The rapid integration of photovoltaic (PV) systems into low-voltage distribution networks has intensified voltage instability challenges. This paper proposes a distributed control strategy that coordinates PV inverters and energy storage inverters using a consensus algorithm to address voltage violations. By prioritizing cost-effective voltage regulation resources and optimizing group coordination, this approach enhances system stability while minimizing operational costs.
Voltage-Cost Sensitivity Analysis
The voltage-cost sensitivity factor (FU-C) quantifies the economic efficiency of voltage regulation devices. For a PV inverter at node \( j \) influencing node \( i \), FU-C is defined as:
$$ F_{U-C}^{PV,ij} = \frac{S_{U-Q}^{ij}}{c_{PV}} $$
where \( S_{U-Q}^{ij} \) represents the voltage-reactive power sensitivity, and \( c_{PV} \) denotes the unit reactive power cost (¥0.067/kvar·h). For energy storage inverters:
$$ F_{U-C}^{ESS,ij} = \frac{S_{U-P}^{ij}}{c_{ESS}} $$
where \( S_{U-P}^{ij} \) is the voltage-active power sensitivity, and \( c_{ESS} \) is the unit active power cost (¥0.6–1.0/kWh). The economic superiority of PV inverters is demonstrated through:
$$ \frac{F_{U-C}^{ESS,ij}}{F_{U-C}^{PV,ij}} = \frac{R}{X} \cdot \frac{c_{PV}}{c_{ESS}} < 1 $$
| Device Type | Sensitivity Component | Unit Cost | Typical FU-C Ratio |
|---|---|---|---|
| PV Inverter | \( S_{U-Q} = \frac{\sum X_n}{U_0} \) | ¥0.067/kvar·h | 1.14–5.56× higher |
| Energy Storage Inverter | \( S_{U-P} = \frac{\sum R_n}{U_0} \) | ¥0.6–1.0/kWh | Baseline |
Group Coordination Framework
The control architecture divides voltage regulation devices into groups based on nodal FU-C values:
$$ \text{Group Priority} = \begin{cases}
\text{GV2 (Nodes 7,9,13,14)} & \text{if } F_{U-C}^{downstream} \geq 1.5F_{U-C}^{upstream} \\
\text{GV1 (Nodes 3,4,5,8)} & \text{otherwise}
\end{cases} $$
Consensus-Based Control Algorithm
PV Inverter Phase: Reactive power utilization ratio \( \mu \) serves as the consensus variable:
$$ \mu_{GVi,j}(k+1) = \sum_{m=1}^{N_P} \beta_{jm}^{PV} \mu_{GVi,m}(k) + d_j^{PV} \lambda_1 (\mu_{GVi,j}(k) – \mu_{ref}^{GVi}(k)) $$
Energy Storage Inverter Phase: SOC variation \( \Delta S \) coordinates active power dispatch:
$$ \Delta S_{GVi,j}(k+1) = \sum_{m=1}^{N_b} \beta_{jm}^{ESS} \Delta S_{GVi,m}(k) + d_j^{ESS} \lambda_2 (\Delta S_{GVi,j}(k) – \Delta S_{ref}^{GVi}(k)) $$
| Control Parameter | PV Phase | Energy Storage Phase |
|---|---|---|
| Consensus Variable | Reactive Utilization (\( \mu \)) | SOC Variation (\( \Delta S \)) |
| Weight Factor (\( \beta \)) | 0.35 | 0.40 |
| Communication Links | Bidirectional within GV2 | Cross-group coordination |
Simulation Results
Comparative analysis of control strategies demonstrates the superiority of the proposed method:
| Strategy | ESS Capacity Used | Voltage Regulation Cost | Convergence Time |
|---|---|---|---|
| S1 (PV Only) | N/A | ¥5.85 | 208 iterations |
| S2 (ESS Only) | 50.81 kWh | ¥30.49 | 173 iterations |
| S3 (Proposed) | 8.03 kWh | ¥10.67 | 154 iterations |
The energy storage inverter coordination reduces required capacity by 84.2% compared to standalone ESS control. The hierarchical activation of PV and energy storage inverters maintains voltage within 1.05 pu throughout the 3-hour simulation.
Economic Optimization
The multi-stage regulation cost model confirms the strategy’s effectiveness:
$$ C_{total} = \sum_{t=1}^{T} (0.067Q_{PV}(t) + 0.6P_{ESS}(t)) $$
Where \( Q_{PV} \) and \( P_{ESS} \) represent hourly reactive and active power adjustments. The proposed method achieves 65% cost reduction compared with global consensus approaches.
Conclusion
This paper establishes a distributed voltage control framework that optimally coordinates PV inverters and energy storage inverters through FU-C-based grouping and consensus algorithms. The hierarchical activation mechanism significantly enhances the economic efficiency of voltage regulation while ensuring system stability. Future work will investigate dynamic group reconfiguration under varying network topologies.