The global shift towards sustainable energy has propelled photovoltaic (PV) generation to the forefront of power system development. As public awareness and regulatory pressures concerning environmental protection intensify, PV technology has seen deep and widespread application across many nations, driving its rapid growth. This proliferation, however, introduces significant challenges for the operation of existing distribution networks. One of the most pressing issues is voltage regulation. The traditional paradigm of voltage control in distribution networks often relies on devices like On-Load Tap Changers (OLTCs) on distribution transformers. These devices adjust the voltage by changing transformer taps in response to system-wide voltage fluctuations, aiming to keep nodal voltages within statutory limits. This method, while established, has notable drawbacks: it requires frequent mechanical operations, involves complex infrastructure, and incurs high costs, leading to many transformers lacking such dynamic regulation capabilities.
The integration of distributed PV systems, particularly at scale, exacerbates voltage problems. During periods of high solar irradiance and low local load, reverse power flow can occur, causing voltage rises at the Point of Common Coupling (PCC) and along the feeder that may exceed acceptable upper limits. Conversely, during peak load times with minimal generation, voltage sags can occur. This bidirectional power flow and voltage volatility necessitate more agile and distributed control solutions. Fortunately, the advancement of power electronics and inverter control technology presents a powerful tool. Modern solar inverters are not merely DC-AC converters; they are intelligent grid interfaces capable of providing ancillary services. By coordinating the active (P) and reactive (Q) power output of these solar inverters, it is possible to regulate distribution network voltage effectively without substantial additional hardware investment. This approach leverages the existing inverter capacity, making it a cost-effective and strategically vital method for managing modern grids with high PV penetration. This article delves into the research of voltage regulation methods based on the coordinated power control of solar inverters, analyzing traditional strategies and proposing an advanced, optimized coordination framework.
1. Review of Conventional Voltage Regulation Strategies for Solar Inverters
For distributed PV systems connected to the grid, voltage regulation at the point of interconnection is typically achieved through two primary mechanisms: 1) curtailment of active power output (Active Power Curtailment – APC), and 2) utilization of the solar inverter‘s spare capacity to inject or absorb reactive power (Q support). In practice, grid-connected solar inverters often employ dual-loop control strategies (e.g., current control inner loop, power control outer loop), enabling them to adjust their P and Q output based on grid conditions. Critically, solar inverters are usually rated at a capacity greater than the maximum power their PV arrays can produce. This spare capacity is the key resource for providing reactive power support without affecting active power generation under normal conditions. The prevalent reactive power control strategies are Q(U) and Q(P) droop controls.
1.1 Q(U) Droop Control Strategy
The Q(U) strategy adjusts the reactive power output of the solar inverter as a function of the local voltage magnitude. A typical characteristic curve is shown conceptually below and can be summarized by the following piecewise function:
$$
Q_{pv}(U) =
\begin{cases}
Q_{max}^{abs} & \text{if } U \ge U_{max} \\
\frac{Q_{max}^{abs}}{U_{max} – U_{dead}} (U – U_{dead}) & \text{if } U_{dead} < U < U_{max} \\
0 & \text{if } U_{min} \le U \le U_{dead} \\
\frac{Q_{max}^{inj}}{U_{min} – U_{dead}} (U – U_{dead}) & \text{if } U_{min} > U \ge U_{dead} \\
Q_{max}^{inj} & \text{if } U < U_{min}
\end{cases}
$$
Where:
- $Q_{pv}$ is the reactive power setpoint for the solar inverter.
- $U$ is the measured voltage at the PCC.
- $U_{dead}$ is the center of a deadband where no reactive power is exchanged.
- $U_{max}$ and $U_{min}$ are the upper and lower voltage limits.
- $Q_{max}^{abs}$ and $Q_{max}^{inj}$ are the maximum absorb and inject reactive power limits, constrained by the inverter’s apparent power rating $S_{rated}$ and its current active power output $P_{pv}$: $Q_{max} = \sqrt{S_{rated}^2 – P_{pv}^2}$.
Advantages: The Q(U) strategy is decentralized, requires only local voltage measurement, and responds directly to the parameter of concern (voltage). It is effective in mitigating overvoltage by absorbing Q when voltage is high.
