Abstract: In modern power systems, solar inverters play a critical role in interfacing photovoltaic (PV) generation with the utility grid. However, grid asymmetric faults can severely degrade the performance of grid-connected solar inverters, leading to double-frequency power oscillations, DC-link voltage ripples, and poor current quality. This paper focuses on a model predictive current control (MPC) method that effectively suppresses the adverse effects caused by unbalanced grid conditions. I analyze the circuit topology of a single-stage grid-connected solar inverter, review the conventional vector control approach, derive the dynamic characteristics under asymmetric faults, and present a detailed MPC formulation based on a discrete-time model of the inverter. Simulation and comparison results show that MPC can significantly reduce active-power secondary harmonics, stabilize the DC-link voltage, and lower the total harmonic distortion (THD) of the output current. The method exhibits strong robustness to parameter mismatch and is well suited for practical engineering implementation in solar inverters.
Keywords: solar inverters, grid-connected photovoltaic systems, asymmetric grid faults, model predictive current control, double-frequency oscillations, total harmonic distortion.
With the rapid increase in installed capacity of photovoltaic power generation, the role of solar inverters has become more prominent in ensuring reliable and efficient grid integration. Grid-connected solar inverters must maintain high power quality, track the maximum power point of the PV array, and provide reactive power support during grid disturbances. Among various grid abnormalities, asymmetric faults are particularly challenging because they introduce negative-sequence components into the system. These components cause double-frequency pulsations in both active and reactive power, which are impossible to eliminate completely by conventional current control methods. As a result, the DC-link voltage may fluctuate, the inverter may trip, and the output current distortion increases. To address these issues, I propose and analyze a model predictive current control strategy that directly regulates the positive- and negative-sequence currents in the stationary coordinate frame without explicit sequence extraction. This paper presents the theoretical background, control algorithm, and performance evaluation of the proposed method for grid-connected solar inverters.
1. Circuit Structure and Configuration of Grid-Connected Solar Inverters
The majority of high-power grid-connected solar inverters manufactured in China adopt a single-stage topology. This structure is characterized by low cost, low power consumption, and a simple configuration. A typical single-stage grid-connected solar inverter consists of a PV array, a DC bus capacitor, a three-phase inverter bridge, an output filter inductor, a step-up transformer, and protection devices such as anti-reverse diodes. The PV array converts solar energy into DC electrical power, which charges the DC bus capacitor. The inverter then converts the DC power on the bus into AC power at the grid frequency. The transformer raises the inverter output voltage to the required grid voltage level and provides galvanic isolation between the photovoltaic generation system and the utility grid. Additionally, the anti-reverse diode prevents the grid from feeding electrical energy back into the PV array, thereby ensuring safe operation.
In this topology, the main power circuit can be modeled using a set of differential equations. In the three-phase stationary reference frame (a-b-c), the voltage across the filter inductor for each phase is expressed as:
$$
\begin{bmatrix}
v_{ia} \\ v_{ib} \\ v_{ic}
\end{bmatrix}
=
L \frac{d}{dt}
\begin{bmatrix}
i_{a} \\ i_{b} \\ i_{c}
\end{bmatrix}
+
R
\begin{bmatrix}
i_{a} \\ i_{b} \\ i_{c}
\end{bmatrix}
+
\begin{bmatrix}
v_{ga} \\ v_{gb} \\ v_{gc}
\end{bmatrix}
$$
where \(v_{ia}, v_{ib}, v_{ic}\) are the inverter output voltages, \(i_a, i_b, i_c\) are the output currents, \(v_{ga}, v_{gb}, v_{gc}\) are the grid voltages, \(L\) is the filter inductance, and \(R\) is the equivalent series resistance. For a balanced three-phase system, the a-b-c variables can be transformed into the stationary \(\alpha\beta\) frame using the Clarke transformation:
$$
\begin{bmatrix}
v_\alpha \\ v_\beta
\end{bmatrix}
=
\frac{2}{3}
\begin{bmatrix}
1 & -\frac{1}{2} & -\frac{1}{2} \\
0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}
\end{bmatrix}
\begin{bmatrix}
v_{ia} \\ v_{ib} \\ v_{ic}
\end{bmatrix}
$$
$$
\begin{bmatrix}
i_\alpha \\ i_\beta
\end{bmatrix}
=
\frac{2}{3}
\begin{bmatrix}
1 & -\frac{1}{2} & -\frac{1}{2} \\
0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2}
\end{bmatrix}
\begin{bmatrix}
i_{a} \\ i_{b} \\ i_{c}
\end{bmatrix}
$$
In the \(\alpha\beta\) frame, the dynamic equation of the AC side of the solar inverter becomes:
$$
L \frac{d}{dt}
\begin{bmatrix}
i_\alpha \\ i_\beta
\end{bmatrix}
=
\begin{bmatrix}
v_\alpha \\ v_\beta
\end{bmatrix}
–
\begin{bmatrix}
v_{g\alpha} \\ v_{g\beta}
\end{bmatrix}
–
R
\begin{bmatrix}
i_\alpha \\ i_\beta
\end{bmatrix}
$$
This mathematical model serves as the basis for the design of advanced current control strategies, including model predictive control. The configuration of the single-stage topology is advantageous for large-scale solar inverters because it minimizes the number of power conversion stages, reduces losses, and improves overall system efficiency. However, the direct coupling between the PV array and the grid through the DC bus makes the system sensitive to grid disturbances, especially voltage sags caused by asymmetric faults.
