I have designed and analyzed a low-voltage ride-through strategy for a two-stage solar inverter that uses a Boost converter as the front-end stage and a three-phase voltage-source inverter as the grid-side stage. My main concern is not only to keep the solar inverter connected during a grid voltage sag, but also to coordinate active and reactive current so that the solar inverter remains safe, the DC bus voltage remains bounded, and the grid receives useful reactive support. I treat the solar inverter as a power-electronics system whose AC-side and DC-side power must remain matched within a short transient window. When this match is lost, the DC bus capacitor absorbs or releases energy, and the solar inverter may trip because of overvoltage or overcurrent. Therefore, I focus on a control-level solution that does not require extra hardware such as a chopper, supercapacitor, or auxiliary energy storage.
In my approach, the Boost stage normally performs maximum power point tracking for the photovoltaic array. During a voltage sag, I change the Boost stage from maximum power point tracking to DC bus voltage regulation. The regulation loop uses a feedforward term equal to the pre-fault maximum power point voltage. This feedforward term allows the photovoltaic operating point to move quickly to the right side of the maximum power point, which reduces the array output power faster than moving to the left side. At the same time, the grid-side solar inverter current controller reduces the active current reference according to the sag depth and injects a reactive current reference within the current limit. This coordinated action allows the solar inverter to ride through the fault and support the grid.
I use PSCAD/EMTDC to verify the strategy on a 100 kW two-stage solar inverter. The simulation results show that the DC bus voltage is restrained, the AC current does not exhibit a severe transient overcurrent, the photovoltaic array output power is rapidly reduced, and the point of common coupling voltage is improved when reactive current is injected. I also compare the behavior with and without reactive support, and I quantify the benefit in terms of point of common coupling voltage.
1. Solar Inverter Architecture and Normal Operation
I consider a two-stage solar inverter in which the first stage is a Boost converter and the second stage is a three-phase DC/AC inverter. The Boost stage interfaces the photovoltaic array to a DC bus capacitor. The DC/AC stage connects the DC bus to the AC grid through an LCL filter. The main variables are the photovoltaic array voltage \(u_{pv}\), the photovoltaic array current \(i_{pv}\), the DC bus voltage \(u_{dc}\), the DC bus capacitance \(C\), the inverter-side filter inductance \(L_1\), the grid-side inductance \(L_2\), and the filter capacitance \(C_L\). I write the DC-side power balance in a form that is useful for ride-through analysis:
$$P_{pv} = P_{out} + P_C + P_{loss}$$
Here, \(P_{pv}\) is the power extracted from the photovoltaic array, \(P_{out}\) is the power delivered to the AC grid, \(P_C\) is the power absorbed by the DC bus capacitor, and \(P_{loss}\) represents converter losses. In the ideal lossless case, I use
$$P_{pv} – P_{out} = \frac{1}{2}C\frac{d u_{dc}^{2}}{dt}$$
This equation is the foundation of my control logic. If \(P_{pv} > P_{out}\), the DC bus voltage rises. If \(P_{pv} < P_{out}\), the DC bus voltage falls. A solar inverter must therefore regulate either the photovoltaic power or the AC-side power when a disturbance occurs. In normal operation, the Boost stage usually regulates the photovoltaic voltage for maximum power point tracking, and the grid-side solar inverter regulates the DC bus voltage through the active current. When the grid voltage drops, the AC-side power capability collapses, so the solar inverter can no longer maintain both maximum power extraction and DC bus regulation with the same control structure. My strategy changes the responsibility of each stage during the fault.
I express the Boost converter voltage relationship in continuous conduction mode as
$$u_{dc} = \frac{u_{pv}}{1-D}$$
where \(D\) is the Boost duty cycle. This equation shows that increasing the photovoltaic voltage for a given DC bus voltage reduces the duty cycle. In my fault-mode control, I prefer to move the photovoltaic operating point to a higher voltage, on the right side of the maximum power point. This action reduces the duty cycle and also reduces the photovoltaic power, which helps to prevent DC bus overvoltage.
The LCL filter and the grid-side current control can be described in the synchronous \(dq\) reference frame. The grid voltage components are \(e_d\) and \(e_q\), and the current components are \(i_d\) and \(i_q\). The inverter voltage references are formed by proportional-integral current controllers plus decoupling terms:
$$u_d = \left(k_{ip} + \frac{k_{ii}}{s}\right)\left(i_d^{*} – i_d\right) – \omega L i_q + e_d$$
$$u_q = \left(k_{ip} + \frac{k_{ii}}{s}\right)\left(i_q^{*} – i_q\right) + \omega L i_d + e_q$$
where \(k_{ip}\) and \(k_{ii}\) are the current-loop gains, \(\omega\) is the grid angular frequency, and \(L\) is the equivalent inductance of the LCL filter when the capacitor branch is neglected. The solar inverter typically uses space-vector pulse-width modulation to generate switching signals from \(u_d\) and \(u_q\).
