1. Introduction
With the rapid transformation of the global energy structure and the accelerated development of renewable energy technologies, photovoltaic-energy storage microgrids have emerged as a novel energy supply paradigm that efficiently integrates solar power generation with energy storage systems. However, due to the inherent volatility and uncertainty of photovoltaic output, the frequent charging and discharging cycles of energy storage batteries may lead to overcharging and overdischarging issues, which significantly accelerate battery aging and reduce the operational lifespan of the energy storage system. The state of charge (SOC) of an energy storage battery not only affects the charging and discharging efficiency but is also closely related to the battery’s lifespan and stability.
Traditional virtual synchronous generator (VSG) control strategies often employ fixed damping coefficients and linear droop control for voltage regulation, which fail to provide adequate active support during grid faults and load fluctuations. In particular, the voltage stability problem caused by active-reactive power coupling in VSG control remains insufficiently addressed. To overcome these limitations, this paper proposes a cooperative control strategy for photovoltaic-energy storage AC microgrids that considers the SOC characteristics of the energy storage battery. The main contributions of this work are as follows:
- A three-region division method based on the nonlinear characteristics of battery terminal voltage versus SOC is proposed. Mode switching is achieved through front-end converter control, which not only leverages the regulation capability of the energy storage battery but also effectively prevents overcharging and overdischarging, thereby extending battery life.
- Based on the third-order model of synchronous machines, a first-order transient voltage equation is introduced as the excitation controller to form a third-order grid-forming control strategy. Additionally, dynamic damping control based on the deviation between grid angular velocity and virtual angular velocity is incorporated to enhance the disturbance rejection capability and voltage support ability of the system.
- A collaborative optimization framework integrating battery life, dynamic response, and grid support is constructed to achieve simultaneous breakthroughs in dynamic response speed and fault ride-through capability while ensuring battery health.
2. System Configuration and Cooperative Control Structure
The photovoltaic-energy storage AC microgrid studied in this work consists of a photovoltaic system, an energy storage battery system, power converters, local loads, and the utility grid. Both the photovoltaic inverter and the energy storage inverter adopt a two-stage structure, connected to the DC bus through their respective DC/DC converters. The DC power is converted to AC power through inverters and then delivered to local loads and the grid via filter circuits.
The DC/DC converter of the photovoltaic system employs a Boost circuit, which determines whether the photovoltaic unit operates in maximum power point tracking (MPPT) mode or constant power mode based on the photovoltaic output power, load demand, and SOC of the energy storage battery. The energy storage battery system utilizes a bidirectional DC/DC converter, connected in parallel with the photovoltaic unit, which can switch between Buck mode and Boost mode depending on the photovoltaic output and load demand, thereby maintaining a constant DC bus voltage and achieving power decoupling between the front-end and back-end stages.
The back-end inverter adopts a third-order grid-forming control strategy. By introducing a first-order transient voltage equation to optimize the second-order model, the mechanical characteristics of synchronous machines are simulated, thereby enhancing the active power-frequency and reactive power-voltage support capability during system faults.
3. Characteristics of Energy Storage Battery and Energy Management Strategy
3.1 Charging and Discharging Characteristics of Energy Storage Battery under Different SOC Levels
Lithium-ion batteries are selected as the energy storage units in this system. A first-order RC equivalent circuit model is employed to simulate the terminal voltage characteristics of the lithium-ion battery. The battery terminal voltage consists of three components: the open-circuit voltage, the voltage drop caused by ohmic resistance, and the polarization voltage.
The open-circuit voltage as a function of SOC can be expressed as:
$$V_{oc}=K_1+K_2 S_{SOC}+K_3 S_{SOC}^2+K_4 S_{SOC}^3+K_5/S_{SOC}+K_6 \ln S_{SOC}+K_7 \ln (1-S_{SOC})$$
The SOC of the energy storage battery at different sampling instants is given by:
$$S_{SOC,t}=S_{SOC,t_0}-\frac{\eta I \Delta t}{C_N}$$
where η is the charging/discharging efficiency, I is the current flowing through the battery, and CN is the nominal capacity of the battery.
