In recent years, the integration of distributed photovoltaic (PV) generation systems into distribution networks has significantly transformed traditional grid operations, introducing complexities in security, stability, and control. Among these challenges, short-term voltage stability issues arising from voltage sags are critical, as they can lead to cascading failures and solar inverter disconnections. To adapt to high-penetration distributed PV systems and enhance the dynamic voltage support capability of active distribution networks, this paper proposes a novel dynamic voltage support strategy that considers the current margin of solar inverters. This strategy leverages the voltage sensitivity of distribution networks and fully utilizes the maximum allowable current of solar inverters during voltage sag events, maximizing active power output and improving short-term voltage stability. The impact of inverter current margin on static var compensation systems is analyzed, and simulation comparisons with conventional reactive power compensation methods validate the feasibility and effectiveness of the proposed approach. Throughout this work, the term “solar inverter” is emphasized to highlight its pivotal role in modern grid support.
The proliferation of distributed solar inverter-based generation has made distribution networks more active and dynamic, but it also exacerbates voltage instability during faults. Traditional synchronous generators provide inherent reactive power support, but solar inverters, unless properly controlled, lack this capability. Consequently, severe voltage sags can trigger solar inverter tripping, aggravating grid disturbances. Existing solutions often involve installing additional reactive power compensation devices or leveraging the reactive power regulation of solar inverters. However, these methods typically overlook the current design margin of solar inverters and the voltage sensitivity of distribution networks, limiting their efficiency during deep voltage sags. This paper addresses these gaps by proposing a comprehensive strategy that integrates solar inverter current margin with voltage sensitivity analysis to optimize dynamic voltage support.
Solar inverters are key components in PV systems, converting DC power from panels to AC power for grid integration. Their control strategies, often based on dq-coordinate transformation, enable precise management of active and reactive current components. Typically, solar inverters operate at unity power factor under normal conditions, but during faults, they must comply with low-voltage ride-through (LVRT) requirements to remain connected and support grid voltage. According to grid codes, when grid voltage drops below a threshold (e.g., 0.5 per unit), solar inverters should inject reactive current, often up to 100% of rated current. The output currents of a solar inverter can be expressed as:
$$I_d = I_n, \quad I_q = 0 \quad \text{for} \quad 0.95 < U_g < 1.05$$
$$I_d = 0, \quad I_q = 0 \quad \text{otherwise}$$
where \(I_d\) and \(I_q\) are the active and reactive current components, \(I_n\) is the rated current, and \(U_g\) is the grid voltage in per unit. For LVRT, the reactive current injection is often defined as:
$$I_q = \lambda (1 – U_g) I_n \quad \text{for} \quad U_g \leq 0.95$$
with \(\lambda \geq 2\) ensuring full reactive current injection at 0.5 p.u. voltage. However, solar inverters usually have a current design margin, allowing temporary overload above rated current. This margin, denoted as \(\alpha\), where \(\alpha = I_{\text{max}} / I_n > 1\), is crucial for enhancing dynamic voltage support but is often underutilized in conventional strategies.
The proposed dynamic voltage control strategy builds on the constant peak current control method, where the solar inverter’s maximum current is maintained at a constant value, often the rated current. However, by incorporating the current margin \(\alpha\), the solar inverter can inject higher currents during faults, thus providing more active and reactive power. The injected currents are derived as follows. For grid voltage in the range \((1 – 1/\lambda) \leq U_g \leq 0.95\):
$$I_d = \sqrt{(\alpha I_n)^2 – I_q^2}, \quad I_q = \lambda (1 – U_g) I_n$$
For severe voltage sags where \(U_g < (1 – 1/\lambda)\):
$$I_d = I_n \sqrt{\alpha^2 – 1}, \quad I_q = I_n$$
This allows the solar inverter to utilize its full current capacity, enhancing voltage support. To optimize this, voltage sensitivity analysis is essential. In distribution networks, the voltage change at a node due to power injections can be modeled using sensitivity coefficients. For a radial distribution network with n nodes, the voltage drop across a line segment k is:
$$\Delta U_k = U_{k-1} – U_k = \frac{P_k R_k + Q_k X_k}{U_k}$$
where \(P_k\) and \(Q_k\) are the active and reactive power flows, and \(R_k\) and \(X_k\) are the line resistance and reactance. The sensitivity of node voltage to power injections can be derived as:
$$\Delta U = L_P \Delta P + L_Q \Delta Q$$
Here, \(L_P\) and \(L_Q\) are the sensitivity coefficients for active and reactive power, respectively. In distribution networks with high R/X ratios, \(L_P\) can be significantly larger than \(L_Q\), meaning active power injection has a greater impact on voltage rise. This insight is critical for designing effective solar inverter control strategies, as maximizing active power output during voltage sags can rapidly restore voltage stability.