In normal operation, the outer DC bus voltage loop gives the active current reference \(i_d^{*}\). The reactive current reference \(i_q^{*}\) is usually set to zero for unity power factor. The Boost stage performs maximum power point tracking. I use a perturbation-and-observation method in the normal mode. The method perturbs the photovoltaic voltage and observes the power change. If the power increases, the next perturbation continues in the same direction; if the power decreases, the perturbation reverses. I summarize the normal and fault-mode responsibilities in Table 1.
| Operating condition | Boost stage objective | Grid-side solar inverter objective | Active current reference | Reactive current reference |
|---|---|---|---|---|
| Normal grid voltage | Maximum power point tracking | Regulate DC bus voltage and inject active power | From DC bus voltage loop | Usually zero |
| Voltage sag below 0.9 p.u. | Regulate DC bus voltage and reduce photovoltaic power | Limit current and provide reactive support | Reduced according to sag depth | Increased within current limit |
| Voltage recovery | Return to maximum power point tracking | Restore active current and reduce reactive current | Gradually restored | Gradually reduced |
Table 1 clarifies that the solar inverter changes its control hierarchy during a fault. The DC bus voltage becomes the main concern of the Boost stage, while the grid-side solar inverter prioritizes current limitation and reactive support. This coordination is the core of my low-voltage ride-through strategy.
2. Conventional Control and Its Limitations During Voltage Sags
I first examine the conventional control structure because it explains why a two-stage solar inverter may fail during a deep voltage sag. In the normal mode, the Boost stage extracts the maximum available power from the photovoltaic array. The grid-side solar inverter regulates the DC bus voltage by adjusting \(i_d^{*}\). If the grid voltage is nominal, the AC-side power can follow the DC-side power, and the DC bus voltage remains near its reference. The power balance is approximately
$$P_{pv} \approx P_{out} = \frac{3}{2}\left(e_d i_d + e_q i_q\right)$$
If the solar inverter is operated at unity power factor, \(i_q = 0\), and the AC-side power becomes
$$P_{out} \approx \frac{3}{2}e_d i_d$$
When a low-voltage fault occurs, \(e_d\) decreases. If the current controller tries to maintain the same power, \(i_d\) must increase. However, the solar inverter has a maximum current limit. If the voltage sag is deep, the required current may exceed the semiconductor and filter ratings. The solar inverter then either saturates or trips. In addition, the Boost stage continues to extract near-maximum power, so the DC bus capacitor receives the difference between \(P_{pv}\) and \(P_{out}\). The DC bus voltage rises according to
$$\Delta P = P_{pv} – P_{out} = \frac{1}{2}C\frac{u_{dc,f}^{2} – u_{dc,i}^{2}}{\Delta t}$$
where \(u_{dc,i}\) and \(u_{dc,f}\) are the initial and final DC bus voltages over the interval \(\Delta t\). If \(\Delta P\) is large and \(\Delta t\) is long, the DC bus voltage can exceed the protection threshold. A conventional solar inverter without a ride-through strategy may disconnect to protect the DC capacitor and the switching devices. My goal is to avoid this disconnection by changing the power balance quickly.
The limitations of the conventional strategy can be summarized as follows. First, maximum power point tracking is not desirable during a severe sag because the solar inverter cannot deliver all the extracted power to the grid. Second, the DC bus voltage loop alone may demand an active current that exceeds the current limit. Third, unity power factor operation provides no reactive support, even though grid codes may require reactive current injection during faults. Fourth, a sudden blocking of the solar inverter is undesirable for grid stability because it removes active power and may worsen the fault recovery. These limitations motivate my coordinated control strategy.
3. Grid Code Requirements and Fault Impact
I design the strategy around the requirement that a solar inverter must remain connected when the grid voltage stays above a specified ride-through curve. In general terms, the solar inverter must not disconnect for a voltage sag that remains above the lower boundary. During the ride-through period, the solar inverter should also provide reactive current to support voltage recovery. I represent the voltage sag depth by
$$k = \frac{u_f}{u_N}$$
where \(u_f\) is the measured positive-sequence voltage during the fault and \(u_N\) is the nominal voltage. I use \(k < 0.9\) as the detection condition for entering the low-voltage ride-through mode. The value 0.9 is consistent with common grid-code thresholds. I also use the sag depth to determine the active and reactive current references. Table 2 gives a generalized mapping that I use in my control logic.
| Voltage depth \(k\) | Fault severity | Expected solar inverter action | Reactive current priority | Active current priority |
|---|---|---|---|---|
| \(k \ge 0.9\) | Normal or minor disturbance | Maximum power point tracking and unity power factor | Low | High |
| \(0.6 \le k < 0.9\) | Moderate sag | Reduce active current and inject reactive current | Medium | Medium |
| \(0.2 \le k < 0.6\) | Deep sag | Strong active current reduction and high reactive current | High | Low |
| \(k < 0.2\) | Very deep sag | Maintain synchronization with minimum active current and maximum reactive support | Very high | Very low |
Table 2 shows that reactive current priority increases as the voltage sag becomes deeper. I do not disconnect the solar inverter merely because the voltage is low; instead, I limit the current and provide reactive support. The DC bus voltage is regulated by the Boost stage, so the grid-side solar inverter can use its current capacity for grid support.