Limitations: Its primary drawback is the lack of coordination. In a long feeder with multiple PV units, voltage levels vary along the line. Units closer to the substation (with lower voltage) may provide little to no reactive power support, while units at the far end (experiencing overvoltage) operate at their Q absorption limit. This leads to an inefficient use of the total available reactive power capacity from all solar inverters in the network. Furthermore, in low-voltage distribution networks where the R/X ratio is high, reactive power control is less effective for voltage regulation, as voltage magnitude is more sensitive to active power flow.
| Feature | Q(U) Control | Q(P) Control |
|---|---|---|
| Control Variable | Local Voltage (U) | Local Active Power Output (P) |
| Communication Need | None (Local) | None (Local) |
| Primary Objective | Direct voltage support/limitation | Utilize inverter capacity; mitigate overvoltage from reverse power flow |
| Key Strength | Direct response to voltage violations. | Full utilization of inverter capacity across all nodes. |
| Key Weakness | Inefficient capacity use; poor coordination. | May operate unnecessarily (increasing losses) when no overvoltage exists; less effective for low R/X grids. |
| Optimal Use Case | Networks with high X/R ratio. | Scenarios with clear correlation between high P and overvoltage. |
1.2 Q(P) Droop Control Strategy
The Q(P) strategy modulates reactive power based on the solar inverter‘s active power output. The logic is that periods of high PV generation (high P) are more likely to cause overvoltage due to reverse power flow. A typical characteristic is:
$$
Q_{pv}(P) =
\begin{cases}
0 & \text{if } P \le P_1 \\
\frac{Q_{max}^{abs}}{P_2 – P_1} (P – P_1) & \text{if } P_1 < P < P_2 \\
Q_{max}^{abs} & \text{if } P \ge P_2
\end{cases}
$$
Where $P_1$ and $P_2$ are active power thresholds that define the start and full activation of reactive power absorption.
Advantages: This strategy ensures that all solar inverters, regardless of their position on the feeder, contribute reactive power when their generation is high, potentially making better use of the total available inverter capacity.
Limitations: The fundamental assumption can be flawed. If a period of high PV generation coincides with high local load ($P_{pv} < P_{load}$), overvoltage may not occur, yet the solar inverters would still absorb reactive power. This unnecessary Q flow increases system losses ($$P_{loss} = \frac{P^2 + Q^2}{V^2} R$$) without providing any voltage benefit. Furthermore, as with Q(U), its effectiveness is limited in networks with low X/R ratios.
1.3 Active Power Curtailment (APC)
When reactive power control is insufficient to mitigate overvoltage, the last resort is to curtail active power from the PV system. This is essentially a “spill of energy” or “derating” strategy. While effective for voltage control, APC directly reduces the utilization of renewable energy, leading to economic losses and contradicting the goal of maximizing green energy production.
The limitations of these decentralized, single-objective strategies—inefficient resource use, lack of coordination, increased losses, and energy waste—highlight the need for a more sophisticated approach. An ideal method would coordinate all controllable solar inverters in the network to achieve the global objective of maintaining voltage within limits while minimizing active power curtailment and system losses.
2. A Coordinated Power Control Framework for Voltage Regulation
To overcome the shortcomings of local droop controls, we propose a centralized, optimization-based coordinated control framework. This method synergistically combines APC and reactive power control from all available solar inverters in a feeder or section of the network. The core idea is to treat the collection of solar inverters as a distributed actuator system managed by a central controller.
2.1 System Architecture and Control Flow
The control structure adopts a point-to-multi-point architecture, consisting of a Central Controller (CC) and multiple Local Controllers (LCs) embedded within each solar inverter.
- Data Acquisition: Each LC measures its local bus voltage ($U_i$) and available maximum PV power ($P_{i, pv}^{max}$) and sends this data to the CC via a communication link (e.g., fiber, power line carrier, wireless mesh).
- State Assessment & Triggering: The CC monitors all received voltages. If all voltages are within the permissible deadband ($U_{min} \le U_i \le U_{max}$), no action is taken. If any voltage violation is detected (e.g., $U_i > U_{max}$), a trigger ($U_{alert}$) activates the optimization routine.
- Optimization & Dispatch: The CC formulates and solves a constrained optimization problem. The solution determines the optimal setpoints for active power curtailment ($P_{i, curt}$) and reactive power absorption/injection ($Q_{i, pv}$) for each solar inverter $i$ under its control.
- Command Execution: The CC sends the individual setpoint commands ($P_{i, curt}^*$, $Q_{i, pv}^*$) to the respective LCs. The LCs then adjust their solar inverter‘s operation accordingly.
This closed-loop process typically operates on a time scale of seconds to minutes, making it suitable for managing voltage fluctuations caused by variable PV generation.
2.2 Mathematical Problem Formulation
The voltage regulation problem is cast as a nonlinear constrained optimization problem. The objective is twofold: 1) minimize the total reactive power intervention to reduce losses, and 2) minimize active power curtailment to maximize PV utilization. These are combined into a single objective function with a weighting factor $\omega$ that prioritizes avoiding curtailment.