To formalize the strategy, we define an objective function that maximizes the voltage increase at the point of common coupling (PCC) where the solar inverter is connected:
$$\max F = \Delta U = L_P \Delta P + L_Q \Delta Q$$
subject to constraints:
$$\Delta P \geq 0, \quad \Delta Q \geq 0, \quad I_g \leq \alpha I_n$$
where \(I_g\) is the solar inverter output current magnitude. Using the power equations \(P = \frac{1}{2} U_g I_d\) and \(Q = \frac{1}{2} U_g I_q\), we can express the objective function in terms of solar inverter currents. For traditional constant peak current control (with \(\alpha = 1\)), the function becomes:
$$F_C = \frac{\rho}{2} U_g I_n – \frac{\epsilon}{2}$$
where \(\rho = L_P / L_Q\) and \(\epsilon\) is a constant. For the proposed strategy with current margin \(\alpha > 1\):
$$F_P = \frac{\rho}{2} U_g I_n (\alpha \sqrt{1 – (1 – U_g)^2}) – \frac{\epsilon}{2}$$
Comparing these, it is clear that \(F_P > F_C\) when \(\alpha > 1\) and \(\rho > 0\), confirming the superiority of the proposed approach. This theoretical foundation demonstrates how leveraging the solar inverter current margin can enhance dynamic voltage support, especially in resistive networks.
The impact of solar inverter current margin on short-term voltage stability is further analyzed through sensitivity studies. For instance, consider a distribution network with varying R/X ratios. The voltage increase sensitivity, defined as the change in voltage per unit change in solar inverter current, is plotted against current margin \(\alpha\). Results show that as \(\alpha\) increases, the sensitivity rises, particularly for deeper voltage sags. This indicates that solar inverters with higher current margins can more effectively mitigate voltage dips. However, there is a trade-off: increasing \(\alpha\) raises solar inverter cost. A balanced design with \(\alpha = 1.25\) p.u. is often optimal, providing significant stability improvements without excessive cost. This underscores the importance of considering solar inverter specifications in grid planning.
To validate the strategy, simulations were conducted on modified IEEE 4-node and IEEE 13-node distribution test systems using PSCAD/EMTDC. The solar inverter penetration was set to 50% and 20%, respectively, with three-phase faults applied to induce voltage sags. The proposed strategy was compared against two cases: no voltage control and conventional reactive power support without current margin consideration. Key performance metrics include voltage recovery time, active power output, and solar inverter current usage.
For the IEEE 4-node system, the voltage at the PCC (node 5) under a 0.2 s fault is shown in Table 1. The proposed strategy reduces recovery time to 0.38 s, compared to 1.19 s for conventional control and voltage collapse for no control. The solar inverter’s active power output during the fault is maximized, as detailed in Table 2. Additionally, the solar inverter current remains within the allowable limit of \(\alpha I_n\), preventing overcurrent trips.
| Control Strategy | Voltage Recovery Time (s) | Minimum Voltage (p.u.) | Solar Inverter Current Usage (%) |
|---|---|---|---|
| No Control | N/A (collapse) | 0.3 | 0 |
| Conventional Control | 1.19 | 0.45 | 85 |
| Proposed Strategy | 0.38 | 0.55 | 100 |
| Time (s) | Active Power (p.u.) – Proposed | Reactive Power (p.u.) – Proposed | Active Power (p.u.) – Conventional |
|---|---|---|---|
| 0.2 | 0.8 | 0.6 | 0 |
| 0.3 | 1.0 | 0.5 | 0.2 |
| 0.4 | 1.2 | 0.3 | 0.5 |
The solar inverter current characteristics are summarized by the equation:
$$I_g = \sqrt{I_d^2 + I_q^2} \leq \alpha I_n$$
with \(\alpha = 1.25\) in our simulations. This ensures safe operation while providing enhanced support. The voltage sensitivity coefficients for this system are calculated as \(L_P = 0.15\) and \(L_Q = 0.05\), confirming the dominance of active power in voltage regulation.
