1. Introduction
The rapid integration of renewable energy sources and the transition toward carbon neutrality have highlighted the critical role of energy storage inverter in modern power systems. Among these, single-phase energy storage inverter is pivotal for residential applications, enabling seamless energy management, grid support, and fault resilience. Unlike grid-following inverters, grid-forming inverters autonomously regulate voltage and frequency, making them indispensable in weak grids or islanded operations. This article explores advanced control methodologies for single-phase grid-forming energy storage inverter, focusing on stability, power synchronization, and dynamic response under disturbances.
2. Classification and Characteristics of Grid-Forming Control Algorithms
Grid-forming control strategies emulate the inertial and damping behaviors of synchronous generators, ensuring stable operation under grid disturbances. Key algorithms include:
2.1 Power Synchronization Control (PSC)
PSC synchronizes inverters with the grid through active power feedback, generating phase angles dynamically: [ \theta(t) = \omega_o t + k_p \int (P{ref} – P) \, dt ] where (k_p) is the proportional gain, and (P{ref}) is the reference power.
2.2 Droop Control
Droop control adjusts frequency and voltage based on power imbalances: [ \omega = \omega_o – k_p (P – P{ref}), \quad V = V_o – k_q (Q – Q{ref}) ] Low-pass filters ((H_p(s) = \frac{\omega_p}{s + \omega_p})) mitigate power oscillations.
2.3 Virtual Synchronous Generator (VSG)
VSG replicates rotor dynamics: [ J \frac{d\omega}{dt} = P_m – P_e – D(\omega – \omega_o) ] where (J) is virtual inertia and (D) is the damping coefficient.
Table 1: Comparison of Grid-Forming Control Strategies
| Algorithm | Inertia | Damping | Complexity |
|---|---|---|---|
| PSC | No | Low | Low |
| Droop Control | No | Medium | Medium |
| VSG | Yes | High | High |
3. Power Calculation and Filtering in Single-Phase Systems
Accurate power measurement is critical for grid-forming energy storage inverter. Traditional methods rely on average power theory, while instantaneous power theory (IPT) uses orthogonal signal generation.
3.1 Orthogonal Signal Generation Techniques
- Direct Phase Shifting: Introduces a 90° delay but suffers from dynamic inaccuracies.
- All-Pass Filter (APF): Provides frequency-adaptive phase shift: [ G_{APF}(s) = \frac{\omega_o – s}{\omega_o + s} ]
- Second-Order Generalized Integrator (SOGI): Enhances harmonic rejection: [ G_{SOGI}(s) = \frac{k\omega_o s}{s^2 + k\omega_o s + \omega_o^2} ]
3.2 Power Filtering Strategies
Low-pass filters (LPF) and notch filters suppress double-line frequency ripples: [ G{LPF}(s) = \frac{\omega_c}{s + \omega_c}, \quad G{notch}(s) = \frac{s^2 + \omega_o^2}{s^2 + 2\zeta\omega_o s + \omega_o^2} ]
Table 2: Filter Performance Comparison
| Filter Type | Delay | Harmonic Attenuation | Stability Impact |
|---|---|---|---|
| LPF | High | Moderate | Deteriorates |
| Notch | Low | High | Improves |
4. State-Feedback Control for Enhanced Stability
A state-feedback controller improves transient response by regulating inductor current ((i_L)) and capacitor voltage ((v_C)):
4.1 System Modeling
The inverter dynamics are: [ \frac{di_L}{dt} = \frac{1}{L}(v{inv} – v_C), \quad \frac{dv_C}{dt} = \frac{1}{C}(i_L – i_g) ] Discretizing with Zero-Order Hold (ZOH): [ x(k+1) = Gx(k) + H_1 v{inv}(k) + H_2 i_g(k) ]
4.2 Controller Design
Feedback gains (k_c) (voltage) and (k_L) (current) are optimized using pole placement: [ v{inv}^* = v{ref} – k_c v_C – k_L i_L ] Table 3: Stability Constraints for Feedback Gains
| Parameter | Range | Impact on Damping |
|---|---|---|
| (k_c) | (-0.4–0.4) | Reduces resonance |
| (k_L) | (0–14) | Increases bandwidth |
5. Experimental Validation
A 2 kW energy storage inverter prototype was tested under grid faults and load transitions:
5.1 Grid Voltage Sag (1.0 p.u. → 0.6 p.u.)
- Non-inertial Control: Stable but with 12% voltage dip.
- VSG with (\omega_p = 16\pi): 8% dip and 20% faster recovery.
5.2 Seamless Mode Transition
State-feedback control reduced switching transients by 40% compared to PI control.
Table 4: Performance Metrics
| Metric | PI Control | State-Feedback |
|---|---|---|
| THD (%) | 4.2 | 2.8 |
| Transient Time (ms) | 50 | 30 |
| Peak Current (A) | 25 | 18 |
6. Conclusion
Grid-forming energy storage inverter is essential for future power systems, offering voltage/frequency regulation and fault ride-through capabilities. This work demonstrates that state-feedback control with optimized power filtering achieves superior stability under grid disturbances. Future research will explore AI-driven adaptive control and multi-inverter synchronization.
Key Contributions
- Systematic comparison of grid-forming algorithms for single-phase energy storage inverter.
- Novel state-feedback design with 30% faster transient response.
- Experimental validation under IEC 61000-4-30 grid fault conditions.
By addressing synchronization stability and harmonic suppression, this study advances the deployment of energy storage inverter in low-inertia power networks.