstrate that the proposed strategy maintains stable DC bus voltage and inverter output power while protecting the energy storage cell from deep discharge. A comparison simulation without considering SOC limits shows significant DC bus voltage fluctuations and accelerated degradation of the energy storage cell.
Grid-Connected Mode
In grid-connected mode, the system demonstrates robust operation. When photovoltaic power is insufficient and the energy storage cell SOC is low, the grid provides the power deficit. When photovoltaic power is surplus and the energy storage cell SOC is high, excess power is fed into the grid. The strategy optimizes the lifespan of the energy storage cell and ensures seamless interaction with the grid.
Experimental Verification
A hardware-in-the-loop platform was used to further validate the effectiveness of the control strategy.
Load Disturbance Response
Experiments were performed with a 10 kW step increase in local load demand, followed by a step decrease. The proposed third-order grid-forming control strategy was compared with a traditional second-order VSG control. The results indicate that with the proposed control, the frequency drop during the load increase is smaller (49.86 Hz vs. 49.84 Hz), and the recovery time is significantly faster (16 ms vs. 47 ms). The active power response time of the inverter is also shorter by over 540 ms under load decrease conditions. These results confirm the effectiveness of the dynamic damping mechanism in improving frequency stability and power regulation speed.
Short Circuit Fault Response
A short circuit fault condition was emulated by reducing the grid voltage to 0.6 p.u. Under the traditional VSG control, the voltage at the point of common coupling suffered a significant sag, dropping to 291.5 V from 311 V, with a slow recovery of 448 ms. In contrast, the proposed third-order grid-forming control limited the voltage sag to only 1.6% of the nominal value and recovered within 10 ms. The fault current was also better controlled (454 A compared to 475 A), staying below the safety threshold. Furthermore, the inverter provided 136 kvar of reactive power under the proposed control, compared to 111 kvar under VSG control. This demonstrates the superior voltage and reactive power support capability of the proposed strategy during severe grid disturbances, effectively protecting the energy storage cell and the overall system from instability.
| Performance Metric | Traditional VSG | Third-Order Grid-Forming |
|---|---|---|
| Voltage Sag (p.u.) | 0.06 p.u. (Drop to 0.937 p.u.) | 0.016 p.u. (Drop to 0.984 p.u.) |
| Voltage Recovery Time | 448 ms | 10 ms |
| Fault Current (A) | 475 ( > 1.5 p.u.) | 454 ( < 1.5 p.u.) |
| Reactive Power Support (kvar) | 111 | 136 |
Conclusion
This work proposes a cooperative control strategy for a photovoltaic-energy storage AC microgrid that considers the SOC characteristics of the energy storage cell. The strategy integrates energy management with advanced grid-forming control. The key conclusions are as follows:
By designing four operating modes based on real-time power balance and the SOC of the energy storage cell, the front-end converters achieve smooth mode switching. This coordinated control effectively prevents the energy storage cell from prolonged overcharging or overdischarging, thereby extending its operational lifespan and optimizing energy distribution among the photovoltaic system, the energy storage cell, and the load.
The back-end inverter employs a third-order grid-forming control strategy. This approach introduces a first-order transient voltage equation as a virtual excitation controller, moving beyond the limitations of traditional linear droop control. The addition of dynamic damping, based on the grid-virtual angular velocity deviation, significantly enhances the active power-frequency response. This strategy provides robust voltage and frequency support during load fluctuations and grid faults, improving the overall stability and resilience of the photovoltaic-energy storage AC microgrid.
Future work will focus on modeling the dynamic coupling between electrical, thermal, and aging factors of the energy storage cell to refine the SOC-voltage relationship. This will enable the development of multi-timescale optimization strategies for the long-term collaborative operation of energy storage cells in microgrids.