In the expanding landscape of distributed energy resources, the proliferation of photovoltaic (PV) systems represents a significant shift toward sustainable power generation. As a power systems engineer deeply involved in grid integration studies, I have observed firsthand the complex interactions between these new generation assets and the existing power grid. Among the myriad of power quality phenomena, voltage sags—short-duration reductions in RMS voltage—stand out as a particularly critical and frequent disturbance. While much research has focused on how solar inverters affect grid stability and protection, the inverse relationship—how grid disturbances like voltage sags affect the inverters themselves—is equally vital for ensuring reliable operation. This analysis delves into the transient electrical behavior of solar inverters during such events, moving beyond high-level concepts to examine the precise switching dynamics and control limitations that dictate their response.
The fundamental challenge arises from the core function of a grid-connected solar inverter: to synchronize and inject a controlled current into the grid. Under normal, steady-state conditions, the inverter’s power electronics and control algorithms maintain perfect harmony. However, a voltage sag is a violent, sub-cycle disturbance that disrupts this balance instantaneously. The primary mechanism of disruption is the inductor, a fundamental component placed between the inverter’s output and the grid for filtering and energy transfer. According to Faraday’s law, the voltage across an inductor is proportional to the rate of change of current through it ($v_L = L \frac{di}{dt}$). When the grid voltage collapses during a sag, the voltage impressed across this filter inductor changes abruptly. This sudden change in voltage demands an equally sudden change in the current’s slope, a dynamic that occurs far faster than the inverter’s digital control loop can process and counteract. The result is an uncontrollable inrush or decay of current within the first few switching cycles post-sag, the characteristics of which depend on the exact moment the sag occurs relative to the inverter’s switching state.
To understand this, let’s first consider a single-phase, full-bridge solar inverter. At any given instant within its Pulse Width Modulation (PWM) cycle, its switches are in one of two conductive states. The first is the active state, where two switches are turned on, connecting the DC-link voltage ($U_{dc}$) across the filter inductor and the grid. If a voltage sag occurs at time $t$ while the inverter is in this state, the current in phase $a$ ($i_a$) evolves according to:
$$i_a = i_a(0) + \frac{1}{L}\int_{t}^{t+\Delta t_{(on)}} (U_{dc} – u_{an}) dt$$
where $i_a(0)$ is the current at the sag inception, $L$ is the filter inductance, $u_{an}$ is the diminished grid voltage, and $\Delta t_{(on)}$ is the remaining on-time of the switches in that PWM period. Since $U_{dc}$ is typically much larger than $u_{an}$ during a deep sag, the integral term is strongly positive, leading to a rapid, uncontrolled increase in the output current from the solar inverters.
The second state is the freewheeling state, where only one switch is on, and current circulates through the anti-parallel diodes. In this scenario, the current is described by:
$$i_a = i_a(0) – \frac{1}{L}\int_{t}^{t+\Delta t_{(off)}} u_{an} dt$$
Here, the direction of current change depends on the sign of the grid voltage $u_{an}$ at the instant of the sag. If the voltage is positive, the current will decay. The key takeaway is that the immediate, uncontrolled current response of single-phase solar inverters is wholly determined by the pre-sag current level and the switching state at the exact nanosecond the grid voltage falters.
The analysis for three-phase solar inverters, typically employing Space Vector Pulse Width Modulation (SVPWM), is more complex but follows the same principles. A three-phase inverter’s state can be decomposed into combinations of the single-phase active and freewheeling states across different phases. For instance, during one of the active vector intervals where two phases are effectively connected to the DC bus, the currents in those phases will surge. In an interval where a phase is freewheeling through a diode against a low grid voltage, its current may decay. The mathematical expressions for the phase currents $i_a$ and $i_c$ during different SVPWM segments (A, B, C, etc.) confirm this behavior, showing terms like $(U_{dc} + u_b – u_a)$ leading to increase, or simply $(u_b – u_c)$ leading to decrease. Therefore, the magnitude and even the direction of the current transient in three-phase solar inverters are acutely sensitive to the voltage sag’s point-on-wave.