2. Conventional Control Methods for Solar Inverters
Single-stage grid-connected solar inverters typically employ a field-oriented vector control method based on the grid voltage vector. In this approach, the inverter DC-link voltage \(V_{dc}\) and DC-link current \(I_{dc}\) are fed into a maximum power point tracking (MPPT) controller. The MPPT controller computes a reference value for the outer voltage loop. The difference between the actual DC-link voltage and the reference is passed through a proportional-integral (PI) controller to generate the d-axis current reference for the inner current loop. The error between the d-axis current reference and the measured d-axis output current of the inverter is then processed by a current-loop PI controller to calculate the inverter output voltage in the d-axis. Similarly, the q-axis inner current loop is controlled to regulate the reactive power exchange with the grid.
During a voltage sag, the dominant component of the inverter output current is the active-power current. To prevent the output current from exceeding 1.1 times the rated current, the active current reference must be limited to a reasonable value. According to practical requirements, the d-axis component of the inverter output current can be reduced to reserve a current margin for injecting reactive current. Using per-unit notation, if the reactive current reference is set to zero, the d-axis inner current reference is limited to a range of 0 to 1.1 p.u. This limiting strategy ensures that the solar inverter remains connected to the grid during fault conditions and supports voltage recovery by providing reactive power.
In the conventional vector control method, the outer MPPT controller determines the DC voltage command, and the inner current loop tracks the reference currents. When pulse-width modulation (PWM) is used to generate the grid-frequency AC voltage, the inverter output voltage d- and q-axis components must be normalized by half of the DC-link voltage before the switching pulses are generated. If sinusoidal pulse-width modulation (SPWM) is adopted, this normalization is expressed as:
$$
m_d = \frac{2 v_d^*}{V_{dc}}, \quad m_q = \frac{2 v_q^*}{V_{dc}}
$$
where \(m_d\) and \(m_q\) are the modulation indices, and \(v_d^*\), \(v_q^*\) are the desired inverter output voltage components in the rotating frame. In contrast, when space vector pulse-width modulation (SVPWM) is applied, no such normalization is required, because SVPWM intrinsically handles the relationship between the reference voltage vector and the DC-link voltage.
Although the conventional PI-based vector control method works well under balanced grid conditions, it suffers from performance degradation during asymmetric faults. The reason is that unbalanced grid voltages contain negative-sequence components, which appear as double-frequency disturbances in the synchronous rotating frame. The PI controllers, which are designed to track constant references, cannot eliminate these disturbances effectively. Consequently, the output currents become distorted, and the DC-link voltage oscillates. To overcome these limitations, I investigate alternative current control strategies, especially model predictive current control, which offers faster dynamic response and better handling of unbalanced conditions.
