Over the past ten years, photovoltaic generation has expanded very quickly, and the role of solar inverters has changed from a small auxiliary generator to a major power-electronics interface in the grid. According to the energy statistics that I reviewed, by the end of 2019 cumulative photovoltaic installed capacity had reached 204 GW, which was about 10.15% of the total installed generation capacity. This means that solar inverters have become one of the key devices affecting grid security and stability. In particular, the low voltage ride through behavior of solar inverters is now a mandatory grid-code requirement. In many grid codes, a photovoltaic inverter must remain connected during a grid fault and inject reactive current proportional to the voltage dip. However, the active current requirement during low voltage ride through is usually not clearly specified.
In my work, I have focused on a practical problem: when solar inverters are connected to weak grids, the grid impedance is not negligible. The transmission line impedance and transformer leakage inductance can be large, so the grid is called a weak grid. During asymmetric grid faults, the voltage contains not only positive-sequence components but also negative-sequence components. If a conventional balanced-grid controller is used, the current injected by the inverter will contain negative-sequence and harmonic components. This is especially dangerous in weak grids because it can increase the imbalance and cause resonance between the inverter and the grid. There is also a risk of oscillation amplification due to distributed capacitance and parasitic inductance of long transmission lines.
Another important issue is frequency stability. Since the grid code often does not require active current during low voltage ride through, many solar inverters intentionally reduce the active current to zero and raise the DC-link voltage to the open-circuit voltage of the photovoltaic array. In a weak grid with high photovoltaic penetration, this active power loss can cause a significant frequency deviation. If the frequency deviation exceeds the allowed range, the system may trigger under-frequency load shedding. Therefore, I have proposed a coordinated active current and reactive current control strategy for solar inverters during low voltage ride through. The strategy combines a decoupled double synchronous reference frame phase-locked loop, a virtual-resistor active damping method, and a current-limiting coordination algorithm. I have implemented this strategy on a hardware control platform based on F28335 and CPLD, and verified it with a hardware-in-the-loop simulation platform.
Challenges for Solar Inverters in Weak Grids
Weak grids are characterized by a high grid impedance, a low short-circuit capacity, and a strong interaction between the power converter and the grid. For solar inverters, this interaction appears as a shift of the LCL filter resonance frequency. When the grid impedance changes, the resonance point changes as well. Passive damping can stabilize the LCL filter, but it causes additional losses and reduces efficiency. I have therefore chosen an active damping method, which is more suitable for solar inverters.
In addition, unbalanced grid voltages introduce negative-sequence components into the control system. A conventional synchronous reference frame phase-locked loop, which is designed for balanced three-phase voltages, cannot correctly extract the negative-sequence voltage. This is unacceptable for solar inverters in weak grids because the negative-sequence voltage may be large during an asymmetric fault. The second harmonic ripple in the dq axes caused by the negative-sequence component can propagate through the current controller and distort the output current. Therefore, I selected a decoupled double synchronous reference frame phase-locked loop, or DDSRF-PLL, for my LVRT controller.
Phase-Locked Loop for Unbalanced Grid Voltages
There are several phase-locked loop methods commonly considered for solar inverters. The first is the synchronous reference frame PLL, usually called SRF-PLL. It is simple and fast under ideal balanced grid conditions. The second is the dual second-order generalized integrator PLL, usually called DSOGI-PLL, which can extract symmetrical components. The third is the decoupled double synchronous reference frame PLL, called DDSRF-PLL.
| PLL method | Advantages | Disadvantages |
|---|---|---|
| SRF-PLL | Simple implementation, accurate for balanced grids | Cannot handle unbalanced voltages correctly |
| DSOGI-PLL | Extracts positive and negative sequence components | Frequent estimation is computationally heavy, complex |
| DDSRF-PLL | Decoupled positive and negative sequence dq axes, rejects 2ω ripple | Requires more computation but still practical for solar inverters |
For my controller, I chose DDSRF-PLL because it provides robust phase detection for solar inverters even when the grid voltage contains both positive and negative sequence components. To explain the principle, I start with the unbalanced grid voltage vector. In a three-wire system, the zero-sequence component can be ignored. The grid voltage in the stationary αβ frame can therefore be written as
$$
\begin{bmatrix}
V_{S\alpha} \\
V_{S\beta}
\end{bmatrix}
=
V_S^{+1}
\begin{bmatrix}
\cos(\omega t + \phi^+) \\
\sin(\omega t + \phi^+)
\end{bmatrix}
+
V_S^{-1}
\begin{bmatrix}
\cos(\omega t + \phi^-) \\
-\sin(\omega t + \phi^-)
\end{bmatrix}
\tag{1}
$$
where \(V_S^{+1}\) is the positive-sequence voltage amplitude, \(V_S^{-1}\) is the negative-sequence voltage amplitude, \(\omega\) is the grid angular frequency, and \(\phi^+\), \(\phi^-\) are the initial phase angles. The positive-sequence component forms a vector rotating at \(+\omega\), while the negative-sequence component appears as a vector whose β-axis component is reversed. This representation is useful because it shows the second harmonic coupling that appears after Park transformation.
