In the research on wind-solar microgrid systems, I have identified critical challenges such as unstable DC bus voltage, slow power response of energy storage systems, and irrational power allocation caused by sudden load changes and significant fluctuations in wind and solar power generation. To address these issues, I propose a novel control strategy that integrates adaptive power allocation for hybrid energy storage systems (HESS) with an improved model predictive control (MPC) algorithm. The hybrid system comprises battery energy storage systems and flywheel energy storage systems. This approach aims to leverage the rapid response characteristics of flywheels to mitigate the impact of sudden power changes on battery energy storage systems, thereby extending their lifespan and enhancing overall system stability.
Introduction
Renewable energy sources such as wind and solar power exhibit randomness and intermittency, leading to output power fluctuations in microgrid systems that can compromise operational safety and stability. Energy storage devices are crucial components for maintaining power balance by regulating charging and discharging states in real-time. However, single-type storage technologies often fail to simultaneously meet the demands for long cycle life, rapid system response, and high power density. Therefore, I adopt a hybrid configuration combining battery energy storage systems and flywheel energy storage systems. The flywheel storage excels in power density and fast charging/discharging rates, while battery energy storage systems provide high energy density and stable power release. Optimizing this configuration improves the comprehensive performance of the storage system and the stability of the microgrid.
System Modeling and Control
Wind-Solar Microgrid Architecture
The AC/DC wind-solar microgrid integrates photovoltaic arrays, direct-drive wind turbines, hybrid energy storage, power conversion devices, and AC/DC loads. The photovoltaic (PV) and wind systems operate under maximum power point tracking (MPPT) control. The PV system uses the perturbation and observation (P&O) method, while the wind system employs the optimal tip-speed ratio (TSR) control. When the microgrid operates in islanding mode, the hybrid energy storage system must compensate for power imbalances arising from fluctuations in renewable generation and load variations.
Modeling of Battery Energy Storage Systems
I model the battery energy storage system (BESS) to manage charging and discharging for voltage stabilization. The topology includes a battery, capacitor \( C_b \), inductor \( L_b \), and a bidirectional DC/DC converter. During discharging (Boost mode), the dynamics are:
$$ L_b \frac{di_b}{dt} = U_b – R_b i_b – U_{dc} $$
$$ C_b \frac{dU_{dc}}{dt} = i_b – \frac{U_{dc}}{R} $$
During charging (Buck mode), the equations become:
$$ L_b \frac{di_b}{dt} = U_b – R_b i_b $$
$$ C_b \frac{dU_{dc}}{dt} = -\frac{U_{dc}}{R} $$
The control strategy for BESS uses a voltage outer loop and current inner loop to regulate the DC bus voltage by adjusting PI controller parameters.
Modeling of Flywheel Energy Storage Systems
The flywheel energy storage system (FESS) uses a permanent magnet synchronous motor (PMSM). The voltage equations in the dq rotating coordinate system are:
$$ u_d = R_s i_d + L_d \frac{di_d}{dt} – \omega_e L_q i_q $$
$$ u_q = R_s i_q + L_q \frac{di_q}{dt} + \omega_e (L_d i_d + \psi_f) $$
The electromagnetic torque \( T_e \) is given by:
$$ T_e = \frac{3}{2} p [\psi_f i_q + (L_d – L_q) i_d i_q] $$
For surface-mounted PMSMs where \( L_d = L_q \), the torque simplifies to:
$$ T_e = \frac{3}{2} p \psi_f i_q $$
The flywheel power is related to the q-axis current reference as:
$$ i_{q,ref} = \frac{2 P_{ref}}{3 p \psi_f \omega_e} $$
The flywheel state of charge (SOC) is defined to monitor its energy status:
$$ SOC_{flywheel} = \frac{\omega^2 – \omega_{min}^2}{\omega_{max}^2 – \omega_{min}^2} $$
This ensures safe operation within speed limits.
