1. Introduction
The integration of renewable energy sources and distributed generation into modern power systems has accelerated the electrification of grids. Three-phase grid-tied inverters play a pivotal role in interfacing renewable energy systems with the grid. However, unbalanced grid voltages—caused by asymmetrical loads, transmission line faults, or aging infrastructure—severely degrade inverter performance, leading to power oscillations, harmonic distortions, and even system disconnections. Addressing these challenges requires advanced control strategies that ensure stable power delivery while maintaining grid current quality.
Traditional control methods for three-phase grid-tied inverters often prioritize either power stability or current balance, creating inherent trade-offs. For instance:
- Negative-sequence current suppression ensures balanced grid currents but allows power oscillations.
- Active power stabilization eliminates active power fluctuations but introduces unbalanced currents.
- Reactive power stabilization maintains constant reactive power but exacerbates active power oscillations.
This paper proposes a power-current cooperative control strategy for three-phase grid-tied inverters under unbalanced grid conditions. By integrating an improved double second-order generalized integrator phase-locked loop (DSOGI-PLL) and a unified reference current formulation with adjustable coordination coefficients, the strategy achieves seamless transitions between control objectives. The effectiveness of this approach is validated through simulations and hardware-in-the-loop (HIL) experiments.
2. System Modeling and Control Strategy
2.1 Topology of Three-phase Grid-tied Inverters
The studied system comprises an LCL-filtered three-phase grid-tied inverter (Fig. 1). Key parameters include:
- DC-link voltage Udc=1000 VUdc=1000V
- Grid voltage ug=220 Vug=220V (nominal)
- Filter components: L1=5 mH,L2=1.5 mH,Cf=5 μFL1=5mH,L2=1.5mH,Cf=5μF
The control framework operates in the stationary αβαβ-axis to avoid coupling issues inherent in dqdq-axis transformations.
2.2 Improved DSOGI-PLL for Unbalanced Grids
Under unbalanced conditions, grid voltages contain positive- and negative-sequence components. Conventional phase-locked loops (PLLs) struggle to separate these components accurately. The proposed improved DSOGI-PLL addresses this by:
- Utilizing dual second-order generalized integrators (SOGIs) for sequence separation.
- Incorporating a DC-offset rejection mechanism to enhance harmonic immunity.
The transfer functions of the modified SOGI are:D2(s)=kω0ss2+kω0s+ω02,Q2(s)=k(ω02−s2)(s2+kω0s+ω02)(1+τs)D2(s)=s2+kω0s+ω02kω0s,Q2(s)=(s2+kω0s+ω02)(1+τs)k(ω02−s2)
where kk is the damping factor, ω0ω0 is the resonant frequency, and ττ mitigates DC offsets.
2.3 Unified Reference Current Formulation
The instantaneous power under unbalanced voltages is expressed as:{p=P0+P1cos(2ωt)+P2sin(2ωt)q=Q0+Q1cos(2ωt)+Q2sin(2ωt){p=P0+P1cos(2ωt)+P2sin(2ωt)q=Q0+Q1cos(2ωt)+Q2sin(2ωt)
where P0,Q0P0,Q0 are steady-state terms, and P1,P2,Q1,Q2P1,P2,Q1,Q2 represent oscillatory components.
To harmonize conflicting control objectives, a unified reference current formula is derived:{iα∗=2P∗3⋅uα++kuα−M12+kM22+2Q∗3⋅uβ+−kuβ−M12−kM22iβ∗=2P∗3⋅uβ++kuβ−M12+kM22+2Q∗3⋅−uα++kuα−M12−kM22⎩⎨⎧iα∗=32P∗⋅M12+kM22uα++kuα−+32Q∗⋅M12−kM22uβ+−kuβ−iβ∗=32P∗⋅M12+kM22uβ++kuβ−+32Q∗⋅M12−kM22−uα++kuα−
where M12=(uα+)2+(uβ+)2M12=(uα+)2+(uβ+)2 and M22=(uα−)2+(uβ−)2M22=(uα−)2+(uβ−)2. The coordination coefficient kk enables dynamic prioritization:
- k=0k=0: Suppresses negative-sequence currents.
- k=1k=1: Stabilizes active power.
- k=−1k=−1: Stabilizes reactive power.
3. Simulation and Experimental Validation
3.1 Simulation Parameters
Key parameters for Matlab/Simulink simulations are summarized in Table 1.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| DC-link voltage UdcUdc | 1000 V | Filter capacitor CfCf | 5 μF |
| Grid voltage ugug | 220 V | QPR controller KpKp | 0.15 |
| Switching frequency | 20 kHz | QPR controller KrKr | 20 |
3.2 Performance of Improved DSOGI-PLL
The improved DSOGI-PLL demonstrates superior phase-locking accuracy under distorted and unbalanced voltages (Fig. 2). Compared to traditional SRF-PLL, it reduces frequency jitter by 60% when harmonics (5th and 7th) and DC offsets are introduced.
3.3 Dynamic Control with Adjustable kk
- Case 1 (k=0k=0): Balanced grid currents are achieved, but active/reactive power oscillate at 100 Hz (Fig. 3a).
- Case 2 (k=1k=1): Active power stabilizes, but currents become unbalanced, and reactive power fluctuates (Fig. 3b).
- Case 3 (k=−1k=−1): Reactive power stabilizes, while active power oscillates (Fig. 3c).
Smooth transitions between these modes validate the flexibility of the coordination coefficient kk.
4. Discussion
The proposed strategy offers three key advantages for three-phase grid-tied inverters:
- Adaptability: Adjusting kk allows prioritization of power stability or current balance based on grid requirements.
- Robustness: The improved DSOGI-PLL ensures accurate phase detection even under severe voltage distortions.
- Simplicity: A unified control framework reduces computational complexity compared to multi-loop designs.
However, trade-offs persist:
- Stabilizing power increases current asymmetry.
- Eliminating negative-sequence currents exacerbates power oscillations.
Future work will explore adaptive kk-tuning algorithms to optimize performance dynamically.
5. Conclusion
This paper presents a power-current cooperative control strategy for three-phase grid-tied inverters under unbalanced grid conditions. By integrating an improved DSOGI-PLL and a unified reference current formulation with adjustable coordination coefficients, the strategy enables seamless transitions between power stabilization and current balance objectives. Simulations and HIL experiments confirm its effectiveness in enhancing grid stability and power quality. The proposed method holds significant potential for advancing renewable energy integration in modern power systems.