The ohmic voltage drop Vo and polarization voltage Vp are expressed as:
$$V_o=\begin{cases}
I R_{od} & \text{discharging} \\
I R_{oc} & \text{charging}
\end{cases}$$
$$\frac{dV_p}{dt}=-\frac{1}{C_p R_p}V_p+\frac{1}{C_p}I$$
The terminal voltage of the lithium-ion energy storage battery is:
$$V_t=V_{oc}-V_p-V_o$$
Based on the charging and discharging characteristics of the energy storage battery, the battery operation process can be divided into three regions according to SOC levels. In different regions, the energy storage battery exhibits distinct charging and discharging characteristics. To protect the energy storage battery, when the photovoltaic output varies, the battery SOC must be strictly monitored and energy management must be performed to prevent accelerated aging caused by overcharging or overdischarging.
3.2 Energy Management Strategy of the System
In the photovoltaic-energy storage AC microgrid, the photovoltaic system serves as the primary energy source, while the energy storage battery acts as an energy reserve to smooth the fluctuations in photovoltaic output. When the system operates in island mode, charging and discharging management is performed based on the real-time power difference and the SOC of the energy storage battery.
Let Ppv denote the photovoltaic output power, Pbat denote the energy storage battery output power, and Pm denote the inverter power command, which equals the load power Pload. Four operating modes are designed, as summarized in the following table:
| Mode | Condition | PV Converter Mode | Battery Converter Mode | Battery State | Description |
|---|---|---|---|---|---|
| I | Ppv ≥ Pm & SOC < 80% | MPPT | Buck | Charging | Excess power from PV charges the energy storage battery |
| II | Ppv ≥ Pm & SOC ≥ 80% | Constant Power | Boost | Idle / Discharging | PV output limited to load demand; battery provides frequency regulation |
| III | Ppv < Pm & SOC > 20% | MPPT | Boost | Discharging | Battery compensates for power deficit |
| IV | Ppv < Pm & SOC ≤ 20% | MPPT | Shutdown | Off | Non-critical loads are shed; PV alone supplies power |
When the microgrid operates in grid-connected mode, the photovoltaic DC/DC converter always operates in MPPT mode to continuously output maximum power, while the bidirectional DC/DC converter of the energy storage battery selects Buck or Boost mode based on the real-time power difference and SOC. Unlike island mode, when the photovoltaic output is insufficient to meet the inverter power command and the SOC is below 20%, loads are not shed; instead, the grid supplies the additional power. When the photovoltaic output exceeds the inverter power command and the SOC is above 80%, the excess power flows into the grid.
4. Control Strategies for Power Converters
4.1 Bidirectional DC/DC Converter Control for Energy Storage Battery
To achieve energy storage and release of the energy storage battery, a bidirectional DC/DC converter is employed to connect the battery to the DC bus. This converter suppresses power oscillations caused by load changes and photovoltaic fluctuations. When the inverter power command is less than the photovoltaic output, the DC bus voltage is higher than the battery terminal voltage, and the converter operates in Buck mode with the battery absorbing excess energy. When the inverter power command exceeds the photovoltaic output, the converter operates in Boost mode with the battery releasing energy.
The bidirectional DC/DC converter adopts constant voltage control. The DC bus voltage reference value Vdcref is compared with the measured DC bus voltage Vdc, and the difference serves as the control signal to regulate energy storage and release, thereby maintaining a constant DC bus voltage and achieving power decoupling between the front-end and back-end stages.
4.2 Photovoltaic DC/DC Converter Control
The photovoltaic array output voltage is relatively low and needs to be boosted through a Boost converter to access the DC bus. The control implements switching between MPPT mode and constant power mode. When the SOC of the energy storage battery is below 80%, the photovoltaic converter operates in MPPT mode. When the SOC reaches 80% or above and the photovoltaic output exceeds the inverter power command, the converter switches to constant power mode to prevent overcharging of the energy storage battery.
The perturb and observe method is used for MPPT due to its fast response to environmental changes, simple implementation, and low cost. The MPPT mode provides the reference operating voltage Vref, while the constant power control mode provides the output power reference value Pref.
4.3 Third-Order Grid-Forming Control Based on Synchronous Machine Model
Existing grid-forming control strategies have limitations in two main aspects. In power-frequency control, traditional VSG control uses a fixed damping coefficient D, making it difficult to balance dynamic response speed and overshoot suppression. In voltage control, traditional VSG control adopts linear droop control, which cannot accurately simulate the transient electromotive force characteristics of synchronous machines.
4.3.1 Power-Frequency Control with Dynamic Damping
The power-frequency control of the third-order grid-forming model adopts the rotor motion equation identical to that of traditional generators:
$$2H\frac{d\omega}{dt}=P_m-P_e-D\Delta\omega$$
$$\frac{d\delta}{dt}=\omega_0\Delta\omega$$
where H is the virtual inertia, ω is the actual angular velocity, ω0 is the rated angular velocity, Δω is the deviation between the rated and actual angular velocities, Pm is the mechanical power, Pe is the electromagnetic power, and δ is the power angle of the VSG.