Adaptive Power Allocation and Predictive Control Strategy
The core of my approach is to use the flywheel storage for high-frequency, short-duration power fluctuations and battery energy storage systems for low-frequency, long-duration power regulation. This hybrid coordination enhances system dynamic response and extends battery life. The power allocation is based on the net power imbalance in the microgrid:
$$ P_{dc} = P_{pv} + P_{wind} + P_{HESS} – P_{DC} – P_{AC} $$
where \( P_{HESS} \) is the total power from the hybrid storage. I use a fuzzy logic controller to adaptively adjust the time constant of a low-pass filter that splits the reference power into high-frequency and low-frequency components. The fuzzy controller takes the DC bus voltage change rate \( dU_{dc}/dt \) and flywheel SOC as inputs. The output modifies the filter time constant \( T_c \), which defines the cutoff frequency:
$$ G(s) = \frac{1}{1 + T_c s}, \quad f_c = \frac{1}{2\pi T_c} $$
The membership functions for the inputs are designed as follows:
| Voltage Change Rate / Flywheel SOC | NB | NS | ZE | PS | PB |
|---|---|---|---|---|---|
| NB | Large | Large | Medium | Small | Small |
| NS | Large | Medium | Medium | Small | Small |
| NZ / PZ | Medium | Medium | Small | Medium | Medium |
| PS | Small | Small | Medium | Medium | Large |
| PB | Small | Small | Medium | Large | Large |
This adaptive allocation ensures that flywheel storage absorbs high-frequency transients, protecting battery energy storage systems from stress due to sudden power surges.
Three-Step Model Predictive Control for Fast Response
To overcome the lag in conventional PI controllers, I implement a three-step model predictive control (Ts-MPC) for both the flywheel AC/DC converter and the battery DC/DC converter. For the flywheel, instantaneous power in the dq frame is:
$$ \begin{bmatrix} P \\ Q \end{bmatrix} = \begin{bmatrix} V_d & V_q \\ V_q & -V_d \end{bmatrix} \begin{bmatrix} i_d \\ i_q \end{bmatrix} $$
Using forward Euler discretization, the power at the next time step is predicted:
$$ \begin{bmatrix} P(k+1) \\ Q(k+1) \end{bmatrix} = \begin{bmatrix} V_d(k) & V_q(k) \\ V_q(k) & -V_d(k) \end{bmatrix} \begin{bmatrix} i_d(k+1) \\ i_q(k+1) \end{bmatrix} $$
where the predicted currents are derived from the converter voltage equation. The three-step prediction optimizes the control sequence by considering the system state over three consecutive control periods, minimizing a cost function:
$$ J_{flywheel} = [P(k+2) – P^*(k)]^2 + [Q(k+2) – Q^*(k)]^2 $$
The resulting optimal converter voltage \( U_{opt}(k+2) \) is applied after compensation for delays:
$$ \begin{bmatrix} U_d(k) \\ U_q(k) \end{bmatrix} = \frac{1}{V_d^2 + V_q^2} \begin{bmatrix} V_d(k) & -V_q(k) \\ V_q(k) & V_d(k) \end{bmatrix} \begin{bmatrix} \frac{L}{T_s} [P^*(k+2) – P(k)] + V_d(k) + \epsilon_P(k) \\ \frac{L}{T_s} [Q^*(k+2) – Q(k)] + V_q(k) + \epsilon_Q(k) \end{bmatrix} $$
For the battery energy storage systems, the discrete-time power model during discharge is:
$$ P_b(k+1) = (1 – \frac{R_b T_s}{L_b}) P_b(k) + \frac{T_s}{L_b} U_b^2 $$
During charging, it becomes:
$$ P_b(k+1) = (1 – \frac{R_b T_s}{L_b}) P_b(k) + \frac{T_s}{L_b} U_b (U_b – U_{dc}) $$
The cost function for battery control is:
$$ J_{battery} = [P_b(k+2) – P_b^*(k)]^2 $$
The system constraints ensure safe operation:
$$ \min |U_{dc,ref} – U_{dc}| $$
$$ P_{b,min} \leq P_b \leq P_{b,max} $$
$$ P_{f,min} \leq P_f \leq P_{f,max} $$
$$ 0.2 \leq SOC_{Li} \leq 0.8, \quad 0.05 \leq SOC_f \leq 0.95 $$
Simulation Results and Analysis
I built a simulation model in Matlab/Simulink to verify the proposed strategy. The simulation parameters are summarized below:
| Parameter | Value |
|---|---|
| Battery Voltage (V) | 400 |
| Battery Capacity (Ah) | 40 |
| Battery Initial SOC (%) | 60 |
| Flywheel Pole Pairs | 4 |
| Flywheel Initial Speed (rad/s) | 314 |
| Flywheel Inertia (kg·m²) | 19.5 |
| Stator Resistance (Ω) | 0.001506 |
| d,q-axis Inductance (H) | 0.00013 |
| Flux Linkage (Wb) | 0.318 |
| DC Bus Voltage (V) | 750 |
Flywheel Dynamic Response Verification
I first tested the flywheel’s ability to track load power. The output power followed the reference within 0.01 seconds, confirming the millisecond-level response capability.
