1. Introduction
The rapid integration of renewable energy sources and the global push toward carbon neutrality have underscored the critical role of energy storage inverter in modern power systems. These inverters, particularly in single-phase residential applications, must ensure stable operation under weak grid conditions and high renewable penetration. Unlike grid-following inverters, which rely on external voltage references, grid-forming inverters autonomously regulate voltage and frequency, mimicking synchronous generators to enhance system stability. However, their application in single-phase systems faces challenges, including accurate power measurement, control loop design, and stability under large-signal disturbances. This paper addresses these challenges by analyzing control algorithms, power detection methods, and digital control strategies for single-phase energy storage inverter.
2. Control Algorithm Analysis for Grid-Forming Inverters
Grid-forming control strategies are classified into non-inertial and inertial methods based on their dynamic response characteristics.
2.1 Non-Inertial Control
- Power Synchronization Control (PSC):
Regulates voltage phase angle (θ) and magnitude (V) through integral and proportional actions:{θ=ωot+kP∫(Po−P)dtV=Vo+kq(Qo−Q)Here, kP and kq are gains for active and reactive power loops. - Droop Control:
Adjusts frequency (ω) and voltage based on power deviations:{ω=ωo+kP(Po−P)V=Vo+kq(Qo−Q)
2.2 Inertial Control
- Virtual Synchronous Generator (VSG):
Emulates rotor dynamics of synchronous machines:Jdtdω=Tm−Te−D(ω−ωo)where J is virtual inertia, D is damping coefficient, and Tm, Te are mechanical and electromagnetic torques. - Low-Pass Filter (LPF)-Based Droop Control:
Introduces inertia via filtering power signals:{ω=ωo+kP⋅s+ωpωp(Po−P)V=Vo+kq⋅s+ωqωq(Qo−Q)
Table 1: Comparison of Grid-Forming Control Strategies
| Method | Order | Key Parameters | Stability Characteristics |
|---|---|---|---|
| PSC | 1st | kP,kq | Fast response, limited damping |
| Droop Control | 1st | kP,kq | Simple implementation, steady-state error |
| VSG | 2nd | J,D | Inertia support, oscillation damping |
| LPF-Based Droop | 2nd | ωp,ωq | Tunable inertia, delayed response |
3. Power Detection in Single-Phase Systems
Accurate measurement of active (P) and reactive (Q) power is critical for control stability.
3.1 Traditional vs. Instantaneous Power Theory
- Traditional Method:
Computes average power over a cycle, suitable for sinusoidal conditions:P=T1∫0Tv(t)⋅i(t)dt - Instantaneous Power Theory:
Uses orthogonal signal generation (e.g., SOGI, APF) for real-time computation:{p=vαiα+vβiβq=vαiβ−vβiα
Table 2: Orthogonal Signal Generation Techniques
| Method | Advantages | Limitations |
|---|---|---|
| Direct Phase Shift | Simple implementation | Poor dynamic performance |
| All-Pass Filter | Frequency adaptability | Susceptible to harmonics |
| SOGI | Harmonic rejection | Complex parameter tuning |
3.2 Filtering Techniques for Power Feedback
- Low-Pass Filter (LPF):GLPF(s)=s+ωcωc
- Notch Filter:GNotch(s)=s2+2ζωos+ωo2s2+ωo2
Figure 1 demonstrates the impact of LPF cutoff frequency (ωc) on power signal smoothing. Lower ωc reduces ripple but increases delay, affecting transient response.
4. Digital Control Loop Design
4.1 Dual-Loop Voltage-Current Control
The inner current loop and outer voltage loop ensure fast tracking and stability.
- Current Loop Transfer Function:Gi(s)=s2+(kpi+R/L)s+kii/Lkpis+kii
- Voltage Loop Transfer Function:Gv(s)=s(Cs+kpv)kpvs+kiv
4.2 State Feedback Control
Enhances stability by feeding back inverter current (iL1) and PCC voltage (vpcc):u=K1iL1+K2vpcc
Table 3: Stability Analysis with State Feedback
| Feedback Gain | Damping Ratio (ζ) | Settling Time (ms) |
|---|---|---|
| K1=0.5 | 0.7 | 12.5 |
| K1=1.0 | 1.2 | 8.2 |
5. Experimental Validation
A 2 kW single-phase energy storage inverter prototype was tested under grid-connected and islanded modes. Key results include:
- Islanded Mode:
The inverter maintained vpcc at 220 V ± 2% with a THD < 3% under nonlinear loads. - Grid Fault Recovery:
With state feedback control, the system stabilized within 15 ms after a 50% voltage sag.
Table 4: Performance Comparison Under Different Controls
| Control Method | Voltage THD (%) | Recovery Time (ms) |
|---|---|---|
| Dual-Loop | 3.5 | 25 |
| State Feedback | 2.8 | 15 |
6. Conclusion and Future Directions
This work establishes a framework for designing stable single-phase grid-forming energy storage inverter. Key contributions include:
- Classification of control algorithms based on inertia and damping characteristics.
- Analysis of power detection delays and their impact on large-signal stability.
- Development of a state feedback controller to enhance transient performance.
Future research will focus on adaptive parameter tuning and hybrid control strategies for multi-inverter systems.