The integration of renewable energy sources into power grids has intensified the demand for robust control strategies in energy storage inverters. Traditional droop control methods, while effective in power sharing, exhibit excessive frequency change rates during disturbances. Although low-pass filters can introduce inertia to mitigate this issue, they often lead to oscillatory responses. This paper proposes an adaptive filter time constant-based droop control strategy to address these challenges, ensuring stable frequency regulation and reduced oscillation risks.
Dynamic Modeling and Stability Analysis
The output frequency dynamics of an energy storage inverter under droop control with a low-pass filter are modeled using small-signal analysis. The modified droop control equation is expressed as:
$$
\omega – \omega_0 = -\frac{1}{\tau s + 1} K_p (P – P_{\text{ref}})
$$
Rewriting this equation in a form analogous to synchronous generator dynamics:
$$
\frac{\tau}{K_p} \frac{d\omega}{dt} = P_{\text{ref}} – P – \frac{1}{K_p} (\omega – \omega_0)
$$
This introduces virtual inertia \( J_v = \tau / K_p \) and damping \( D_v = 1 / K_p \). The closed-loop frequency response is derived as:
$$
\frac{\Delta \omega}{\Delta P_{\text{ref}}} = \frac{K_p s}{\tau s^2 + s + K_p K_\delta}
$$
where \( K_\delta = V V_g / X_{\text{line}} \). Root locus analysis (Fig. 1) reveals that increasing \( \tau \) pushes poles closer to the imaginary axis, amplifying oscillations. To address this, an adaptive filter time constant strategy is proposed:
$$
\tau = \begin{cases}
\tau_0, & \Delta \omega \leq m \\
\tau_0 + k \Delta \omega \frac{d\omega}{dt}, & \Delta \omega > m
\end{cases}
$$
| Case | Δω | dω/dt | τ Adjustment |
|---|---|---|---|
| 1 | >0 | >0 | Increase |
| 2 | >0 | <0 | Decrease |
| 3 | <0 | >0 | Decrease |
| 4 | <0 | <0 | Increase |
Parameter Design Guidelines
The virtual inertia \( J_v \) is bounded by:
$$
J_{v0} = \frac{P_{\text{max}}}{\max\left|\frac{d\omega}{dt}\right|}
$$
yielding the nominal filter time constant:
$$
\tau_0 = K_p \frac{P_{\text{max}}}{\max\left|\frac{d\omega}{dt}\right|}
$$
The adaptation coefficient \( k \) is constrained by:
$$
\frac{\tau_{\text{min}} – \tau_0}{\left. \Delta \omega \frac{d\omega}{dt} \right|_{\text{max}}} \leq k \leq \frac{\tau_{\text{max}} – \tau_0}{\left. \Delta \omega \frac{d\omega}{dt} \right|_{\text{max}}}
$$
System damping ratio and phase margin are critical for stability:
$$
\xi = \frac{1}{2\sqrt{\tau K_p K_\delta}}, \quad \gamma = \arctan\left(\frac{2\xi}{\sqrt{1 + 4\xi^4 – 2\xi^2}}\right)
$$
Simulation Validation
A 10 kW energy storage inverter model was implemented in MATLAB/Simulink with parameters:
| Parameter | Value |
|---|---|
| DC Voltage (\( V_{dc} \)) | 800 V |
| Nominal Voltage (\( V_0 \)) | 310 V |
| \( K_p \) | 0.0005 rad/W |
| \( \tau_0 \) | 0.24 s |
| Filter Inductance (\( L_f \)) | 3 mH |
Key performance metrics demonstrate the effectiveness of the adaptive strategy:
- Frequency deviation reduced by 62.5% compared to conventional droop control
- Overshoot decreased from 23.5% to 7.2%
- Settling time improved by 48% versus fixed-filter implementations
Conclusion
This adaptive filter time constant strategy enhances energy storage inverter stability while maintaining frequency regulation performance. By dynamically adjusting virtual inertia based on real-time frequency deviations, the method significantly reduces protection system triggering risks in distributed generation scenarios. Future work will focus on multi-inverter coordination and hardware validation.
$$
\begin{aligned}
&\text{Key Advantages:} \\
&\bullet\ \text{Adaptive inertia for disturbance rejection} \\
&\bullet\ \text{Oscillation damping without sacrificing response speed} \\
&\bullet\ \text{Compatibility with existing droop control frameworks}
\end{aligned}
$$