The rapid integration of distributed photovoltaic (PV) systems into low-voltage distribution networks (LVDNs) has intensified challenges related to voltage stability. Voltage violations caused by reverse power flow and intermittent PV generation require adaptive control strategies. This paper proposes a consensus algorithm-based hierarchical coordination strategy between energy storage inverters and PV inverters to mitigate voltage fluctuations while optimizing operational costs.
1. Voltage-Cost Sensitivity Analysis
Voltage regulation efficiency depends on the cost-effectiveness of control devices. The voltage-cost sensitivity factor (FU-C) quantifies the economic impact of reactive or active power adjustments. For PV inverters and energy storage inverters, FU-C is defined as:
[ F{U-C}^{PV, ij} = \frac{S{U-Q}^{ij}}{c{PV}}, \quad F{U-C}^{ESS, ij} = \frac{S{U-P}^{ij}}{c{ESS}} ]
where (S{U-Q}^{ij}) and (S{U-P}^{ij}) are voltage-reactive and voltage-active sensitivities, and (c{PV}) (¥0.067/kvar·h) and (c{ESS}) (¥0.6–1.0/kWh) represent unit regulation costs. The ratio of FU-C for energy storage inverters to PV inverters is:
[ \frac{F{U-C}^{ESS, ij}}{F{U-C}^{PV, ij}} = \frac{R}{X} \cdot \frac{c{PV}}{c{ESS}} ]
In LVDNs with high R/X ratios (1.14–5.56), PV inverters exhibit superior cost-effectiveness. Thus, voltage regulation should prioritize PV reactive power before activating energy storage inverters.
2. Hierarchical Control Framework
The proposed strategy divides control into two stages: PV inverter reactive control and energy storage inverter active control, further categorized into groups based on nodal FU-C.
2.1 Group Classification
- Group 1 (GV1): Nodes 3, 4, 5, 8 (upstream, lower FU-C).
- Group 2 (GV2): Nodes 7, 9, 13, 14 (downstream, higher FU-C).
2.2 PV Inverter Reactive Control
Consensus variables are defined as reactive power utilization ratios ((μ)). The reference value (μ_{ref}) for critical nodes (e.g., Node 14) updates dynamically:
[ μ{ref}(k+1) = \begin{cases} μ{ref}(k) – \alpha \left[ U(k+1) – U{max} \right], & U > U{max} \ μ{ref}(k), & U{min} \leq U \leq U{max} \ μ{ref}(k) – \alpha \left[ U(k+1) – U{min} \right], & U < U{min} \end{cases} ]
Local PV inverters adjust reactive power outputs using distributed consensus:
[ μj(k+1) = \sum{m=1}^{N} \beta{jm} μm(k) + d_j \lambda_1 \left( μj(k) – μ{ref}(k) \right) ]
where (β{jm}) is the weighting factor, (d_j) indicates leader-follower communication, and (λ1) regulates convergence speed.
2.3 Energy Storage Inverter Active Control
If voltage violations persist, energy storage inverters adjust active power using state-of-charge (SOC) deviation ((ΔS)) as consensus variables:
[ ΔS{ref}(k+1) = \begin{cases} ΔS{ref}(k) – \beta \left[ U(k+1) – U{max} \right], & U > U{max} \ ΔS{ref}(k), & U{min} \leq U \leq U{max} \ ΔS{ref}(k) – \beta \left[ U(k+1) – U{min} \right], & U < U{min} \end{cases} ]
The active power output of energy storage inverters is:
[ P{ESS,j} = \frac{ΔS_j(k+1) \cdot S{ESS,j}}{\eta \Delta t} ]
3. Case Study and Results
An IEEE 14-node LVDN with 8 PV systems and energy storage inverters was simulated under varying irradiance (Figure 1). Key parameters include:
| Parameter | Value |
|---|---|
| Line impedance | 0.602 + j0.232 Ω/km |
| PV capacity (Nodes 3–14) | 10–12 kVA |
| Energy storage capacity | 8–10 kWh |
| SOC limits | 20%–80% |
3.1 Voltage Regulation Performance
- Scenario 1: Uncontrolled system experiences severe overvoltage (up to 1.07 pu).
- Scenario 2: PV-only control reduces violations but fails to fully stabilize voltage due to reactive limits.
- Scenario 3: Proposed strategy eliminates violations with minimal energy storage inverter usage (Table 1).
Table 1. Comparative Analysis of Control Strategies
| Metric | PV-Only | ESS-Only | Proposed Strategy |
|---|---|---|---|
| Reactive power (kvar·h) | 87.31 | 0 | 87.31 |
| Active power (kWh) | 0 | 50.81 | 8.03 |
| Total cost (¥) | 5.85 | 30.49 | 10.67 |
3.2 Cost Efficiency
The energy storage inverter’s contribution is reduced by 84.2% compared to ESS-only strategies. Coordination with PV inverters lowers regulation costs by 65%.
4. Consensus Algorithm Robustness
The proposed hierarchical consensus ensures voltage stability under communication delays or partial failures. Key convergence criteria include:
[ \lim{k \to \infty} |μj(k) – μ{ref}(k)| < \epsilon, \quad \lim{k \to \infty} |ΔS_j(k) – ΔS_{ref}(k)| < \epsilon ]
Simulations confirm convergence within 200 iterations for α=1 and β=1, balancing speed and precision.
5. Conclusion
This study demonstrates that coordinating energy storage inverters with PV systems via consensus algorithms significantly enhances voltage stability while minimizing operational costs. Prioritizing PV reactive power and grouping devices based on FU-C optimizes resource utilization, making the strategy scalable for large-scale LVDNs with high PV penetration. Future work will explore real-time adaptability under dynamic load conditions.
Keywords: energy storage inverter, photovoltaic systems, voltage regulation, consensus algorithm, low-voltage distribution networks, hierarchical control, cost sensitivity.