When the grid voltage drops, the AC-side power capability is reduced almost immediately. The DC-side power from the photovoltaic array changes more slowly if maximum power point tracking continues. The resulting power imbalance charges the DC bus capacitor. I express the instantaneous capacitor power as
$$P_C = u_{dc} C \frac{d u_{dc}}{dt}$$
Combining this with the power balance gives
$$u_{dc} C \frac{d u_{dc}}{dt} = P_{pv} – P_{out}$$
This differential equation shows that reducing \(P_{pv}\) or increasing \(P_{out}\) can reduce the DC bus voltage rise. During a fault, \(P_{out}\) is limited by the grid voltage and the current limit, so the practical control variable is \(P_{pv}\). My Boost-mode transition directly controls \(P_{pv}\) by moving the photovoltaic operating point away from the maximum power point. I choose the right side of the maximum power point because the power reduction per voltage change is larger there, and because the Boost duty cycle decreases rather than increases.
I also consider the current limit. Let \(I_N\) be the rated current of the solar inverter. In my strategy, I allow a maximum transient current \(i_{max} = 1.1 I_N\). The current references must satisfy
$$i_d^{2} + i_q^{2} \le i_{max}^{2}$$
If I give priority to reactive current during a deep sag, I can express the active current limit as
$$i_d^{*} \le \sqrt{i_{max}^{2} – i_q^{*2}}$$
This inequality is important because it prevents the solar inverter from overcurrent while still allowing reactive support. In my selected implementation, I instead define the active current first and then compute the reactive current as
$$i_q^{*} = \sqrt{i_{max}^{2} – i_d^{*2}}$$
This choice keeps the total current at the limit and ensures that the solar inverter uses all remaining capacity for reactive support. I discuss this trade-off further in the current-control section.
4. Proposed Boost Control for DC Bus Voltage Regulation
My proposed Boost control changes the photovoltaic voltage reference during a voltage sag. In normal mode, the reference is the maximum power point voltage obtained by perturbation and observation. In fault mode, I add a DC bus voltage correction term to the pre-fault maximum power point voltage. The reference voltage is
$$u_{pv}^{*} = u_{max} + \Delta u_{dc}$$
where \(u_{max}\) is the pre-fault maximum power point voltage and \(\Delta u_{dc}\) is generated by a proportional-integral controller on the DC bus voltage error. I write the correction as
$$\Delta u_{dc} = k_{p,dc}\left(u_{dc} – u_{dc}^{*}\right) + k_{i,dc}\int \left(u_{dc} – u_{dc}^{*}\right)dt$$
Here, \(u_{dc}^{*}\) is the DC bus voltage reference. When the DC bus voltage rises above the reference, the correction term becomes positive. The photovoltaic voltage reference then moves above the maximum power point voltage. Because the photovoltaic power curve falls on the right side of the maximum power point, the array output power decreases. This reduction counteracts the DC bus voltage rise. The control law is simple, but its dynamic behavior depends on the shape of the photovoltaic curve and the DC bus capacitance.
I choose the right side of the maximum power point for two reasons. First, the power-voltage curve is steeper on the right side near the maximum power point. For two voltage deviations of equal magnitude, the power reduction on the right side is larger than on the left side. I express this as
$$\left| \frac{dP_{pv}}{du_{pv}} \right|_{u_{max}+\Delta u} > \left| \frac{dP_{pv}}{du_{pv}} \right|_{u_{max}-\Delta u}$$
for small positive \(\Delta u\). This means that moving to a higher voltage gives a faster power reduction. Second, moving to a higher voltage reduces the Boost duty cycle according to
$$D = 1 – \frac{u_{pv}}{u_{dc}}$$
If the photovoltaic voltage increases, the duty cycle decreases. A lower duty cycle is easier to control than a duty cycle close to unity. If I tried to reduce power by moving the photovoltaic voltage toward zero, the duty cycle would approach one, and the Boost converter would operate near a difficult limit. Therefore, the right-side operating point is preferable for both speed and controllability.