For the IEEE 13-node system, similar trends are observed. The voltage at node 611 recovers faster with the proposed strategy, as shown in Table 3. The solar inverter effectively utilizes its current margin to inject both active and reactive power, stabilizing the network. To quantify stability improvement, a transient voltage severity index (VSI) is used:
$$VSI = \frac{1}{N(T_c – T)} \sum_{i=1}^{N} \sum_{t=T}^{T_c} VDI_{i,t}$$
where \(VDI\) is the voltage deviation index, \(N\) is the number of buses, \(T\) is fault onset time, and \(T_c\) is clearance time. Lower VSI indicates better stability. As seen in Table 4, the proposed strategy achieves the lowest VSI, highlighting its efficacy.
| Strategy | Recovery Time (s) | Voltage Dip (p.u.) |
|---|---|---|
| No Control | 2.5 | 0.35 |
| Conventional | 1.8 | 0.42 |
| Proposed | 0.9 | 0.48 |
| Test System | No Control VSI | Conventional VSI | Proposed VSI |
|---|---|---|---|
| IEEE 4-node | 0.85 | 0.45 | 0.20 |
| IEEE 13-node | 0.78 | 0.40 | 0.18 |
Further analysis involves the effect of solar inverter current margin on system parameters. We derive the relationship between margin \(\alpha\) and voltage sensitivity \(L_P\) using a linearized model:
$$\frac{\partial L_P}{\partial \alpha} = k \cdot \frac{R}{X}$$
where \(k\) is a constant dependent on network topology. This shows that in networks with high R/X ratios, increasing solar inverter current margin significantly boosts voltage support capability. Additionally, the optimal power injection during faults can be found by solving the Lagrangian:
$$\mathcal{L} = L_P P + L_Q Q + \mu (\alpha I_n – \sqrt{I_d^2 + I_q^2})$$
where \(\mu\) is a Lagrange multiplier. The solution yields the optimal currents:
$$I_d^* = \frac{L_P U_g}{2\mu}, \quad I_q^* = \frac{L_Q U_g}{2\mu}$$
subject to the constraint. This formulation ensures that the solar inverter operates at its maximum capacity while prioritizing active power injection when \(L_P > L_Q\).
In practice, implementing this strategy requires real-time monitoring of grid voltage and solar inverter status. The control algorithm for the solar inverter can be summarized in steps: (1) measure grid voltage \(U_g\); (2) compute voltage sensitivity coefficients \(L_P\) and \(L_Q\) based on network impedance data; (3) determine current references \(I_d\) and \(I_q\) using the proposed equations; (4) adjust pulse-width modulation (PWM) signals to achieve these currents. This process emphasizes the solar inverter’s role as a dynamic voltage supporter.
Comparisons with other methods, such as static var compensators (SVCs) or energy storage systems, reveal that the proposed strategy is cost-effective because it utilizes existing solar inverter infrastructure without major hardware upgrades. However, challenges include coordinating multiple solar inverters in a network and ensuring communication reliability. Future work could explore distributed control schemes where solar inverters collaborate based on local measurements, further enhancing scalability.
The integration of solar inverter current margin into voltage support also has implications for grid codes. Current standards often limit solar inverter overload capabilities, but revising them to allow temporary overcurrent during faults could improve grid resilience. This aligns with the trend toward grid-forming inverters that provide synthetic inertia and frequency support. By expanding the functionality of solar inverters, we can build more robust active distribution networks.
In conclusion, this paper presents a dynamic voltage support strategy for active distribution networks that considers the current margin of solar inverters. By analyzing voltage sensitivity and leveraging the solar inverter’s maximum allowable current, the strategy maximizes active power injection during voltage sags, significantly improving short-term voltage stability. Theoretical analysis and simulations on IEEE test systems demonstrate faster voltage recovery, lower severity indices, and efficient solar inverter utilization compared to conventional methods. The proposed approach highlights the critical role of solar inverters in modern grid support and offers a practical solution for enhancing distribution network resilience. Future research will focus on real-world implementation and coordination with other grid assets.
Throughout this discussion, the term “solar inverter” has been repeatedly emphasized to underscore its importance in achieving dynamic voltage support. As distributed generation grows, optimizing solar inverter controls will be key to maintaining grid stability. This work contributes to that goal by providing a framework that integrates current margin and sensitivity analysis, paving the way for smarter and more responsive distribution networks.