1. Introduction
The rapid integration of distributed energy resources (DERs), such as photovoltaic (PV) systems and wind turbines, has introduced challenges related to grid stability. These systems inherently lack inertia and damping, leading to frequency fluctuations and power oscillations during grid disturbances. To address this, the concept of Virtual Synchronous Generator (VSG) technology has emerged, mimicking the rotational inertia and damping characteristics of traditional synchronous generators. However, conventional VSG control strategies often neglect the dynamic constraints imposed by energy storage inverters, such as state-of-charge (SOC) limits and charge/discharge rates. This paper proposes a fuzzy adaptive control strategy tailored for energy storage inverters, combining VSG principles with fuzzy logic to enhance system stability and power quality.
2. System Architecture and Key Components
2.1 Three-Level NPC Inverter Topology
The energy storage inverter adopts a Neutral-Point Clamped (NPC) three-level circuit (Figure 1). Compared to traditional two-level inverters, this topology reduces output voltage and current Total Harmonic Distortion (THD) to 0.02% and 0.01%, respectively, significantly improving compliance with grid standards. Key features include:
- Four IGBTs and two clamping diodes per phase.
- Midpoint voltage balancing to prevent simultaneous conduction of upper and lower switches.
- Enhanced efficiency for medium-power applications.
2.2 Energy Storage Integration
The DC side integrates a PV array and a battery energy storage system (BESS) through Boost and bidirectional Buck/Boost converters. The PV operates under Maximum Power Point Tracking (MPPT), while the BESS employs dual-loop control:
- Outer loop: Regulates DC-link voltage.
- Inner loop: Controls battery current.
The DC-link voltage remains stable at 750 V, ensuring continuous power delivery to the grid.
3. VSG Control Framework
3.1 VSG Rotational Dynamics
The VSG emulates synchronous generator behavior using the rotor motion equation:{dωdt=Pm−PeJω0−D(ω−ω0)Jdδdt=ω−ω0{dtdω=Jω0Pm−Pe−JD(ω−ω0)dtdδ=ω−ω0
where:
- JJ: Virtual inertia ().
- DD: Damping coefficient ().
- ω0ω0: Grid reference frequency (314 rad/s314rad/s).
- Pm,PePm,Pe: Mechanical and electromagnetic power.
3.2 Stability Analysis
The second-order transfer function of VSG active power is derived as:Φ(s)=P(s)Pref(s)=MtJω0s2+Dω0+KwJω0s+MtJω0Φ(s)=Pref(s)P(s)=s2+Jω0Dω0+Kws+Jω0MtJω0Mt
Natural oscillation frequency (ωnωn) and damping ratio (ξξ) are:ωn=MtJω0,ξ=D2JMt+Kw2JMtωn=Jω0Mt,ξ=2JMtD+2JMtKw
Increasing JJ reduces ωnωn, causing slower responses, while higher DD suppresses oscillations but prolongs settling time.
4. Fuzzy Adaptive Control Strategy
4.1 Inputs and Outputs
The fuzzy controller uses two inputs:
- Angular velocity deviation (ΔωΔω).
- Angular velocity change rate (dω/dtdω/dt).
Outputs adjust JJ and DD dynamically to balance stability and responsiveness.
4.2 Fuzzy Rule Tables
Table 1: Rules for inertia adjustment (ΔJΔJ).
| Δω\dω/dtΔω\dω/dt | NL | NS | ZO | PS | PL |
|---|---|---|---|---|---|
| NL | PL | PL | PS | ZO | NS |
| NS | PL | PS | ZO | NS | NS |
| ZO | NS | PS | ZO | PS | NS |
| PS | NS | NS | ZO | PS | PL |
| PL | NS | ZO | PS | PL | PL |
Table 2: Rules for damping adjustment (ΔDΔD).
| Δω\dω/dtΔω\dω/dt | NL | NS | ZO | PS | PL |
|---|---|---|---|---|---|
| NL | PL | PS | ZO | PS | NS |
| NS | PS | PL | ZO | PS | NS |
| ZO | PS | PL | ZO | PS | NS |
| PS | PS | ZO | PS | PS | PL |
| PL | PS | ZO | PS | PS | PL |
4.3 Membership Functions
- Inputs: Triangular and S-shaped functions with universe [-1, 1].
- Outputs: Triangular functions with universe [-6, 6].
4.4 Constraints on Virtual Inertia
Energy storage inverters impose bounds on JJ:
- Lower bound: Limited by maximum Rate-of-Change-of-Frequency (RoCoF):
Jmin=ΔPmax2πω0⋅RoCoFmaxJmin=2πω0⋅RoCoFmaxΔPmax
- Upper bound: Limited by BESS power capacity (Pmax-BESSPmax-BESS):
Jmax=Pmax-BESS⋅ΔtΔωJmax=ΔωPmax-BESS⋅Δt
5. Simulation and Performance Evaluation
5.1 Test Conditions
- Simulation platform: MATLAB/Simulink.
- Parameters:
- DC-link voltage: 750 V.
- Initial inertia (J0J0): 0.4 .
- Initial damping (D0D0): 15 .
- Load step: 20 kW → 10 kW at 0.5 s; 10 kW → 20 kW at 1 s.
5.2 Comparative Results
Table 3: Frequency overshoot comparison.
| Control Strategy | Max Frequency Overshoot (Hz) | Settling Time (s) |
|---|---|---|
| Fixed-parameter VSG | 0.21 | >1.5 |
| Conventional adaptive VSG | 0.14 | 1.2 |
| Fuzzy adaptive VSG | 0.12 | 0.8 |
Key observations:
- Fuzzy adaptive control reduces frequency fluctuations by 42.8% compared to fixed-parameter VSG.
- Power oscillations are damped faster, minimizing stress on the energy storage inverter.
5.3 Power Quality Analysis
- Voltage THD: 0.02%.
- Current THD: 0.01%.
- DC-link voltage ripple: <2.67%, within 5% tolerance.
6. Conclusion
This work presents a fuzzy adaptive control strategy for energy storage inverters, integrating VSG dynamics with fuzzy logic to address grid stability challenges. The NPC three-level inverter topology ensures ultra-low harmonic distortion, while the adaptive tuning of JJ and DD enhances transient response and frequency support. Simulation results validate the superiority of the proposed method over conventional approaches, demonstrating its potential for large-scale renewable energy integration. Future work will focus on hardware-in-the-loop validation and multi-inverter coordination.