I summarize the Boost-mode transition in Table 3. The transition is controlled by the measured grid voltage. When \(k\) falls below 0.9, the solar inverter enters fault mode. When the voltage recovers and remains above the threshold for a short confirmation time, the solar inverter returns to normal mode.
| Signal or condition | Normal mode | Fault mode | Recovery mode |
|---|---|---|---|
| Grid voltage depth \(k\) | \(k \ge 0.9\) | \(k < 0.9\) | \(k \ge 0.9\) for confirmation time |
| Photovoltaic voltage reference | From maximum power point tracking | \(u_{max} + \Delta u_{dc}\) | Gradually returns to maximum power point tracking |
| Boost objective | Maximum power extraction | DC bus voltage regulation | Power restoration |
| DC bus voltage loop | Located in grid-side solar inverter | Located in Boost stage | Transferred back to grid-side solar inverter |
| Active current reference | From DC bus voltage loop | Reduced according to \(k\) | Gradually restored |
Table 3 shows that the DC bus voltage regulation responsibility moves from the grid-side solar inverter to the Boost stage during the fault. This transfer is central to my strategy. The grid-side solar inverter no longer needs to increase active current to regulate the DC bus, so it can reduce active current and use the remaining current capacity for reactive support.
The feedforward term \(u_{max}\) is important because it provides an immediate starting point close to the pre-fault maximum power point. Without the feedforward term, the DC bus voltage controller would have to drive the photovoltaic voltage from an arbitrary initial value. With the feedforward term, the controller only needs to add a small correction to reduce power. This reduces the transient and improves the speed of the DC bus voltage suppression. I also freeze \(u_{max}\) at the moment the fault is detected so that the reference does not drift during the fault. After the fault clears, I gradually release the frozen value and allow maximum power point tracking to resume.
5. Coordinated Active and Reactive Current Control
The second part of my strategy is the grid-side current control. In normal operation, the active current reference comes from the DC bus voltage loop, and the reactive current reference is zero. During a fault, I generate the active current reference according to the voltage sag depth and then calculate the reactive current reference from the current limit. I define the fault-mode active current reference as a piecewise function. From the detection time \(t_0\) to \(t_1\), I hold the pre-fault active current reference for 3 ms. This short hold prevents an abrupt current change and reduces the risk of transient overcurrent. From \(t_1\) to \(t_2\), I reduce the active current linearly. After \(t_2\), the active current remains at a minimum value determined by the sag depth. The equations are
$$i_d^{*}(t) = i_{d,pre}, \quad t_0 \le t < t_1$$
$$i_d^{*}(t) = i_{max} – i_R(t-t_1), \quad t_1 \le t < t_2$$
$$i_d^{*}(t) = k i_{max}, \quad t \ge t_2$$
Here, \(i_{d,pre}\) is the pre-fault active current reference, \(i_R\) is the active current reduction rate, and \(i_{max}\) is the maximum allowed current magnitude. The condition \(i_d^{*} \ge k i_{max}\) must be satisfied during the linear reduction. The reactive current reference is then
$$i_q^{*} = \sqrt{i_{max}^{2} – i_d^{*2}}$$
This equation ensures that the total current magnitude remains at or below the limit. If the active current is reduced, the reactive current can be increased. If the active current is at the minimum, the reactive current is at its maximum for the given current limit. I summarize the current-reference logic in Table 4.
| Time interval | Active current reference | Reactive current reference | Purpose |
|---|---|---|---|
| \(t_0 \le t < t_1\) | Hold pre-fault value | Start increasing if needed | Avoid abrupt current change |
| \(t_1 \le t < t_2\) | Linear reduction | Calculated from current limit | Limit current and provide reactive support |
| \(t \ge t_2\) | \(k i_{max}\) | \(\sqrt{i_{max}^{2} – k^{2} i_{max}^{2}}\) | Maintain deep-sag ride-through |
| Voltage recovery | Gradually restored | Gradually reduced | Smooth return to normal operation |
Table 4 shows that the solar inverter does not simply shut down the active current. Instead, it reduces active current in a controlled manner and uses the remaining current capacity for reactive support. This is important because the grid needs reactive current during a fault to help restore voltage. The active current reduction also reduces the AC-side power, which helps the Boost stage regulate the DC bus voltage. The coordination between the two stages is therefore twofold: the Boost stage reduces photovoltaic power, and the grid-side solar inverter reduces active current while increasing reactive current.
