1. Introduction
The increasing integration of renewable energy sources (RES) into power systems has highlighted the importance of microgrids in enhancing energy reliability and efficiency. Energy storage inverters, as critical components in islanded microgrids, stabilize voltage and frequency while managing power fluctuations. However, parallel operation of multiple energy storage inverters faces challenges such as reactive power misallocation due to unequal line impedances and State of Charge (SOC) imbalances among battery units. This study proposes an adaptive control strategy combining virtual impedance and SOC coordination to address these issues, ensuring efficient and stable microgrid operation.
2. Energy Storage System Modeling and SOC Estimation
2.1 ESS Electrical Model
The energy storage system (ESS) is modeled using a simplified equivalent circuit for batteries (Figure 1). The terminal voltage UbatUbat is derived as:Ubat=n⋅(E−IbatR)Ubat=n⋅(E−IbatR)
where EE is the battery electromotive force, RR is the internal resistance, and nn is the number of series-connected cells.
2.2 SOC Estimation
SOC is calculated using the ampere-hour integral method:SOC=SOC0−∫ibatdtCnomSOC=SOC0−Cnom∫ibatdt
where SOC0SOC0 is the initial SOC, ibatibat is the discharge current, and CnomCnom is the nominal capacity.
Table 1: Key Parameters of Battery and Supercapacitor
| Parameter | Battery | Supercapacitor |
|---|---|---|
| Energy Density | High | Low |
| Power Density | Low | High |
| Cycle Life (cycles) | 500–1000 | 5×1065×106 |
3. Inverter Modeling and Control Design
3.1 Inverter Mathematical Model
A three-phase voltage-source inverter with LC filters is modeled in the dq-axis:{Ldiddt=ud−uod+ωLiqLdiqdt=uq−uoq−ωLidCduoddt=id−iod+ωCuoqCduoqdt=iq−ioq−ωCuod⎩⎨⎧Ldtdid=ud−uod+ωLiqLdtdiq=uq−uoq−ωLidCdtduod=id−iod+ωCuoqCdtduoq=iq−ioq−ωCuod
where ud,uqud,uq, id,iqid,iq, and uod,uoquod,uoq represent dq-axis voltages, currents, and output voltages, respectively.
3.2 Dual-Loop Control Design
The voltage-current dual-loop control parameters are designed as follows:
- Current Inner Loop:kpi=55,kii=1570kpi=55,kii=1570
- Voltage Outer Loop:kpv=10,kiv=500kpv=10,kiv=500
Table 2: LC Filter Parameters
| Parameter | Symbol | Value |
|---|---|---|
| Inductance | LL | 0.77 mH |
| Capacitance | CC | 50 μF |
| Switching Frequency | fswfsw | 10 kHz |
4. Parallel Control Strategy for Energy Storage Inverters
4.1 Traditional Droop Control Limitations
The conventional droop control equations are:{f=fref−m(P−Pref)U=Uref−n(Q−Qref){f=fref−m(P−Pref)U=Uref−n(Q−Qref)
However, unequal line impedances lead to reactive power sharing errors and circulating currents.
4.2 Adaptive Virtual Impedance Design
To mitigate impedance mismatch, an adaptive virtual impedance ZvZv is introduced:Zv=Rv+jωLvZv=Rv+jωLv
The reference voltage is adjusted as:Uref∗=Uref−Zv⋅ioUref∗=Uref−Zv⋅io
Table 3: Simulation Cases for Virtual Impedance
| Case | Line Impedance (Ω) | Capacity Ratio |
|---|---|---|
| 1 | 0.24 + j1.2 (Both) | 1:1 |
| 2 | 0.24 + j1.2 vs. 0.4 + j2 | 1:1 |
| 3 | 0.24 + j1.2 vs. 0.4 + j2 | 3:1 |
5. SOC Coordination Control Strategy
5.1 Multiplicative Factor-Based SOC Control
The frequency adjustment equation is modified as:fi=fref−mpPi⋅[1−kSOC⋅SOCi]fi=fref−mpPi⋅[1−kSOC⋅SOCi]
However, this method causes frequency deviations during SOC balancing.
5.2 Exponential Factor-Based SOC Control
An improved strategy using exponential factors ensures faster convergence and minimal frequency offset:fi=fref−mpPiCiexp[−α(SOCi−SOCave)]fi=fref−CimpPiexp[−α(SOCi−SOCave)]
where αα is the coordination factor, and SOCaveSOCave is the average SOC.
Table 4: SOC Coordination Performance
| Case | Coordination Factor (αα) | Convergence Time (s) | Frequency Deviation (Hz) |
|---|---|---|---|
| 1 | 10 | 3.0 | ≤0.05 |
| 2 | 20 | 2.0 | ≤0.05 |
| 3 | 80 | 1.0 | ≤0.15 |
6. Multi-Agent Consensus Algorithm
A distributed consensus algorithm enables plug-and-play operation without centralized control:xi(k+1)=xi(k)+∑j∈Niaij[xj(k)−xi(k)]xi(k+1)=xi(k)+j∈Ni∑aij[xj(k)−xi(k)]
Table 5: Consensus Algorithm Parameters
| Parameter | Value |
|---|---|
| Convergence Threshold (γγ) | 0.01 |
| Iterations | 20 |
7. Simulation and Validation
7.1 Case 1: Equal Capacity Inverters
- SOC Coordination: Initial SOCs = 0.8, 0.7, 0.6 → Balanced to 0.7 within 3s.
- Frequency Stability: Δf<0.05 HzΔf<0.05Hz.
7.2 Case 2: Unequal Capacity Inverters
- Power Sharing: Proportional to capacity ratios (15Ah:20Ah:25Ah).
- Unbalance Degree: εi<5%εi<5%.
8. Conclusion and Future Work
This study proposes an adaptive control strategy combining virtual impedance and SOC coordination for energy storage inverters in islanded microgrids. Key contributions include:
- Adaptive Virtual Impedance: Enhances reactive power sharing accuracy.
- Exponential SOC Coordination: Achieves rapid balancing with minimal frequency deviation.
- Consensus Algorithm: Enables decentralized plug-and-play operation.
Future Directions:
- Experimental validation of control strategies.
- Integration with RES in hybrid AC/DC microgrids.
- Extension to grid-connected scenarios.
By addressing impedance mismatches and SOC imbalances, this work advances the reliability and efficiency of energy storage inverters in modern power systems.