1. Introduction
The rapid integration of renewable energy sources, such as photovoltaic (PV) systems, into power grids has introduced challenges related to grid stability, dynamic response, and power quality. Energy storage inverters play a pivotal role in addressing these challenges by enabling efficient energy conversion, grid support, and load management. This study focuses on a 10 kW single-phase photovoltaic energy storage inverter, employing a Virtual Synchronous Generator (VSG) strategy to enhance parallel operation performance. The primary objectives include improving dynamic response stability, optimizing power distribution accuracy, and mitigating harmonic distortions.
2. Circuit Topology and Hardware Design
2.1 Bidirectional DC/DC Converter
The bidirectional DC/DC converter facilitates energy transfer between the battery and the DC bus. Key design considerations include efficiency, voltage stress, and component count. A half-bridge topology was selected due to its low switching losses, reduced voltage stress on components, and simplicity.
Table 1: Comparison of DC/DC Topologies
| Topology | Voltage Stress | Inductor Current | Switching Losses | Efficiency |
|---|---|---|---|---|
| Boost/Buck | High | High | Moderate | 92-95% |
| Half-Bridge | Low | Moderate | Low | 96-98% |
| Cuk | High | High | High | 90-93% |
| SEPIC/Zeta | High | High | High | 88-91% |
The half-bridge converter operates in boost mode during discharge (battery to DC bus) and buck mode during charge (DC bus to battery). Key parameters include:
- Inductor: L=1mH (designed for 151.8 A peak current)
- Capacitors: CBUS=1μF,CBAT=1μF
- Switching Devices: IGBTs (1000 V, 240 A) and fast-recovery diodes.
Equations for Inductor Design:L≥ΔI⋅fs⋅UBUSUBAT⋅(UBUS−UBAT)
where ΔI is the current ripple (20% of average current) and fs=20kHz.
2.2 DC/AC Inverter
The HERIC (Highly Efficient and Reliable Inverter Concept) topology was chosen for the DC/AC stage due to its low leakage current, high efficiency (>98%), and sinusoidal output.
Key Components:
- Switching Devices: IGBTs (1200 V, 240 A)
- Filter: L=0.2mH×2, C=10μF
- Modulation: Unipolar SPWM with dead-time compensation.
Output Voltage Equation:Uout=2UBUS⋅D
where D is the modulation index.
3. VSG-Based Control Strategy for Parallel Operation
3.1 Virtual Synchronous Generator Fundamentals
The VSG algorithm emulates the inertia and damping characteristics of synchronous generators, enhancing grid stability. The mechanical dynamics are modeled as:Jdtdω=Pref−Pout−D(ω−ωgrid)
where J is the virtual inertia, D is the damping coefficient, and ωgrid is the grid angular frequency.
Power Loop Equations:
- Active Power Control:
ω=ωref−kp(Pref−Pout)
- Reactive Power Control:
U=Uref−kq(Qref−Qout)
3.2 Parameter Optimization for Dynamic Response
The dynamic performance of the energy storage inverter is influenced by J, D, and droop coefficients (kp,kq).
Table 2: Impact of VSG Parameters
| Parameter | Effect on Dynamic Response | Optimal Range |
|---|---|---|
| J | Higher J reduces frequency fluctuations | 10–25 kg·m² |
| D | Higher D dampens oscillations | 500–1500 N·m·s/rad |
| kp | Larger kp improves active power sharing | 0.5–2.0 rad/W |
| kq | Larger kq enhances reactive power accuracy | 0.1–0.5 V/VAr |
Transfer Function Analysis:G(s)=Pref(s)Pout(s)=Js2+Ds+kp1
Root locus analysis confirmed that J=15kg\cdotpm² and D=1000N\cdotpm\cdotps/rad achieve a damping ratio (ζ) of 0.7, balancing response speed and stability.
3.3 Decoupling Power Control with Virtual Impedance
Line impedance mismatch in parallel operation causes uneven power distribution. A virtual impedance loop was introduced to decouple active and reactive power:Zvirtual=Rv+jωLv
where Rv=0.1Ω and Lv=2mH. This ensures inductive dominance, aligning with VSG requirements.
Second-Order Generalized Integrator (SOGI) was employed for current tracking:GSOGI(s)=s2+kωs+ω2kωs
where k=1.414 for optimal filtering.
4. Adaptive Frequency Control with Quantum-Inspired ABC Algorithm
4.1 Frequency Adaptive Strategy
A frequency adaptive loop adjusts J and D in real-time based on grid disturbances:ΔJ=KJ⋅(Δω+Td⋅dtdΔω)ΔD=KD⋅(Δω+Ti⋅∫Δωdt)
where KJ=0.1, KD=0.05, Td=0.01s, and Ti=0.1s.
4.2 Quantum Artificial Bee Colony (QABC) Optimization
The QABC algorithm optimizes J and D to minimize THD and settling time.
Algorithm Steps:
- Initialization: Generate a population of J and D pairs.
- Employed Bees: Evaluate fitness using THD+0.5⋅tsettling.
- Onlooker Bees: Select solutions probabilistically.
- Scout Bees: Replace stagnant solutions with random values.
- Quantum Rotation: Update parameters using:
θi+1=θi+Δθ⋅sign(fbest−fi)
Table 3: QABC Performance Comparison
| Metric | Conventional VSG | QABC-Optimized VSG | Improvement |
|---|---|---|---|
| Settling Time (s) | 0.15 | 0.08 | 46.7% |
| THD (Current) | 4.2% | 3.5% | 16.7% |
| Active Power Error | 8.3% | 2.9% | 64.6% |
| Reactive Power Error | 6.7% | 3.5% | 47.0% |
5. Experimental Validation
A 10 kW prototype energy storage inverter was tested under grid-connected, islanded, and parallel modes.
Key Results:
- DC/DC Efficiency: 97.2% at full load.
- Inverter THD: 2.8% (voltage), 3.1% (current).
- Mode Transition: Seamless switching within 20 ms.
- Parallel Operation: Active/reactive power deviations <3% for 2:1 capacity ratio.
Table 4: Experimental Performance Summary
| Test Scenario | Voltage Sag | THD Reduction | Power Deviation |
|---|---|---|---|
| Grid-Connected | 1.2% | 15.6% | N/A |
| Islanded | 0.8% | 16.3% | N/A |
| Parallel (2:1 Load) | 1.5% | 14.9% | <3% |
6. Conclusion
This study demonstrates that integrating VSG control with adaptive parameter optimization significantly enhances the performance of single-phase photovoltaic energy storage inverters. The proposed strategies improve dynamic response, reduce harmonic distortions, and ensure accurate power sharing in parallel configurations. Future work will explore multi-objective optimization for hybrid renewable systems.