To improve the response speed and stability, dynamic damping control is incorporated by introducing the angular velocity deviation between the grid side and the rotor motion equation:
$$2H\frac{d\omega}{dt}=P_m-P_e-D\Delta\omega-K_\omega(\omega-\omega_g)$$
where Kω is the frequency regulation parameter and ωg is the grid-side angular velocity. This dynamic damping mechanism offers dual advantages: (1) during the initial stage of power突变, the angular velocity deviation is large, increasing the damping coefficient to suppress frequency fluctuations; (2) during the steady-state recovery phase, the angular velocity deviation approaches zero, automatically reducing damping to avoid power oscillations.
| Control Method | Damping Characteristic | Response Speed | Overshoot Suppression | Steady-State Performance |
|---|---|---|---|---|
| Fixed Damping (Traditional VSG) | Constant D | Moderate | Limited | May exhibit oscillations |
| Dynamic Damping (Proposed) | Adaptive to Δω | Fast | Enhanced | Smooth recovery |
3.2 Virtual Excitation Control
Traditional second-order VSG control adopts linear droop control for reactive power-voltage regulation, which has relatively low capability to prevent fault disturbances. The traditional VSG reactive power-voltage droop control is expressed as:
$$T_1\frac{dE_{qref}}{dt}=K_u(u_{ref}-u_{meas})+Q_{ref}-Q_e$$
To overcome the limitations of linear droop control, this paper introduces the excitation equation as the virtual excitation voltage regulation control link of the third-order grid-forming control:
$$\frac{U_0-U_{ref}}{K_e}\frac{1+T_e s}{s} = \Delta u_f$$
The relationship between the forced no-load electromotive force Eqe and the excitation voltage uf is:
$$E_{qe}=\frac{x_{ad}}{r_f}u_f=K_f u_f$$
Combining the above equations, the relationship between the grid connection point voltage deviation ΔUb and the no-load electromotive force deviation ΔEqe is obtained:
$$\frac{-\Delta U_b}{K_e}\frac{1+T_e s}{s} = \frac{1}{K_f}\Delta E_{qe}$$
The virtual excitation circuit equation considering the transient electromotive force is:
$$E_{qe}=E_q+T’_{d0}\frac{dE’_q}{dt}$$
$$E_q=E’_q+i_d(x_d-x’_d)$$
Combining these equations yields:
$$T’_{d0}\frac{dE’_q}{dt}=E_{qe}-E’_q-i_d(x_d-x’_d)$$
The relationship between the transient electromotive force variation ΔE’q and the grid connection point voltage variation is:
$$\frac{\Delta E’_q}{U_0-U_{ref}}=\frac{K_e K_f}{(1+T_e s)(sT’_{d0}+1)}$$
| Control Method | Voltage Regulation Model | Transient Support Capability | Nonlinear Adaptability | Reactive Power Allocation |
|---|---|---|---|---|
| Linear Droop Control (2nd-order VSG) | Static linear relationship | Weak | Limited | Fixed proportional |
| Excitation Control (3rd-order GFI) | Dynamic transient model | Strong | Enhanced | Adaptive |
In the third-order model, the virtual excitation control adjusts the excitation voltage based on the deviation between the reference and actual values of the grid connection point voltage, thereby changing the output reactive power and achieving precise voltage control. Compared with traditional droop control, this method avoids regulation lag and ensures rapid voltage recovery during load突变. This approach better adapts to the nonlinear dynamic changes in the power system and enhances the voltage regulation capability and reactive power support capability of the system.
5. Simulation and Experimental Verification
5.1 Simulation Verification
To verify the effectiveness of the proposed energy management strategy, simulations were conducted in MATLAB/Simulink. The simulation parameters are summarized in the following table:
| Parameter | Symbol | Value |
|---|---|---|
| DC bus voltage reference | Vdcref | 700 V |
| Grid voltage (line-to-line RMS) | Vg | 380 V |
| Grid frequency | fg | 50 Hz |
| Filter inductance | Lf | 0.5 mH |
| Filter capacitance | Cf | 150 μF |
| Battery nominal capacity | CN | 200 Ah |
| Battery nominal voltage | Vbat | 480 V |
| PV array rated power | Ppv_rated | 150 kW |
| Load power | Pload | 100 kW |
| Virtual inertia | H | 5 s |
| Damping coefficient | D | 20 |
| Frequency regulation parameter | Kω | 50 |
5.1.1 Island Mode Energy Management Verification
Four operating conditions corresponding to the four working modes were simulated to verify the effectiveness of the energy management strategy in island mode.