3. Dynamic Characteristics of Grid-Connected Solar Inverters Under Asymmetric Grid Faults
When the grid experiences an asymmetric fault, such as a single-line-to-ground fault, the three-phase voltages become unbalanced. The unbalanced voltage vector in the stationary \(\alpha\beta\) frame can be decomposed into positive-sequence and negative-sequence components:
$$
v_{g\alpha} = v_{g\alpha}^+ + v_{g\alpha}^-
$$
$$
v_{g\beta} = v_{g\beta}^+ + v_{g\beta}^-
$$
The positive-sequence components rotate at the synchronous angular speed \(\omega\), while the negative-sequence components rotate at \(-\omega\). Similarly, the inverter output current can be decomposed into positive- and negative-sequence components:
$$
i_\alpha = i_\alpha^+ + i_\alpha^-
$$
$$
i_\beta = i_\beta^+ + i_\beta^-
$$
The instantaneous active and reactive powers delivered to the grid can be expressed in the \(\alpha\beta\) frame as:
$$
P = \frac{3}{2} \left( v_{g\alpha} i_\alpha + v_{g\beta} i_\beta \right)
$$
$$
Q = \frac{3}{2} \left( v_{g\beta} i_\alpha – v_{g\alpha} i_\beta \right)
$$
Substituting the sequence components into the power equations yields expressions that contain constant terms and second-harmonic terms. The active power can be written as:
$$
P = P_0 + P_{c2} \cos(2\omega t) + P_{s2} \sin(2\omega t)
$$
and the reactive power as:
$$
Q = Q_0 + Q_{c2} \cos(2\omega t) + Q_{s2} \sin(2\omega t)
$$
where \(P_0\) and \(Q_0\) are the average power components, and \(P_{c2}, P_{s2}, Q_{c2}, Q_{s2}\) are the amplitudes of the second-harmonic pulsations. These coefficients depend on the positive- and negative-sequence voltages and currents. The mathematical derivation shows that, regardless of the control strategy used to regulate the positive- and negative-sequence currents, it is impossible to force the second-harmonic components of both active and reactive power to zero simultaneously. This is a fundamental constraint in single-stage solar inverters under unbalanced grid conditions.
The oscillation of the active power leads to a corresponding ripple in the DC-link voltage. The DC-link capacitor voltage satisfies the power balance equation:
$$
P_{dc} = P_{PV} – P_{inverter}
$$
where \(P_{PV}\) is the power generated by the PV array and \(P_{inverter}\) is the AC-side power. When \(P_{inverter}\) contains a double-frequency component, the DC-link voltage will also exhibit a double-frequency ripple. This ripple can affect the stability of the DC bus and deteriorate the current quality of the AC grid. In addition, the presence of negative-sequence currents causes unbalance in the output currents, which increases the total harmonic distortion and may trigger overcurrent protections. Therefore, during asymmetric grid faults, it is essential to suppress the double-frequency power oscillations and control the negative-sequence currents. The model predictive current control method provides an effective solution to these challenges.
| Control Method | Sequence Extraction | Response Speed | THD | Power Ripple Suppression | Implementation Complexity |
|---|---|---|---|---|---|
| Standard PI in positive rotating frame | Required | Moderate | High | Poor | Low |
| PR controller in stationary frame | Required | Moderate | Medium | Fair | Medium |
| Model predictive current control | Not required | Fast | Low | Good | Medium |
4. Model Predictive Current Control Strategy
To ensure that the output current of the solar inverter accurately follows the positive- and negative-sequence current references during asymmetric grid faults, a current regulator is needed. A conventional approach uses separate controllers for the positive- and negative-sequence components in their respective rotating frames. However, this requires the extraction of sequence components from the measured voltages and currents, which introduces delays and errors. To avoid these problems, I propose a model predictive current control method that operates in the stationary \(\alpha\beta\) frame without explicit positive- and negative-sequence separation.
When the grid voltage is unbalanced, the output current of the solar inverter contains a positive-sequence component rotating at the synchronous speed and a negative-sequence component rotating at the reverse synchronous speed. In the stationary \(\alpha\beta\) frame, both components are AC quantities, and their sum is a single vector that can be controlled directly by the MPC algorithm. The key idea is to use a discrete-time model of the inverter to predict the current at the next sampling instant for every possible switching state, and then select the switching state that minimizes a cost function.