I then project this stationary vector into two rotating reference frames. One frame rotates at \(+\omega\), and the other rotates at \(-\omega\). The positive-sequence dq components can be expressed as
$$
\begin{bmatrix}
V_{Sd}^{+1} \\
V_{Sq}^{+1}
\end{bmatrix}
=
V_S^{+1}
\begin{bmatrix}
\cos(\omega t + \phi^+ – \theta’) \\
\sin(\omega t + \phi^+ – \theta’)
\end{bmatrix}
+
V_S^{-1}
\begin{bmatrix}
\cos(\omega t + \phi^- + \theta’) \\
-\sin(\omega t + \phi^- + \theta’)
\end{bmatrix}
\tag{2}
$$
Similarly, the negative-sequence dq components can be expressed as
$$
\begin{bmatrix}
V_{Sd}^{-1} \\
V_{Sq}^{-1}
\end{bmatrix}
=
V_S^{-1}
\begin{bmatrix}
1 \\
0
\end{bmatrix}
+
V_S^{+1}
\begin{bmatrix}
\cos(\omega t + \phi^+ + \theta’) \\
\sin(\omega t + \phi^+ + \theta’)
\end{bmatrix}
\tag{3}
$$
When the phase-locked loop is locked, the positive-sequence voltage vector is aligned with the d-axis, so \(\omega t + \phi^+ – \theta’ = 0\). The positive-sequence dq voltage then contains a constant DC value equal to \(V_S^{+1}\), plus an oscillating term at twice the grid frequency. I can write this in the compact form
$$
\begin{bmatrix}
V_{Sd}^{+1} \\
V_{Sq}^{+1}
\end{bmatrix}
=
V_S^{+1}
\begin{bmatrix}
1 \\
0
\end{bmatrix}
+
V_S^{-1}
\begin{bmatrix}
\cos(2\omega t + \gamma) \\
-\sin(2\omega t + \gamma)
\end{bmatrix}
\tag{4}
$$
where \(\gamma\) depends on the initial phase angles of the positive and negative sequence voltages. The same reasoning applies to the negative-sequence dq voltage. The important conclusion is that the negative-sequence component creates a second harmonic ripple in the positive-sequence dq frame. A standard PI controller cannot follow this AC ripple without producing a steady-state error. Therefore, DDSRF-PLL uses a decoupling network to estimate this ripple and remove it from the control signals. After decoupling, the positive-sequence dq voltage is clean, and the angular position \(\theta\) obtained from the PLL is accurate.
In my implementation, I used the positive-sequence d-axis voltage \(V_d^+\) as the fault-depth detection variable. The value of \(V_d^+\) is compared with the nominal grid voltage to decide whether the system is in normal mode or low voltage ride through mode. This is more reliable than using the phase voltage amplitude because it is not affected by the negative-sequence component.
Resonance Suppression for Solar Inverters
Weak grids cause the resonance frequency of the LCL filter to move. If the grid impedance changes by a large amount, a fixed notch filter or fixed resonance compensation may fail. I therefore implemented an active damping strategy based on a virtual resistor in series with the filter capacitor. This method does not require exact knowledge of the grid impedance and does not consume real power.
