With the increasing integration of distributed solar power into distribution networks, voltage violations at grid connection points have become a critical issue. This paper addresses these challenges by proposing a voltage control strategy for solar inverters based on distributed consensus collaboration. The approach leverages power regulation through droop control and a distributed algorithm to coordinate multiple solar inverters, enhancing voltage stability while minimizing active power curtailment. We begin by analyzing the impact of solar power on distribution networks, then detail the control methodology, and present simulation results to validate the effectiveness of the proposed method.
The proliferation of solar energy systems has transformed distribution networks from unidirectional power flow to bidirectional, leading to complex voltage profiles. Solar inverters play a pivotal role in mitigating voltage fluctuations by adjusting active and reactive power outputs. Traditional control methods, such as centralized and local approaches, often fall short in handling the rapid variability of solar generation. Centralized control suffers from communication delays and scalability issues, while local control lacks coordination among solar inverters. Our proposed distributed consensus collaboration method overcomes these limitations by enabling real-time coordination between solar inverters, ensuring optimal voltage regulation across the network.
In this work, we focus on the voltage control capabilities of solar inverters, which can modulate power outputs to maintain voltage within safe limits. The control strategy involves two layers: a local droop control layer for rapid response and a distributed consensus layer for periodic parameter adjustments. By using the active power output ratio of solar inverters as a state variable, the consensus algorithm synchronizes the inverters’ operations, reducing voltage violations and maximizing power utilization. We demonstrate through simulations that this approach significantly improves voltage profiles compared to conventional methods, with reduced active power curtailment and enhanced reactive power support from solar inverters.
Background and Fundamentals
The integration of solar power into distribution networks alters voltage distributions due to variable power injections. To understand this, consider a simplified grid model with a solar inverter connected at a point of common coupling. The voltage at the connection point can be derived from the circuit equations. Let \( V_1 \) be the voltage at the upstream bus, and \( V_2 \) be the voltage at the solar inverter connection point. The voltage difference \( \Delta V \) is given by:
$$ \Delta V = V_1 – V_2 \approx \frac{P R + Q X}{V_2} $$
where \( P \) and \( Q \) represent the net active and reactive power flows, \( R \) and \( X \) are the line resistance and reactance, respectively. When solar generation exceeds local load demand, \( \Delta V \) becomes positive, causing voltage rise at \( V_2 \). Conversely, if load demand is higher, \( \Delta V \) negative leads to voltage drop. This fundamental relationship underscores the need for power control via solar inverters to regulate voltage.
Solar inverters have inherent capabilities to adjust both active and reactive power within their capacity limits. The apparent power constraint for a solar inverter is expressed as:
$$ S_{pv} = \sqrt{P_{pv}^2 + Q_{pv}^2} $$
where \( S_{pv} \) is the rated capacity of the solar inverter, \( P_{pv} \) is the active power output, and \( Q_{pv} \) is the reactive power output. The reactive power capacity varies with active power output, as shown in the following equation:
$$ Q_{pv} = \pm \sqrt{S_{pv}^2 – P_{pv}^2} $$
This equation indicates that when a solar inverter operates at maximum active power (e.g., at the maximum power point tracking, MPPT), its reactive power capacity is zero. As active power decreases, the inverter can provide or absorb more reactive power. This trade-off is crucial for voltage control, as it allows solar inverters to prioritize reactive power support when needed, thereby minimizing active power curtailment.
To operationalize this, we employ a droop-based control strategy for solar inverters, known as \( Q_{pv}(P_{pv}) \) control. This method uses voltage thresholds to trigger power adjustments. The control logic is defined by key voltage points: \( V_{\text{max}} \) (upper voltage limit), \( V_{\text{min}} \) (lower voltage limit), \( V_{tP} \) (active power control start voltage), \( V_{tQ} \) (reactive power absorption start voltage), and \( V_{aQ} \) (reactive power compensation start voltage). The power outputs are regulated as follows:
$$
(P_{pv}, Q_{pv}) =
\begin{cases}
(P_{\text{MPPT}}, Q_{\text{max}}), & V \leq V_{\text{min}} \\
\left( P_{\text{MPPT}}, Q_{\text{max}} \cdot \frac{V – V_{\text{min}}}{V_{aQ} – V_{\text{min}}} \right), & V_{\text{min}} < V \leq V_{aQ} \\
(P_{\text{MPPT}}, 0), & V_{aQ} < V \leq V_{tQ} \\
\left( P_{\text{MPPT}}, -Q_{\text{max}} \cdot \frac{V – V_{tQ}}{V_{tP} – V_{tQ}} \right), & V_{tQ} < V \leq V_{tP} \\
\left( P_{\text{MPPT}} \cdot \frac{V_{\text{max}} – V}{V_{\text{max}} – V_{tP}}, -Q_{\text{max}} \right), & V_{tP} < V \leq V_{\text{max}} \\
(0, -Q_{\text{max}}), & V > V_{\text{max}}
\end{cases}
$$
This piecewise function ensures that solar inverters respond dynamically to voltage changes, with reactive power prioritized initially and active power curtailed only when necessary. However, without coordination, individual solar inverters may operate suboptimally. Hence, we introduce a distributed consensus layer to synchronize their actions.