Performance Under Step Power Disturbances
In this scenario, the microgrid operated in islanding mode with initial conditions: wind speed 12 m/s, irradiance 800 W/m², PV power 50 kW, wind power 25 kW, DC load 35 kW, and AC load 30 kW. Disturbances were introduced: at t=0.5s, irradiance increased to 900 W/m²; at t=1.0s, irradiance decreased to 850 W/m² and wind speed dropped to 11 m/s; at t=1.5s, DC load increased. The hybrid energy storage total power demand changed accordingly. I compared the proposed control with traditional PI double-loop control and traditional droop control. The DC bus voltage responses are quantified in the table below.
| Control Method | Disturbance Time (s) | Settling Time (ms) | Improvement vs. PI (%) | Average Improvement (%) | Overshoot (V) | Improvement vs. PI (%) | Average Improvement (%) |
|---|---|---|---|---|---|---|---|
| Traditional PI | 0.5 | 112 | 0 | 2.30 | 0 | ||
| Traditional PI | 1.0 | 140 | 0 | 2.32 | 0 | ||
| Traditional PI | 1.5 | 99 | 0 | 3.53 | 0 | ||
| Traditional Droop | 0.5 | 51 | 54.5 | -4.8 | 1.18 | 48.7 | 52.1 |
| Traditional Droop | 1.0 | 150 | -7.1 | 1.15 | 50.4 | ||
| Traditional Droop | 1.5 | 160 | -61.6 | 1.51 | 57.2 | ||
| Proposed Strategy | 0.5 | 42 | 62.5 | 46.8 | 0.92 | 60.0 | 68.1 |
| Proposed Strategy | 1.0 | 45 | 67.9 | 0.65 | 72.0 | ||
| Proposed Strategy | 1.5 | 89 | 10.1 | 0.98 | 72.2 |
The results show that the proposed control strategy significantly reduces settling time and voltage overshoot. On average, the settling time improved by 46.8% and the overshoot decreased by 68.1% compared to traditional PI control. The battery SOC remained stable, indicating smooth charging/discharging processes.
Performance Under Random Wind Power Fluctuations
To further validate robustness, I simulated random fluctuations in wind power between 20 kW and 25 kW while maintaining constant load. The proposed strategy resulted in much smaller DC bus voltage deviations compared to traditional PI control, demonstrating superior voltage quality and disturbance rejection capability.
Conclusion
In this work, I have developed a coordinated control strategy for hybrid energy storage systems in islanded wind-solar microgrids. The combination of adaptive fuzzy-based power allocation and three-step model predictive control effectively addresses the challenges of voltage instability and slow response. The adaptive allocation method ensures that flywheel storage handles rapid power transients, protecting battery energy storage systems from stress, while the predictive control enhances tracking accuracy and response speed. Simulation results confirm that the proposed strategy significantly outperforms traditional PI and droop control methods in terms of settling time, voltage overshoot, and overall system stability. This approach provides a viable solution for improving the reliability and efficiency of microgrids with high renewable energy penetration, offering practical guidance for engineering applications of battery energy storage systems in hybrid configurations.