For Mode I: With temperature constant at 25°C, the irradiance decreased from 1000 W/m² to 500 W/m² at t=2 s and recovered to 1000 W/m² at t=4 s, with the SOC of the energy storage battery within [20%, 80%]. During the period [0, 2) s, the inverter active power reference equaled the load demand of 100 kW, and the excess power was absorbed by the energy storage battery. At t=2 s, the photovoltaic output decreased from 150 kW to approximately 70 kW, and the energy storage battery switched from absorbing 50 kW to supplying approximately 30 kW. At t=4 s, the photovoltaic output increased to 150 kW, and the battery resumed absorbing 50 kW.
For Mode II: With temperature constant at 25°C and irradiance maintained at 1000 W/m², the SOC of the energy storage battery exceeded 80% after a period of operation. The photovoltaic initially output 150 kW, with the inverter reference at 100 kW and 50 kW absorbed by the battery. When the SOC reached 80% at approximately t=2.4 s, the photovoltaic switched to constant power control, outputting 100 kW.
For Mode III: With temperature constant at 25°C, the irradiance decreased from 1000 W/m² to 500 W/m² at t=2 s and to 0 at t=4 s. At t=2 s, the photovoltaic output was approximately 70 kW, and at t=4 s it became 0. When the photovoltaic output was insufficient, the energy storage battery rapidly released energy to compensate for the power deficit.
For Mode IV: With temperature constant at 25°C, the irradiance decreased from 1000 W/m² to 500 W/m² at t=2 s, and the SOC of the energy storage battery was below 20%. Since the battery could not discharge, non-critical loads were shed to reduce the inverter output power. The inverter output power was entirely supplied by the photovoltaic unit.
Additionally, a comparative simulation was conducted for Mode IV without considering the SOC constraint. When the SOC was below 20% and the battery continued to discharge, the DC bus voltage exhibited significant fluctuations, which would adversely affect battery lifespan. This comparison confirms that the proposed energy management strategy effectively protects the energy storage battery.
5.1.2 Grid-Connected Mode Energy Management Verification
Two operating conditions were verified in grid-connected mode:
Condition 1: Photovoltaic output of 150 kW, battery SOC ≤ 20%, local load increased from 150 kW to 160 kW at t=2 s and recovered at t=4 s. After the load increase, the photovoltaic output was insufficient to meet the load demand, and since the energy storage battery was in the unidirectional charging region, the additional 10 kW was supplied by the grid.
Condition 2: Irradiance increased from 1000 W/m² to 1100 W/m² at t=2 s, battery SOC ≥ 80%, local load demand constant at 150 kW. After the irradiance increase, the photovoltaic output exceeded the local load demand, and since the battery SOC was above 80%, the battery was in the unidirectional discharging region. The inverter power command rapidly responded to match the photovoltaic output, and the excess power flowed into the grid.
These simulation results demonstrate that the proposed strategy effectively protects the energy storage battery while optimizing lifespan management, outperforming fixed-threshold or simple-limiting strategies in the existing literature.
5.2 Experimental Verification
A semi-physical simulation platform was used for experimental verification. The parameters were consistent with the simulation setup.
5.2.1 Load Disturbance Response in Grid-Connected Mode
To verify the load disturbance response characteristics, a scenario was set where the local load demand suddenly increased by 10 kW and then recovered after a period. The system responses under traditional VSG control and the proposed third-order grid-forming control strategy were compared.
| Control Strategy | Frequency Drop (Hz) | Recovery Time (ms) | Frequency Rise (Hz) | Recovery Time (ms) |
|---|---|---|---|---|
| Traditional VSG Control | 49.84 | 47 | 50.185 | 40 |
| Third-Order GFI Control (Proposed) | 49.86 | 16 | 50.145 | 20 |
When the load suddenly increased, the frequency under VSG control dropped to 49.84 Hz and recovered to 50 Hz after 47 ms, while under the third-order grid-forming control, the frequency dropped to only 49.86 Hz and recovered after 16 ms. When the load suddenly decreased, the third-order control strategy also showed superior performance with faster recovery and smaller frequency deviation.