I must also consider the priority between active and reactive current. If the grid code requires a certain reactive current, the active current must be limited to leave room. If the active current is too high, the reactive current cannot be injected without exceeding the current limit. In my strategy, I choose to compute the reactive current from the active current, which means that the total current magnitude is kept at the limit. This is a practical choice for a solar inverter with a fixed current rating. An alternative is to compute the active current from the reactive current, which gives reactive priority. I compare the two choices in Table 5.
| Priority scheme | Active current expression | Reactive current expression | Advantage | Disadvantage |
|---|---|---|---|---|
| Active-current-first | \(i_d^{*} = i_{max} – i_R(t-t_1)\) | \(i_q^{*} = \sqrt{i_{max}^{2} – i_d^{*2}}\) | Simple and smooth active power reduction | Reactive current may be lower than required |
| Reactive-current-first | \(i_d^{*} = \sqrt{i_{max}^{2} – i_q^{*2}}\) | \(i_q^{*} = f(k)\) | Stronger voltage support | Active power reduction may be faster than desired |
| Weighted coordination | \(i_d^{*} = \alpha \sqrt{i_{max}^{2} – i_q^{*2}}\) | \(i_q^{*} = (1-\alpha) f(k)\) | Flexible trade-off | Requires tuning of \(\alpha\) |
Table 5 shows that my selected scheme is the active-current-first scheme. It is simple and effective for the tested solar inverter. In a practical implementation, I can adjust the reduction rate \(i_R\) and the hold time to match the grid code and the DC bus capacitance. The important point is that the solar inverter maintains current limitation and provides reactive support without additional hardware.
6. DC Bus Voltage Dynamics and Stability Considerations
I analyze the DC bus voltage dynamics because the Boost control must respond quickly without causing oscillation. The DC bus capacitor voltage equation is
$$C u_{dc} \frac{d u_{dc}}{dt} = P_{pv}(u_{pv}) – P_{out}(u_{dc}, i_d, i_q)$$
Linearizing around an operating point gives
$$C u_{dc0} \frac{d \Delta u_{dc}}{dt} = \frac{\partial P_{pv}}{\partial u_{pv}} \Delta u_{pv} – \frac{\partial P_{out}}{\partial u_{dc}} \Delta u_{dc} – \frac{\partial P_{out}}{\partial i_d} \Delta i_d$$
In fault mode, the Boost controller adjusts \(u_{pv}\) according to the DC bus voltage error. If the controller gain is too low, the DC bus voltage rises too much. If the gain is too high, the photovoltaic voltage may oscillate, and the Boost inductor current may become unstable. I therefore use a proportional-integral controller with a moderate proportional gain and a slow integral gain. The proportional term provides fast correction, and the integral term removes steady-state error. The feedforward term \(u_{max}\) reduces the required controller action, which allows lower gains and improves stability.
I also consider the effect of the photovoltaic curve. On the right side of the maximum power point, the derivative \(\partial P_{pv}/\partial u_{pv}\) is negative. A positive DC bus voltage error causes a positive photovoltaic voltage correction, which reduces photovoltaic power. This is negative feedback for the DC bus voltage loop. On the left side of the maximum power point, the same correction would increase photovoltaic power, which would be positive feedback. This is another reason why I choose the right side of the maximum power point. The sign of the derivative is essential for stable DC bus voltage regulation.
I express the sensitivity of the photovoltaic power to voltage as
$$S_{pv} = -\frac{\partial P_{pv}}{\partial u_{pv}} > 0$$
on the right side of the maximum power point. The DC bus voltage error produces a power reduction of approximately
$$\Delta P_{pv} \approx -S_{pv} \Delta u_{pv} = -S_{pv} k_{p,dc} \Delta u_{dc}$$
for the proportional part. This power reduction opposes the voltage rise. The integral part ensures that the DC bus voltage returns to its reference after the transient. The time constant of the DC bus voltage loop is approximately
$$\tau_{dc} \approx \frac{C u_{dc0}}{S_{pv} k_{p,dc}}$$
This expression shows that a larger capacitance or a smaller photovoltaic sensitivity requires a larger controller gain for the same response speed. In my simulation, the 6000 μF capacitor and the selected gains provide a response time of about 6 ms, which is fast enough to limit the DC bus voltage peak.
7. Simulation Model and Test Conditions
I built a 100 kW two-stage solar inverter model in PSCAD/EMTDC. The model includes the photovoltaic array, the Boost converter, the DC bus capacitor, the three-phase inverter, the LCL filter, and the grid. The main parameters are listed in Table 6. I selected these parameters to represent a small utility-scale solar inverter and to make the DC bus voltage dynamics visible during the fault.
| Parameter | Value | Unit |
|---|---|---|
| Rated power | 100 | kW |
| DC bus voltage reference | 800 | V |
| DC bus capacitance | 6000 | μF |
| Grid frequency | 50 | Hz |
| Grid line voltage | 220 | V |
| Rated current | 200 | A |
| Inverter-side inductance \(L_1\) | 0.4 | mH |
| Grid-side inductance \(L_2\) | 0.05 | mH |
| Filter capacitance \(C_L\) | 10 | μF |
| Damping resistance | 1 | Ω |
I applied a three-phase symmetrical voltage sag at 0.3 s. The voltage dropped to 0.2 p.u. and remained there for 0.1 s. After 0.4 s, the voltage returned to normal. I assumed that the maximum power of the photovoltaic array remained available before and after the fault. This assumption allows me to focus on the transient behavior of the solar inverter rather than on irradiance changes. Table 7 summarizes the test conditions.
| Event | Time | Voltage condition | Duration |
|---|---|---|---|
| Pre-fault steady state | Before 0.3 s | 1.0 p.u. | — |
| Voltage sag | 0.3 s | 0.2 p.u. | 0.1 s |
| Voltage recovery | 0.4 s | Returns to 1.0 p.u. | — |
| Post-fault steady state | After 0.4 s | 1.0 p.u. | — |
I observed five key quantities: the three-phase grid current, the active and reactive current components, the DC bus voltage, and the photovoltaic array output power. I also compared the point of common coupling voltage with and without reactive current injection. This comparison shows the benefit of the coordinated reactive support.