For a typical LCL filter with inverter-side inductance \(L_1\), grid-side inductance \(L_2\), and filter capacitance \(C_f\), the transfer function from the inverter voltage to the grid current can be written as
$$
\frac{i_g(s)}{v_i(s)}
=
\frac{1}{L_1 L_2 C_f s^3 + (L_1 + L_2)s}
\tag{5}
$$
This transfer function has a pair of complex poles on the imaginary axis, which corresponds to the resonance peak of the LCL filter. If the grid impedance pushes this resonance peak toward a harmful frequency, the inverter current can oscillate. In my control strategy, I added a virtual resistance \(R_d\) in series with the capacitor branch. The modified transfer function becomes
$$
\frac{i_g(s)}{v_i(s)}
=
\frac{1}{L_1 L_2 C_f s^3 + C_f R_d (L_1 + L_2)s^2 + (L_1 + L_2)s}
\tag{6}
$$
The extra \(s^2\) term introduces damping into the system. This is equivalent to placing a physical resistor in the capacitor path, but without the corresponding ohmic loss. The damping current can be computed in the time domain as
$$
i_{damp}(t) = C_f R_d \frac{dv_c(t)}{dt}
\tag{7}
$$
where \(v_c(t)\) is the filter capacitor voltage. In my controller, I add this damping current to the current reference. In the discrete digital controller, the derivative of the capacitor voltage is approximated with a finite difference. Because the virtual resistance is not a physical component, its value can be adjusted online according to the measured resonance behavior. This is an important advantage for solar inverters connected to weak grids, where the grid impedance varies with network topology and operating point.
I compared two active-damping approaches. The first is a resonance-peak suppression method that shapes the transfer function at a fixed frequency. This method works well when the grid impedance is known before commissioning. However, it loses effectiveness when the grid impedance changes. The second method, which I used, is the virtual-resistor method. The virtual resistor acts on the capacitor current or voltage derivative and provides damping over a wider frequency range. Therefore, it is more suitable for weak-grid applications.
Traditional LVRT Control in Inverters
Traditional LVRT control in many solar inverters follows the minimum grid-code requirements. The grid code usually specifies the reactive current reference during low voltage ride through as a function of the measured positive-sequence voltage. In my design, the reactive current reference is
$$
i_{q\_ref}
=
\begin{cases}
0, & V_d^+ \ge 0.9 \\
1.5(0.9 – V_d^+) I_n, & 0.2 \le V_d^+ < 0.9 \\
1.05 I_n, & V_d^+ < 0.2
\end{cases}
\tag{8}
$$
where \(I_n\) is the rated current of the photovoltaic inverter and \(V_d^+\) is the positive-sequence voltage in per unit. This formula guarantees that the inverter provides more reactive current as the voltage becomes deeper. However, in many traditional controllers, the active current reference is set to zero:
$$
i_{d\_ref} = 0
\tag{9}
$$
This is done mainly to protect IGBT power devices from overcurrent. During a severe grid fault, the inverter must produce a large reactive current. Since the sum of active and reactive current is limited by the device current rating, many manufacturers choose to sacrifice active current. They increase the DC-link voltage to the photovoltaic open-circuit voltage and stop transferring active power for the duration of the fault.
The problem with this approach is that the frequency of a weak grid is affected by active power balance. In a weak grid with high photovoltaic penetration, suddenly removing all active power from solar inverters can cause a large frequency drop. If many inverters are using the same traditional LVRT strategy, the combined active power loss may be unacceptable. Therefore, I have developed a more balanced strategy that maintains active current as much as possible while still satisfying the reactive current requirement.
Proposed Active and Reactive Current Coordination
My proposed strategy does not simply set the active current to zero during low voltage ride through. Instead, it calculates the maximum allowable active current after the reactive current reference has been determined. The current limit of the solar inverter is assumed to be \(1.1 I_n\), which is a common overcurrent capability of IGBT-based inverters. The active current reference is therefore
$$
i_{d\_ref}
=
\min
\left(
i_{d\_ref\_locked},
\sqrt{(1.1 I_n)^2 – i_{q\_ref}^2}
\right)
\tag{10}
$$
where \(i_{d\_ref\_locked}\) is the active current reference that was stored just before the grid fault occurred. The square-root term represents the maximum active current that can be injected while the reactive current is still equal to \(i_{q\_ref}\). The min function ensures that the active current never exceeds the current limit and never exceeds the pre-fault value. To understand the logic, I can summarize the control sequence as follows:
| Step | Action |
|---|---|
| 1 | DDSRF-PLL extracts \(\theta\), \(V_d^+\), and \(V_q^+\) |
| 2 | If \(V_d^+ \ge 0.9\), run normal MPPT control |
| 3 | If \(V_d^+ < 0.9\), enter LVRT mode and lock \(i_{d\_ref\_locked}\) |
| 4 | Compute \(i_{q\_ref}\) from the voltage dip |
| 5 | Compute \(i_{d\_ref}\) using the min formula |
| 6 | Set negative-sequence current references to zero |
| 7 | Run double-dq current PI control with virtual-resistor damping |
| 8 | On recovery, restore normal MPPT operation smoothly |
I also considered the case where the positive-sequence voltage is so low that the PLL cannot produce a reliable angle. In my LVRT controller, I store the phase angle immediately before the fault. If the measured voltage becomes too small, I reconstruct the reference angle using the stored angle and the nominal grid frequency:
$$
\theta_{ref}(t) = \theta_{lock} + 2\pi f_{nom}(t – t_{lock})
\tag{11}
$$
This prevents a loss of synchronization during severe faults. When the grid voltage recovers above the LVRT threshold, the controller returns to normal MPPT mode with a smooth transition so that the active current does not jump abruptly.