For the active power response, when the load suddenly increased, the response time of the third-order grid-forming control was 620 ms shorter than that of the VSG control. When the load suddenly decreased, the response time was 540 ms shorter. These experimental results validate the effectiveness of the adaptive dynamic damping control in resolving the conflict between fast response and overshoot suppression that exists in fixed damping coefficient control.
5.2.2 Short Circuit Fault Response in Grid-Connected Mode
To verify the short circuit fault response characteristics, a scenario was simulated by reducing the grid voltage to 0.6 p.u. The system responses under traditional VSG control and the proposed third-order grid-forming control strategy were compared.
| Control Strategy | Voltage Sag (V) | Voltage Recovery Time (ms) | Fault Current (A) | Reactive Power Support (kvar) |
|---|---|---|---|---|
| Traditional VSG Control | 291.5 | 448 | 475 | 111 |
| Third-Order GFI Control (Proposed) | 306.0 | 10 | 454 | 136 |
Under the VSG control strategy, the grid connection point voltage dropped significantly from 311 V to 291.5 V with a dynamic recovery process lasting 448 ms. In contrast, under the third-order grid-forming control strategy, the voltage experienced only a 1.6% mild sag and rapidly completed voltage reconstruction within 10 ms. The fault current under VSG control reached 475 A (exceeding the safety threshold of 1.5 p.u.), while under the proposed control it was limited to 454 A (below the safety threshold of 1.5 p.u.). The reactive power provided by the inverter under the proposed control reached 136 kvar, compared to 111 kvar under VSG control.
These experimental results confirm that the proposed third-order grid-forming control strategy provides superior voltage support capability, effectively prevents system collapse and load supply degradation caused by excessive voltage drop at the fault point, limits fault current, and significantly enhances the voltage and reactive power support capability of the photovoltaic-energy storage AC microgrid.
6. Conclusion
This paper has proposed a cooperative control strategy for photovoltaic-energy storage AC microgrids that considers the SOC characteristics of the energy storage battery. The main conclusions are as follows:
- Energy Management Optimization: Based on the operating characteristics of the energy storage battery at different SOC levels and real-time power differences, a charging and discharging management scheme is designed for the photovoltaic-energy storage AC microgrid. Through front-end converter control, smooth switching between system operating modes is achieved, realizing energy coordination among the photovoltaic system, the energy storage battery, and loads while effectively preventing prolonged overcharging and overdischarging of the energy storage battery.
- Enhanced Grid Support Capability: The back-end inverter adopts a third-order grid-forming control strategy. By introducing a first-order transient voltage equation as the excitation controller in the third-order model of the synchronous generator, voltage regulation is realized. Additionally, the angular velocity deviation between the grid side and the rotor motion equation is introduced to accelerate the regulation speed of the active power-frequency loop, thereby enhancing the active support capability of the photovoltaic-energy storage AC microgrid.
- Battery Life Extension: The proposed strategy effectively prevents the energy storage battery from operating in overcharging or overdischarging states through SOC-aware mode switching and power management, which significantly contributes to extending the operational lifespan of the energy storage battery.
- Superior Dynamic Performance: The adaptive dynamic damping control resolves the conflict between fast response and overshoot suppression. The third-order grid-forming control provides stronger transient voltage support during grid faults, limits fault current, and ensures system stability.
The simulation and experimental results have collectively validated the effectiveness and superiority of the proposed cooperative control strategy, demonstrating its ability to achieve efficient and coordinated operation of the photovoltaic-energy storage AC microgrid while extending battery life and enhancing the active support capability of the system.
| Performance Metric | Traditional VSG Control | Proposed Third-Order GFI Control | Improvement |
|---|---|---|---|
| Frequency recovery time (load increase) | 47 ms | 16 ms | 66% faster |
| Active power response time (load increase) | Reference | 620 ms faster | Significantly improved |
| Voltage sag under fault | 19.5 V | 5.0 V | 74% reduction |
| Voltage recovery time under fault | 448 ms | 10 ms | 97.8% faster |
| Fault current | 475 A | 454 A | 4.4% reduction |
| Reactive power support under fault | 111 kvar | 136 kvar | 22.5% increase |
| Battery overcharge/overdischarge protection | Not considered | Comprehensive | Extended battery life |
The findings of this research provide a practical framework for the design and operation of photovoltaic-energy storage AC microgrids, particularly in applications where battery longevity and system stability are of paramount importance. Future work will focus on establishing an electro-thermal-aging multi-scale coupled model to further investigate the cooperative optimization control of the energy storage battery during long-term operation.