With the rapid integration of distributed photovoltaic (PV) systems into low-voltage distribution networks, voltage regulation has become critical. This paper proposes a two-stage hierarchical voltage control strategy leveraging the reactive power capability of PV inverters and active power support from energy storage inverters. The methodology combines sensitivity analysis with consensus algorithm-based coordination to optimize voltage stability while minimizing operational costs.
1. Voltage-Cost Sensitivity Framework
The voltage regulation effectiveness per unit cost is quantified through Voltage-Cost Sensitivity Factor (FU-C):
$$F_{U-C}^{PV,ij} = \frac{S_{U-Q}^{ij}}{c_{PV}}$$
$$F_{U-C}^{ESS,ij} = \frac{S_{U-P}^{ij}}{c_{ESS}}$$
Where SU-Q and SU-P represent voltage sensitivities to reactive and active power changes, while cPV (0.067 $/kVar·h) and cESS (0.6-1.0 $/kWh) denote regulation costs. For typical LV networks with R/X ratio 1.14-5.56:
$$\frac{F_{U-C}^{ESS,ij}}{F_{U-C}^{PV,ij}} = \frac{R}{X} \cdot \frac{c_{PV}}{c_{ESS}} < 1$$
| Device Type | Sensitivity Component | Cost Factor | Typical FU-C |
|---|---|---|---|
| PV Inverter | SU-Q = ΣXn/U0 | 0.067 $/kVar·h | 1.82×10-3 V/$ |
| Energy Storage Inverter | SU-P = ΣRn/U0 | 0.8 $/kWh | 0.94×10-3 V/$ |
2. Consensus-Based Hierarchical Control
The control architecture implements sequential optimization:
2.1 PV Inverter Reactive Control Stage
Group voltage controllers (GVCs) coordinate PV clusters based on reactive utilization ratio μ:
$$μ_{GVi,j}(k+1) = \sum_{m=1}^{N_p} β_{jm}^{PV}μ_{GVi,m}(k) + d_j^{PV}λ_1(μ_{GVi,j}(k)-μ_{ref}(k))$$
Where λ1 = 0.35 ensures convergence. Reactive power allocation follows:
$$Q_{GVi,j} = μ_{GVi,j} \cdot Q_{max,j}$$
2.2 Energy Storage Inverter Active Control Stage
Energy storage inverters adjust SOC changes ΔS through distributed consensus:
$$ΔS_{GVi,j}(k+1) = \sum_{m=1}^{N_b} β_{jm}^{ESS}ΔS_{GVi,m}(k) + d_j^{ESS}λ_2(ΔS_{GVi,j}(k)-ΔS_{ref}(k))$$
Active power dispatch is calculated as:
$$P_{ESS,j} = \frac{ΔS_{GVi,j} \cdot S_{ESS,j}}{ηΔt}$$
3. Case Study Implementation
An IEEE 14-node LV network with 8 PV/storage nodes demonstrates the strategy:
| Node Group | PV Capacity (kVA) | ESS Capacity (kWh) | ESS Power Rating (kW) |
|---|---|---|---|
| GV1 (3,4,5,8) | 10-12 | 8-10 | 1.6-2.0 |
| GV2 (7,9,13,14) | 10 | 8 | 1.6 |
Key performance metrics under different strategies:
| Strategy | PV Reactive Cost ($) | ESS Active Cost ($) | Total Cost ($) |
|---|---|---|---|
| S1 (PV Only) | 5.85 | – | 5.85 |
| S2 (ESS Only) | – | 30.49 | 30.49 |
| S3 (Proposed) | 5.85 | 4.82 | 10.67 |
| S4 (Global Consensus) | 6.27 | 6.83 | 13.20 |
4. Advanced Coordination Mechanism
The energy storage inverter control integrates three-layer optimization:
$$min \sum_{t=1}^{T} [c_{PV}Q_{PV}(t) + c_{ESS}P_{ESS}(t)]$$
$$s.t.\quad V_{min} ≤ V_i(t) ≤ V_{max}$$
$$SOC_{min} ≤ SOC(t) ≤ SOC_{max}$$
Real-time adjustment factors for energy storage inverters:
$$α_{ESS} = \frac{\partial V}{\partial P_{ESS}} \cdot \frac{1}{c_{ESS}}$$
$$β_{ESS} = \frac{\partial SOC}{\partial P_{ESS}} \cdot \frac{1}{Δt}$$
5. Conclusion
The proposed hierarchical control strategy demonstrates 35% cost reduction compared with pure energy storage inverter solutions and 19.55% improvement over global consensus approaches. By prioritizing PV reactive support and coordinating energy storage inverters through sensitivity-optimized grouping, the method effectively addresses voltage violations while extending equipment lifespan through balanced utilization.