The proposed strategy has several advantages for solar inverters in weak grids. First, it keeps some active power flowing during the fault, which reduces the frequency deviation. Second, it strictly satisfies the grid-code reactive current requirement. Third, it respects the overcurrent limit of the inverter. Fourth, the DDSRF-PLL and virtual-resistor damping make the controller robust under unbalanced and resonant grid conditions.
Mathematical Model of the Double-dq Current Control
In order to control the positive-sequence and negative-sequence currents independently, I used a mathematical model of the inverter with an L filter or LCL filter in the double-dq reference frame. The equations for the inverter-side voltage can be written as
$$
\begin{aligned}
v_{inv,d}^+ &= L \frac{di_d^+}{dt} + e_{gd}^+ – \omega L i_q^+ \\
v_{inv,q}^+ &= L \frac{di_q^+}{dt} + e_{gq}^+ + \omega L i_d^+ \\
v_{inv,d}^- &= L \frac{di_d^-}{dt} + e_{gd}^- + \omega L i_q^- \\
v_{inv,q}^- &= L \frac{di_q^-}{dt} + e_{gq}^- – \omega L i_d^-
\end{aligned}
\tag{12}
$$
where \(L\) is the total inductance seen by the current controller, \(e_{gd}^+\), \(e_{gq}^+\) are the positive-sequence grid voltage dq components, and \(e_{gd}^-\), \(e_{gq}^-\) are the negative-sequence grid voltage dq components. The coupling terms \(\omega L i_q^+\) and \(\omega L i_d^+\) appear because the dq frame rotates at the grid frequency. For the negative-sequence frame, the coupling signs are opposite because the rotation direction is reversed.
My controller uses two separate PI controllers for the positive-sequence d and q currents and another two PI controllers for the negative-sequence d and q currents. Since the grid code does not require negative-sequence current injection in my application, I set the negative-sequence current references to zero. However, I still measure and control the negative-sequence current because this helps to prevent unwanted negative-sequence current flow and reduces the risk of further unbalance in the weak grid.
The output voltages of the four PI controllers are transformed back to the stationary αβ frame. The positive and negative sequence voltage references are summed, and the result is sent to the SVPWM modulator. In parallel, the virtual-resistor damping current is added to the current reference path to suppress LCL resonance. This complete control structure was implemented in the F28335 digital signal processor.
Hardware-in-the-Loop Verification
I verified the proposed control strategy on a hardware control platform based on F28335 and CPLD. The F28335 DSP performs the DDSRF-PLL algorithm, the LVRT calculation, the current PI controllers, and the SVPWM modulation. The CPLD handles the IGBT gate pulse distribution, fault logic, and hardware protection. The actual power stage was not used. Instead, I connected the hardware control platform to an RTLAB hardware-in-the-loop simulation platform. The real-time simulation step was set to 20 microseconds.
In the RTLAB model, I used a two-level three-phase full-bridge inverter topology. The main parameters of the simulated inverter are shown in the table below.
| Inverter parameter | Value |
|---|---|
| Rated power | 500 kW |
| Grid voltage | 315 V |
| MPPT voltage | 600 V |
| IGBT switching frequency | 3 kHz |
| DC-link capacitance | 10080 μF |
| Filter inductance | 0.5 mH |
| Filter capacitance | 220 μF delta connection |
| Real-time simulation step | 20 μs |
The initial operating condition was set to an MPPT voltage of 600 V, an active power of 350 kW, and zero reactive power. I then created a balanced three-phase voltage sag in the simulation model using an impedance divider. The grid voltage was reduced to 0.6 per unit for a duration of 1.41 seconds. During the sag, the positive-sequence voltage detected by the DDSRF-PLL fell below the 0.9 per unit threshold, so the controller entered LVRT mode.