Objective Function:
$$
\min \quad F = \sum_{i=1}^{N_{PV}} |Q_{i, pv}| + \omega \sum_{i=1}^{N_{PV}} P_{i, curt}
$$
Where $N_{PV}$ is the number of solar inverters. The weighting factor $\omega$ is chosen to be significantly larger than 1 (e.g., 100-1000) to heavily penalize curtailment, ensuring it is used only when reactive power control is insufficient.
Subject to the following constraints:
1. Inverter Capacity Constraint (Apparent Power Limit): The combined P and Q output of each solar inverter must remain within its rated capacity.
$$
(P_{i, pv}^*)^2 + (Q_{i, pv})^2 \le S_{i, rated}^2
$$
Where $P_{i, pv}^* = P_{i, pv}^{max} – P_{i, curt}$ is the dispatched active power output.
2. Active Power Constraint: Curtailment must be non-negative and cannot exceed the available PV power.
$$
0 \le P_{i, curt} \le P_{i, pv}^{max}
$$
3. Power Flow Equations (DistFlow or Simplified Linearized Model): The control actions must satisfy the network physics. For a radial distribution network, the DistFlow equations are common. A simplified but effective linear approximation relating voltage magnitude to power injections is often used for faster computation:
$$
\mathbf{U} \approx \mathbf{U}_0 + \mathbf{R} \mathbf{P} + \mathbf{X} \mathbf{Q}
$$
Where $\mathbf{U}$ is the vector of voltage magnitudes, $\mathbf{U}_0$ is the nominal voltage vector, $\mathbf{P}$ and $\mathbf{Q}$ are vectors of net active and reactive power injections at nodes, and $\mathbf{R}$, $\mathbf{X}$ are matrices derived from the network impedance. For node $i$, the net injection is:
$$
P_i = P_{i, load} – P_{i, pv}^*, \quad Q_i = Q_{i, load} – Q_{i, pv}
$$
4. Voltage Limit Constraint: The primary control objective.
$$
U_{min} \le U_i \le U_{max} \quad \forall i \in \text{Nodes}
$$
| Symbol | Description |
|---|---|
| $N_{PV}$ | Number of PV systems / solar inverters |
| $P_{i, pv}^{max}$ | Maximum available active power from PV array $i$ (MPPT) |
| $P_{i, curt}$ | Decision Variable: Active power curtailment for solar inverter $i$ |
| $Q_{i, pv}$ | Decision Variable: Reactive power setpoint for solar inverter $i$ (positive for injection, negative for absorption) |
| $S_{i, rated}$ | Rated apparent power capacity of solar inverter $i$ |
| $U_i$ | Voltage magnitude at node $i$ (dependent variable) |
| $U_{min}, U_{max}$ | Lower and upper voltage limits (e.g., 0.95 pu, 1.05 pu) |
| $\omega$ | Weighting factor penalizing active power curtailment |
2.3 Solution Algorithm: The Complex Method
The formulated problem is a nonlinear programming (NLP) problem with both linear and nonlinear constraints (the inverter capacity constraint is quadratic). The Complex (or Box) algorithm is a robust and efficient direct search method well-suited for solving such constrained optimization problems, especially when the number of decision variables is moderate (e.g., tens of solar inverters). Its advantages include simplicity, reliability, and not requiring derivative information.
The algorithm works as follows:
- Initialization: Generate an initial “complex” of $k$ feasible points (vertices) in the decision variable space ($P_{i, curt}$, $Q_{i, pv}$). $k$ is typically greater than $2n$, where $n$ is the number of decision variables. Each vertex must satisfy all constraints.
- Iteration: In each iteration:
- Evaluate the objective function $F$ at all vertices.
- Identify the worst vertex (highest $F$) and calculate the centroid of the remaining $k-1$ vertices.
- Reflect the worst vertex through the centroid: $X_{new} = X_{centroid} + \alpha (X_{centroid} – X_{worst})$, where $\alpha > 0$ (typically 1.3).
- Check if $X_{new}$ is feasible. If not, project it back towards the centroid until feasibility is achieved.
- If $F(X_{new})$ is better than $F(X_{worst})$, replace $X_{worst}$ with $X_{new}$. Otherwise, try contracting the point.
- Termination: The algorithm terminates when the vertices converge (the standard deviation of the objective function values falls below a tolerance) or a maximum number of iterations is reached. The best vertex is the optimal solution.
This method efficiently searches the feasible region to find the combination of solar inverter power setpoints that minimizes the objective function while respecting all network and device constraints.
3. Case Study and Performance Analysis
To validate the effectiveness of the proposed coordinated control method, a simulation study is conducted on a modified IEEE 13-node test feeder integrated with multiple PV systems. The scenario represents a sunny midday period with low load, creating a high risk of overvoltage.
System Configuration:
- Four PV systems are connected at nodes 634, 645, 646, and 652, each with a 500 kWp array and a 550 kVA solar inverter (allowing 10% overrating for reactive power support).