8. Simulation Results and Interpretation
The simulation results show that the solar inverter rides through the voltage sag without disconnecting. The DC bus voltage rises during the initial transient but remains within a safe range. The peak DC bus voltage is 861.5 V, which is above the 800 V reference but below the protection threshold. The photovoltaic array output power falls rapidly from its pre-fault value to about 20 kW. The active current is reduced according to the sag depth, and the reactive current is increased within the current limit. The three-phase grid current does not exhibit a severe overcurrent, and the current quality is acceptable during the fault.
The power balance during the fault can be interpreted with the capacitor equation. Before the fault, the photovoltaic power and the AC-side power are approximately equal. At the fault instant, the AC-side power drops because the grid voltage falls. The Boost stage detects the DC bus voltage rise and moves the photovoltaic operating point to the right of the maximum power point. The photovoltaic power decreases, and the DC bus voltage rise is limited. After about 6 ms, the photovoltaic power matches the reduced AC-side power, and the DC bus voltage stabilizes. This behavior is consistent with the differential equation
$$C u_{dc} \frac{d u_{dc}}{dt} = P_{pv} – P_{out}$$
When \(P_{pv}\) is reduced to match \(P_{out}\), the derivative becomes zero, and the DC bus voltage stops rising. The controller then regulates the voltage back toward the reference. The response is fast because the feedforward term \(u_{max}\) provides an immediate voltage reference close to the maximum power point.
I summarize the key simulation results in Table 8. The table includes the pre-fault values, the fault-mode values, and the recovery behavior. The fault-mode values show that the solar inverter reduces active power and increases reactive current. The recovery values show that the solar inverter returns smoothly to normal operation.
| Quantity | Pre-fault value | Fault-mode value | Recovery behavior |
|---|---|---|---|
| DC bus voltage | Approximately 800 V | Peak 861.5 V | Returns to reference |
| Photovoltaic output power | Near rated maximum | About 20 kW | Gradually restored |
| Active current \(i_d\) | Pre-fault reference | Reduced according to \(k\) | Gradually increased |
| Reactive current \(i_q\) | Near zero | Increased within limit | Gradually reduced |
| Three-phase current | Rated | Limited, no severe overcurrent | Smooth restoration |
| DC bus settling time | — | About 6 ms | — |
Table 8 shows that the solar inverter remains in a safe operating region. The DC bus voltage peak is about 7.7% above the reference, which is acceptable for the modeled capacitor and protection threshold. The photovoltaic power reduction is large, but it is necessary to balance the reduced AC-side power. The active current reduction and reactive current increase are coordinated so that the total current stays within the limit. The recovery behavior is smooth because the current references are ramped rather than stepped.
I also compared the point of common coupling voltage with and without reactive current injection. The comparison is shown in Table 9. When reactive current is injected, the point of common coupling voltage is 46.88 V. Without reactive current, the point of common coupling voltage is 41.91 V. The difference is about 4.97 V. This result shows that the solar inverter provides measurable voltage support during the fault. The support is limited by the current rating of the solar inverter, but it is still valuable for grid recovery.
| Case | Point of common coupling voltage | Difference | Interpretation |
|---|---|---|---|
| With reactive current support | 46.88 V | — | Solar inverter injects reactive current |
| Without reactive current support | 41.91 V | — | Solar inverter does not inject reactive current |
| Voltage improvement | — | 4.97 V | Reactive support raises point of common coupling voltage |
Table 9 demonstrates the benefit of the coordinated control. The solar inverter not only rides through the fault but also helps the grid. The reactive support is especially important during a deep sag because the grid voltage is low and the reactive current can help restore the voltage. The active current reduction also helps the solar inverter stay within its current limit, which improves reliability.
9. Comparison With Hardware-Based and Conventional Methods
I compared my control-level strategy with other common approaches. Hardware-based methods may use a DC chopper, a supercapacitor, or an auxiliary energy storage system. These methods can be effective, but they increase cost, volume, and maintenance. Conventional control methods may simply disconnect the solar inverter during a severe sag or may use a DC bus voltage loop that demands excessive active current. My strategy uses the existing Boost stage and the existing grid-side solar inverter, so it does not require additional hardware. It also coordinates active and reactive current, so it provides both ride-through and grid support.