This brings us to the critical limitation: the control system’s bandwidth. Modern solar inverters use fast inner current control loops, often based on a synchronous reference frame (dq) with PI regulators. The closed-loop transfer function of such a current controller can be approximated as a first-order lag:
$$G_{clc}(s) \approx \frac{1}{3T_s s + 1}$$
where $T_s$ is the PWM switching period. This equation reveals a fundamental truth. The current control loop of the solar inverter has an inherent response time on the order of several PWM cycles (approximately $3T_s$). The violent di/dt event caused by the voltage sag happens within a single switching cycle. Consequently, there is a window of vulnerability—several hundred microseconds—where the current runs away before the control algorithm can compute and apply a corrective modulation index. This delay is a primary reason why solar inverters without specifically designed Low Voltage Ride-Through (LVRT) capabilities often trip on overcurrent protection during sags.
Experimental validation of these theoretical principles is crucial. By subjecting a commercial 10 kW solar inverter to controlled voltage sags using a programmable AC source, we can quantify the impact. The tests vary three key parameters: the inverter’s output power level, the depth of the voltage sag, and the point-on-wave (phase angle) at which the sag initiates. The results consistently show current transients that align with the analysis.
The data below illustrates how the peak inrush current scales with the pre-sag output power of the solar inverters during a symmetrical sag to 20% residual voltage initiated at a 0° phase angle.
| Inverter Output Power (kW) | Peak Inrush Current (A) |
|---|---|
| 5.0 | 29.77 |
| 4.0 | 27.37 |
| 2.5 | 25.91 |
| 1.0 | 22.81 |
As anticipated, a higher pre-sag current ($i(0)$) leads to a larger absolute current transient. The relationship with sag depth is even more direct, as shown in tests at a constant 1 kW output power. A deeper sag creates a larger voltage imbalance ($U_{dc} – u_{grid}$), which directly drives a higher di/dt according to the inductor equation.
| Voltage Sag Depth (%) | Peak Inrush Current (A) |
|---|---|
| 80 | 13.43 |
| 60 | 17.55 |
| 40 | 21.93 |
| 20 | 22.59 |
Perhaps the most revealing tests are those that vary the sag initiation angle. The theory predicts that the worst-case inrush should occur when the sag happens near the peak of the grid voltage (90°), as this is when the instantaneous voltage change is greatest for a given RMS sag depth. The experimental data for a 20% sag at 1 kW output confirms this prediction strikingly.
| Sag Initiation Phase Angle (degrees) | Peak Inrush Current (A) |
|---|---|
| 0 | 26.75 |
| 18 | 23.72 |
| 36 | 32.44 |
| 54 | 37.49 |
| 72 | 38.87 |
| 90 | 38.87 |
The consistent observation across all experiments was the timing of the peak current transient. It consistently appeared approximately 0.2 seconds after the sag event. This is not related to the initial, uncontrolled di/dt, but rather to the subsequent response of the inverter’s outer control loops (like the DC-link voltage controller or power controller). After the initial few cycles, the current control regains authority. However, the outer loops, which are much slower, then attempt to restore the operating point, often leading to a second, controlled but significant current peak as the solar inverters strive to maintain power output into a faulted grid. This dynamic underscores the multi-timescale challenge in designing robust solar inverters.
In conclusion, the interaction between voltage sags and solar inverters is a profound electrodynamic and control challenge. The core issue is the inherent conflict between the nearly instantaneous physics of the filter inductor ($v=L di/dt$) and the finite response time of digital control systems. The resulting current transients are not random; they are deterministic functions of the sag depth, point-on-wave, and the inverter’s instantaneous switching state. For solar inverters lacking LVRT algorithms—which typically involve rapid current reference generation, dynamic DC-link control, and sometimes reactive current injection—these transients will almost invariably trigger overcurrent protection, leading to disconnection. This not only results in lost generation but can also exacerbate the grid disturbance by removing a supportive resource. As penetration levels of solar inverters increase, understanding and mitigating these effects through advanced inverter controls becomes not just a matter of equipment security, but a cornerstone of overall grid resilience. Future work must also consider the aggregated, and potentially interacting, responses of hundreds of solar inverters during a widespread voltage sag, a scenario where control parameter variations could lead to complex, emergent system behaviors.