Proposed Distributed Consensus Collaboration Method
The core of our approach is a distributed consensus collaboration algorithm that coordinates multiple solar inverters in the network. This algorithm operates at a slower time scale than the local droop control, periodically adjusting the threshold parameters (e.g., \( V_{tP} \)) based on shared information among solar inverters. Each solar inverter communicates with its neighbors to exchange state variables, specifically the active power output ratio \( f_{pv,i} \), defined as:
$$ f_{pv,i} = \frac{P_{pv,i}}{P_{\text{MPPT},i}} $$
where \( P_{pv,i} \) is the active power output of solar inverter \( i \), and \( P_{\text{MPPT},i} \) is its maximum available power. The goal is to achieve consensus on \( f_{pv,i} \) across all solar inverters, ensuring uniform power utilization. The consensus update for each solar inverter is given by:
$$ x_i(k+1) = x_i(k) + \sum_{j \in N_i} w_{ij}(k) (x_j(k) – x_i(k)) $$
where \( x_i(k) \) represents the state variable (e.g., \( f_{pv,i} \)) of solar inverter \( i \) at iteration \( k \), \( N_i \) is the set of neighboring solar inverters, and \( w_{ij}(k) \) is the weight factor for communication between solar inverters \( i \) and \( j \). The weight matrix \( W \) is constructed to ensure convergence, with elements defined as:
$$ w_{ij} =
\begin{cases}
\frac{1}{1 + \max(n_i, n_j)}, & i \neq j \\
1 – \sum_{j \in N_i} w_{ij}, & i = j
\end{cases} $$
where \( n_i \) and \( n_j \) are the numbers of neighbors for solar inverters \( i \) and \( j \), respectively. This formulation guarantees that the state variables converge to a common value, as expressed by:
$$ \lim_{k \to \infty} X(k) = \frac{1}{n} \mathbf{1} \mathbf{1}^T X(0) $$
where \( X(k) \) is the vector of state variables, and \( \mathbf{1} \) is a vector of ones. Convergence is assessed using an error threshold \( \tau \), such that the algorithm stops when:
$$ \sum_{i \in N} |f_{pv,i}(k+1) – f_{pv,i}(k)| < \tau $$
Once consensus is reached, the threshold voltage \( V_{tP,i} \) for each solar inverter is updated as:
$$ V_{tP,i}(k+1) = V_{\text{max}} – \frac{V_{\text{max}} – V_{\text{min}}}{f_{pv,i}(k+1)} $$
This adjustment ensures that solar inverters initiate active power curtailment in a coordinated manner, prioritizing reactive power support and reducing overall active power losses. The distributed nature of this method allows it to scale efficiently with large numbers of solar inverters, avoiding the bottlenecks of centralized control.
Simulation Setup and Results
To evaluate the proposed method, we conducted simulations using a realistic distribution network model based on a 10 kV/0.38 kV system. The network topology includes multiple feeders with solar inverters connected at various nodes. The solar inverters have a capacity of 12.7 kW each, and the total installed solar capacity is 203.2 kW. Load and solar generation data are derived from a real dataset, with a time resolution of 5 minutes over 24 hours. The solar inverters operate within a power factor range of \([-0.95, 0.95]\), allowing bidirectional reactive power flow.
The communication network for distributed consensus is based on the feeder connections, where solar inverters on the same feeder exchange information. The weight factors for communication are computed according to the adjacency of nodes. We compare the proposed method against two benchmark strategies: local \( Q_{pv}(P_{pv}) \) control and centralized voltage control. Performance metrics include maximum node voltage, total active power curtailment, and total reactive power support from solar inverters.
The simulation results demonstrate that the proposed distributed consensus collaboration method effectively mitigates voltage violations. Below is a summary table comparing the key outcomes:
| Control Method | Maximum Node Voltage (p.u.) | Total Reactive Power (kvar) | Total Active Power Curtailment (kW) |
|---|---|---|---|
| Local \( Q_{pv}(P_{pv}) \) Control | 1.0710 | 225.284 | 55.493 |
| Centralized Control | 1.0704 | 238.945 | 42.697 |
| Proposed Method | 1.0699 | 249.708 | 36.628 |
As shown, the proposed method achieves the lowest maximum voltage, indicating better voltage regulation. Moreover, it reduces active power curtailment by 18.865 kW compared to local control and by 6.069 kW compared to centralized control, while increasing reactive power support by 24.424 kvar and 10.763 kvar, respectively. This highlights the efficiency of distributed consensus in optimizing the use of solar inverters’ capabilities.
Further analysis of voltage profiles at critical nodes, such as node 16 (which experiences the highest voltage rise), reveals that the proposed method maintains voltage within tighter bounds. The voltage curve under distributed consensus is smoother and more stable, reducing fluctuations caused by solar variability. The active power curtailment is minimized, allowing more solar energy to be utilized, and the reactive power absorption is maximized, enhancing voltage support.
The convergence of the consensus algorithm is rapid, with state variables reaching agreement within a few iterations. This ensures timely adjustments to control parameters, enabling solar inverters to adapt to changing network conditions. The distributed approach also improves robustness, as it does not rely on a central controller that could be a single point of failure.
Conclusion
In this paper, we have presented a distributed consensus collaboration strategy for voltage control in networks with high penetration of solar power. The method coordinates solar inverters through a two-layer control system, combining local droop control with distributed algorithm-based parameter tuning. By synchronizing the active power output ratios of solar inverters, the approach minimizes voltage violations while reducing active power curtailment and enhancing reactive power support. Simulation results confirm that the proposed method outperforms traditional local and centralized controls, offering a scalable and efficient solution for modern distribution networks. Future work will explore the integration of forecasting and adaptive weighting to further improve performance under uncertain solar generation.