Table 10 compares the main features of different approaches. The table is qualitative, but it highlights the trade-offs. The control-level strategy is attractive for solar inverters that already have a Boost stage and an LCL filter. It uses the Boost stage for DC bus voltage regulation during the fault and uses the grid-side solar inverter for current limitation and reactive support. This division of labor is the main advantage of my method.
| Approach | Additional hardware | DC bus voltage control | Reactive support | Cost | Control complexity |
|---|---|---|---|---|---|
| DC chopper | Yes | Chopper dissipates excess power | Possible | Medium | Medium |
| Supercapacitor | Yes | Storage absorbs power | Possible | High | High |
| Conventional current limit | No | Limited | Usually none | Low | Low |
| My coordinated control | No | Boost stage regulates DC bus | Yes | Low | Medium |
Table 10 shows that my strategy avoids additional hardware while still providing reactive support. The control complexity is moderate because the Boost stage changes its objective during the fault. The transition logic must be reliable, and the current references must be coordinated with the DC bus voltage controller. However, these functions can be implemented in the existing digital signal processor of the solar inverter.
10. Practical Implementation Considerations
I consider several practical issues for implementing this strategy in a solar inverter. First, the fault detection must be fast and robust. I use the positive-sequence voltage magnitude and a threshold of 0.9 p.u. I also use a short confirmation time to avoid false detection during transient disturbances. Second, the pre-fault maximum power point voltage must be stored when the fault is detected. This value is used as the feedforward term. Third, the active current reduction rate must be selected so that the DC bus voltage does not rise too much and the AC current does not oscillate. Fourth, the reactive current reference must respect the current limit and the grid code. Fifth, the recovery logic must ramp the current references and the photovoltaic voltage reference to avoid a second transient.
I express the current limit constraint in a general form as
$$\left(i_d^{*}\right)^{2} + \left(i_q^{*}\right)^{2} \le \left(i_{max}\right)^{2}$$
If the grid code requires a minimum reactive current \(i_{q,min}\), then the active current must satisfy
$$i_d^{*} \le \sqrt{i_{max}^{2} – i_{q,min}^{2}}$$
This inequality ensures that the solar inverter can meet the reactive current requirement without overcurrent. In my simulation, the reactive current is calculated from the active current, so the total current is exactly at the limit. In a practical implementation, I would add a small margin to avoid hitting the limit during transients.
I also consider the DC bus voltage protection threshold. The peak DC bus voltage in my simulation is 861.5 V, which is below the protection threshold. If the DC bus capacitance is smaller or the fault is deeper, the peak may be higher. In that case, I can increase the proportional gain of the Boost DC bus voltage controller or reduce the active current faster. However, increasing the gain too much may cause oscillation. Therefore, the controller design must balance speed and stability. I summarize the practical design steps in Table 11.
| Step | Design action | Reason |
|---|---|---|
| 1 | Select fault detection threshold and confirmation time | Avoid false tripping and detect real sags |
| 2 | Store pre-fault maximum power point voltage | Provide feedforward for Boost fault mode |
| 3 | Tune DC bus voltage PI controller | Limit DC bus overvoltage and avoid oscillation |
| 4 | Select active current reduction rate | Balance current limitation and power reduction |
| 5 | Calculate reactive current within limit | Provide grid support without overcurrent |
| 6 | Design recovery ramp | Avoid second transient after voltage recovery |
Table 11 shows that the implementation is systematic. The most critical step is the tuning of the Boost DC bus voltage controller. The feedforward term reduces the burden on the controller, but the controller still must respond quickly to the power imbalance. The active current reduction also helps because it reduces the AC-side power demand and allows the DC bus voltage to stabilize. The coordination between the Boost stage and the grid-side solar inverter is therefore essential.
11. Key Equations and Control Logic Summary
I summarize the main equations of my strategy in Table 12. The table lists the equation, the purpose, and the operating mode. This summary is useful for implementing the solar inverter control in a digital controller.