- All PV systems are operating at their maximum power point ($P_{pv}^{max} = 500$ kW).
- Base load is at 50% of nominal.
- Voltage limits: $U_{min} = 0.95$ pu, $U_{max} = 1.05$ pu.
- Weight $\omega = 200$.
Three control strategies are compared:
- Base Case (No Control): PV inverters operate at unity power factor (PF=1).
- Local Q(U) Control: Each solar inverter independently implements a Q(U) droop with a deadband from 1.0 to 1.04 pu, absorbing Q up to its maximum capacity when $U > 1.04$ pu.
- Proposed Coordinated Control: The central controller solves the optimization problem using the Complex method.
| Metric | Base Case (No Control) | Local Q(U) Control | Proposed Coordinated Control |
|---|---|---|---|
| Max Node Voltage (pu) | 1.062 | 1.051 | 1.049 |
| Min Node Voltage (pu) | 0.982 | 0.981 | 0.983 |
| Voltage Violation? | YES (Overvoltage) | NO | NO |
| Total Q Absorption (kVAr) | 0 | 412 | 288 |
| Total P Curtailment (kW) | 0 | 0 | 18.5 |
| Total System Losses (kW) | 15.2 | 18.7 | 16.5 |
| Total PV Energy Used (kWh per interval) | 2000 | 2000 | 1991.5 |
| Inverter Capacity Utilization | Poor (Q unused) | Inefficient (Only far-end inverters saturated) | Efficient (All inverters contribute optimally) |
Analysis of Results:
- The Base Case leads to a clear overvoltage violation (1.062 pu > 1.05 pu), demonstrating the problem.
- The Local Q(U) Control manages to bring the maximum voltage just within limits (1.051 pu). However, it does so inefficiently: only the solar inverters at the far end of the feeder (nodes 646, 652) are forced to absorb significant reactive power, saturating their capacity, while the inverter at node 634 absorbs very little. This suboptimal allocation results in the highest system losses (18.7 kW) due to unnecessary reactive power flow.
- The Proposed Coordinated Control successfully regulates voltage (max 1.049 pu). Crucially, it achieves this with a 32% reduction in total reactive power absorption (288 vs. 412 kVAr) compared to the local Q(U) strategy. This smarter allocation of Q resources from all solar inverters leads to lower system losses (16.5 kW). A minimal amount of active power curtailment (18.5 kW, or 0.9% of total potential generation) was required from one inverter to achieve the strict voltage limit, which was prioritized by the high $\omega$ factor. Overall, this method maximizes the use of the PV resource (99.1% of energy harvested) while minimizing network losses.
The coordinated approach demonstrates a clear advantage in achieving the global objective of voltage control with minimal resource expenditure and energy waste.
4. Conclusion and Future Perspectives
The integration of high levels of photovoltaic generation into distribution networks is indispensable for the energy transition but poses significant operational challenges, with voltage regulation being paramount. Traditional, localized control strategies for solar inverters, such as Q(U) and Q(P) droop, while simple and communication-free, suffer from inefficiencies, lack of coordination, and suboptimal performance. They can lead to increased losses, underutilization of available inverter capacity, and, in severe cases, still necessitate the wasteful curtailment of active power.
This article has presented and explored a centralized, optimization-based coordinated power control framework for voltage regulation. By formulating the problem as a constrained optimization with the dual objectives of minimizing reactive power intervention and active power curtailment, this method intelligently dispatches commands to all participating solar inverters in a feeder. The use of the Complex algorithm provides a robust and efficient means to solve this problem. The case study validates that this coordinated strategy can successfully maintain grid voltage within statutory limits while significantly reducing system losses compared to local methods and minimizing the curtailment of valuable solar energy.
The future of distribution network management lies in such coordinated control schemes, which can be extended in several ways:
- Hierarchical and Distributed Control: To improve scalability and resilience, a hierarchical (centralized-distributed) or fully distributed control architecture using multi-agent systems or consensus algorithms could be developed.
- Integration with Other Resources: The framework can be expanded to coordinate solar inverters with other distributed energy resources (DERs) like battery energy storage systems (BESS) and flexible loads, creating a comprehensive DER management system (DERMS).
- Multi-Objective Optimization: The objective function can include other goals such as loss minimization, phase balancing, and congestion management explicitly.
- Predictive Control: Incorporating forecasts of PV generation and load can transform the method into a model predictive control (MPC) scheme, enabling proactive rather than reactive voltage management.
In conclusion, leveraging the innate capabilities of the modern solar inverter through advanced, coordinated control strategies is a technically sound and economically viable pathway to enabling higher penetrations of renewable energy while ensuring the safe, stable, and efficient operation of the electricity distribution grid.