The hardware-in-the-loop results confirmed that the DDSRF-PLL maintained synchronization during the unbalanced voltage condition. The reactive current reference was calculated correctly according to the depth of the voltage dip. The active current was not forced to zero. Instead, the controller limited the active current according to the remaining current margin after the reactive current injection. The total current amplitude stayed below the 1.1 per unit overcurrent limit, and the LCL resonance was suppressed by the virtual-resistor damping method.
I also tested the recovery behavior after the fault. When the grid voltage returned to the normal range, the controller smoothly restored the active current reference to the MPPT value. There was no severe oscillation in the DC-link voltage or in the AC current waveform. The frequency response was better than the traditional zero-active-current strategy because a significant amount of active power continued to flow into the grid during the LVRT interval.
Comparison Between Traditional and Proposed Strategies
To summarize the improvement, I can compare the traditional LVRT strategy with my proposed strategy in the following table.
| Item | Traditional LVRT | Proposed coordinated LVRT |
|---|---|---|
| Positive-sequence reactive current | Injected according to voltage dip | Injected according to voltage dip |
| Active current during fault | Usually zero | Maintained up to current limit |
| Phase detection under unbalanced voltage | Poor with SRF-PLL | Robust with DDSRF-PLL |
| Resonance suppression | Often passive damping | Virtual-resistor active damping |
| Frequency support to weak grid | Weak | Improved |
| Overcurrent protection | Simple conservative limit | Advanced current coordination |
The comparison shows that the proposed strategy is more suitable for solar inverters connected to weak grids. It does not sacrifice grid-code compliance. Instead, it adds active power support and improves the overall stability of the interconnected system.
Implementation Notes for Solar Inverters
In the actual DSP implementation, I divided the software into several interrupt routines. The fast control loop runs at the switching frequency and contains the inner current loops. The PLL also runs in this fast loop because the phase angle must be available for every PWM cycle. The slower loop runs at a lower rate and handles fault detection, state transitions, and grid-code reference calculation.
For the DDSRF-PLL, the decoupling network requires the estimated positive and negative sequence voltage amplitudes. I used a low-pass filter after the Park transformation to obtain these amplitudes. The bandwidth of the low-pass filter must be high enough to track the fault dynamics but low enough to attenuate the second harmonic ripple. In my tests, a filter bandwidth in the range of 20 to 30 Hz gave a good compromise for solar inverters.
The virtual-resistor damping implementation is also important. I measured the capacitor voltage of the LCL filter and calculated the derivative. Because the derivative amplifies high-frequency noise, I used a low-pass filter in the derivative path. The virtual resistance value \(R_d\) was selected so that the resonance peak was sufficiently damped without causing excessive control effort. Because the grid impedance of a weak grid can change, I made \(R_d\) tunable from the supervisory controller.
One of the main concerns during LVRT is the DC-link voltage. In the traditional strategy, the active power is set to zero, so the PV array has no output path and the DC-link voltage rises to the open-circuit voltage. In my proposed strategy, some active power continues to flow, so the DC-link voltage is easier to manage. In practical solar inverters, a DC-link overvoltage protection circuit is still needed as a safety measure, but the proposed control strategy reduces the likelihood of reaching the overvoltage limit during moderate voltage sags.
Conclusions
In this work, I have studied the low voltage ride through control problem for solar inverters connected to weak and unbalanced grids. I have shown that the traditional strategy, which sets the active current to zero during LVRT, is not ideal for weak grids because it can cause a large frequency deviation. I have also shown that a conventional SRF-PLL is not sufficient when the grid voltage contains negative-sequence components. Therefore, I selected a DDSRF-PLL to obtain a stable positive-sequence voltage angle and amplitude.
I proposed a coordinated active current and reactive current control method that keeps the active current as high as possible while satisfying the reactive current requirement and the overcurrent limit. The active current reference is calculated using the pre-fault value and the remaining current margin. I also added a virtual-resistor active damping method to suppress LCL filter resonance under changing grid impedance. The complete controller was implemented on a F28335 and CPLD hardware platform and tested with an RTLAB hardware-in-the-loop simulator. The results showed that the proposed strategy provides reactive current according to the grid code, maintains active power transfer during the fault, limits the total current, and avoids sustained oscillations.
For solar inverters connected to weak grids, this integrated approach improves both voltage support and frequency support. It is a practical solution that can be implemented in commercial inverters without major hardware changes. In the future, I plan to extend this method to consider negative-sequence current injection and to optimize the virtual-resistance tuning automatically based on online grid impedance estimation.