| Equation | Purpose | Mode |
|---|---|---|
| \(P_{pv} – P_{out} = \frac{1}{2}C\frac{d u_{dc}^{2}}{dt}\) | DC bus power balance | All modes |
| \(u_{dc} = \frac{u_{pv}}{1-D}\) | Boost voltage relationship | All modes |
| \(u_{pv}^{*} = u_{max} + \Delta u_{dc}\) | Fault-mode photovoltaic voltage reference | Fault mode |
| \(\Delta u_{dc} = k_{p,dc}(u_{dc} – u_{dc}^{*}) + k_{i,dc}\int (u_{dc} – u_{dc}^{*})dt\) | DC bus voltage correction | Fault mode |
| \(k = \frac{u_f}{u_N}\) | Voltage sag depth | Fault detection |
| \(i_d^{*} = i_{max} – i_R(t-t_1)\) | Active current reduction | Fault mode |
| \(i_q^{*} = \sqrt{i_{max}^{2} – i_d^{*2}}\) | Reactive current calculation | Fault mode |
| \(i_d^{2} + i_q^{2} \le i_{max}^{2}\) | Current limit | All modes |
Table 12 shows that the control logic is compact. The first two equations describe the physical system. The next two equations describe the Boost fault-mode controller. The remaining equations describe the current references and the current limit. I implement these equations in the solar inverter controller with a fast sampling rate. The fault detection and mode transition are handled by a state machine. The state machine has normal, fault, and recovery states. The transition from normal to fault occurs when \(k < 0.9\). The transition from fault to recovery occurs when \(k \ge 0.9\) for a confirmation time. The recovery state gradually returns the current references and the photovoltaic voltage reference to their normal values.
12. Advantages of the Proposed Solar Inverter Strategy
I see several advantages in my strategy. First, it provides low-voltage ride-through without additional hardware. The existing Boost stage is used for DC bus voltage regulation during the fault. This reduces cost and improves reliability. Second, it coordinates active and reactive current. The solar inverter reduces active current according to the sag depth and injects reactive current within the current limit. Third, it limits the DC bus voltage rise. The feedforward term and the right-side photovoltaic operating point allow fast power reduction. Fourth, it maintains current quality. The hold time and the linear reduction avoid abrupt current changes. Fifth, it supports grid recovery. The reactive current raises the point of common coupling voltage, as shown in the simulation.
I also note that the strategy is flexible. The active current reduction rate, the hold time, and the reactive current calculation can be adjusted for different grid codes and different solar inverter ratings. The Boost DC bus voltage controller can be tuned for different DC bus capacitances and photovoltaic array characteristics. The strategy can be applied to symmetrical voltage sags, and with appropriate positive-sequence detection, it can be extended to unbalanced sags. The main requirement is that the solar inverter has a Boost stage and a controllable grid-side current loop. These features are common in modern two-stage solar inverters.
13. Limitations and Future Work
I also recognize the limitations of my study. The simulation uses a symmetrical voltage sag and a fixed photovoltaic maximum power. In reality, irradiance and temperature may change during the fault, and the grid voltage may be unbalanced. The photovoltaic array output power may not be exactly known, and the maximum power point voltage may vary. The feedforward term uses the pre-fault maximum power point voltage, which is a good approximation for a short fault, but it may be less accurate for a long fault. The DC bus voltage controller must therefore be robust to variations in the photovoltaic curve. The current limit is assumed to be fixed, but in practice it may depend on temperature and switching frequency. The LCL filter may also have resonances that affect the current control during the fault. These issues should be addressed in future work.
Another limitation is that the reactive current calculation uses the total current limit. If the grid code requires a specific reactive current profile, the active current may need to be reduced more aggressively. This trade-off between active power and reactive power is important for grid stability. In future work, I would add an adaptive weighting factor between active and reactive current. I would also test the strategy under unbalanced voltage sags and different grid strengths. I would also consider the effect of communication delays and measurement noise on the fault detection and mode transition.
14. Conclusion
I have presented a coordinated low-voltage ride-through control strategy for a two-stage solar inverter. The strategy changes the Boost stage from maximum power point tracking to DC bus voltage regulation during a voltage sag. It uses a pre-fault maximum power point voltage as a feedforward term and moves the photovoltaic operating point to the right side of the maximum power point to reduce power quickly. The grid-side solar inverter reduces active current according to the sag depth and injects reactive current within the current limit. The coordination between the Boost stage and the grid-side solar inverter keeps the DC bus voltage within a safe range, prevents overcurrent, and provides reactive support to the grid.
I verified the strategy with a 100 kW two-stage solar inverter model in PSCAD/EMTDC. The simulation results show that the DC bus voltage peaks at 861.5 V, the photovoltaic output power falls to about 20 kW, and the DC bus voltage settles in about 6 ms. The three-phase current does not show severe overcurrent, and the solar inverter remains connected throughout the fault. The reactive current injection raises the point of common coupling voltage from 41.91 V to 46.88 V, a difference of 4.97 V. These results confirm that the proposed strategy improves the low-voltage ride-through capability of the solar inverter and provides useful grid support without additional hardware.
In my view, the main contribution of this work is the coordinated use of the existing Boost stage and the grid-side solar inverter for low-voltage ride-through. The Boost stage handles the DC bus voltage and the photovoltaic power reduction, while the grid-side solar inverter handles current limitation and reactive support. This division of labor is simple, practical, and suitable for modern two-stage solar inverters. I believe the strategy can be adapted to different solar inverter ratings and grid codes by tuning the current references, the DC bus voltage controller, and the mode transition logic.