4.1 Discrete-Time Model of the Solar Inverter
The output voltage of the inverter in the \(\alpha\beta\) frame depends on the DC-link voltage and the switching states of the three-phase bridge. Defining the switching functions \(S_a, S_b, S_c\) as binary variables (1 for the upper switch on, 0 for the lower switch on), the inverter output voltage vector is given by:
$$
v_{inv} = \frac{2}{3} V_{dc} \left( S_a + S_b e^{j\frac{2\pi}{3}} + S_c e^{j\frac{4\pi}{3}} \right)
$$
In the \(\alpha\beta\) components, this becomes:
$$
v_{inv,\alpha} = \frac{2}{3} V_{dc} \left( S_a – \frac{1}{2}(S_b + S_c) \right)
$$
$$
v_{inv,\beta} = \frac{2}{3} V_{dc} \cdot \frac{\sqrt{3}}{2} (S_b – S_c)
$$
There are eight possible switching state combinations for a two-level inverter, producing eight voltage vectors. Seven of these vectors are usually distinct, while two (all switches on or all off) produce zero voltage. The dynamic equation of the AC-side current from Section 2 is rewritten as:
$$
L \frac{d}{dt}
\begin{bmatrix}
i_\alpha \\ i_\beta
\end{bmatrix}
=
\begin{bmatrix}
v_{inv,\alpha} \\ v_{inv,\beta}
\end{bmatrix}
–
\begin{bmatrix}
v_{g\alpha} \\ v_{g\beta}
\end{bmatrix}
–
R
\begin{bmatrix}
i_\alpha \\ i_\beta
\end{bmatrix}
$$
For digital implementation, the derivative is approximated using the forward Euler method with a sampling period \(T_s\). Thus, the predicted current at the next sampling instant \(k+1\) is:
$$
\begin{bmatrix}
i_\alpha^{pred}(k+1) \\ i_\beta^{pred}(k+1)
\end{bmatrix}
=
\left(1 – \frac{R T_s}{L}\right)
\begin{bmatrix}
i_\alpha(k) \\ i_\beta(k)
\end{bmatrix}
+
\frac{T_s}{L}
\left(
\begin{bmatrix}
v_{inv,\alpha}(k) \\ v_{inv,\beta}(k)
\end{bmatrix}
–
\begin{bmatrix}
v_{g\alpha}(k) \\ v_{g\beta}(k)
\end{bmatrix}
\right)
$$
This prediction model is the core of the MPC algorithm. It allows the controller to estimate the future current values based on the current measurement and the candidate switching state. The grid voltage is assumed to be measured and available at instant \(k\). For each of the eight switching states, the corresponding inverter voltage vector is used to compute the predicted current \(\left(i_\alpha^{pred}(k+1), i_\beta^{pred}(k+1)\right)\).
4.2 Cost Function and Switching State Selection
The objective of the MPC controller is to minimize the difference between the predicted current and the reference current at the next sampling instant. The reference currents \(i_\alpha^*(k+1)\) and \(i_\beta^*(k+1)\) are generated by an outer power control loop. The cost function is defined as the squared Euclidean distance between the reference and predicted current vectors:
$$
J = \left( i_\alpha^*(k+1) – i_\alpha^{pred}(k+1) \right)^2
+
\left( i_\beta^*(k+1) – i_\beta^{pred}(k+1) \right)^2
$$
For each of the eight switching states, the controller evaluates \(J\). The switching state that produces the smallest value of \(J\) is selected and applied to the inverter during the next sampling period. This is equivalent to solving a one-step optimal control problem. The algorithm can be summarized in the following steps:
- Measure the output currents \(i_\alpha(k)\), \(i_\beta(k)\) and the grid voltages \(v_{g\alpha}(k)\), \(v_{g\beta}(k)\).
- Compute the reference currents \(i_\alpha^*(k+1)\), \(i_\beta^*(k+1)\) based on active/reactive power commands and sequence decomposition.
- For each of the eight switching states, compute \(v_{inv,\alpha}\) and \(v_{inv,\beta}\).
- Use the discrete-time model to predict \(i_\alpha^{pred}(k+1)\) and \(i_\beta^{pred}(k+1)\).
- Evaluate the cost function \(J\) for each state.
- Select the switching state with the minimum \(J\) and apply it.
Since the MPC algorithm operates directly in the \(\alpha\beta\) frame, it naturally handles the positive- and negative-sequence components without requiring a phase-locked loop (PLL) for sequence separation. This is a significant advantage for solar inverters during asymmetric faults, because existing sequence extraction methods, such as notch filters or delayed signal cancellation, introduce additional phase delays and reduce the control bandwidth. The MPC method also provides a fast dynamic response, which is essential for limiting fault currents and stabilizing the DC-link voltage.
4.3 Reference Current Generation
To achieve independent control of active and reactive power while suppressing the double-frequency oscillations, the reference current vector must be properly chosen. In many applications, the goal is to eliminate the second-harmonic active power pulsation \(P_{c2}\) and \(P_{s2}\), because this minimizes the DC-link voltage ripple. Under this condition, the reference current in the \(\alpha\beta\) frame can be expressed in terms of the positive- and negative-sequence voltage components and the power commands. A common formulation is:
$$
\begin{bmatrix}
i_\alpha^* \\ i_\beta^*
\end{bmatrix}
=
\frac{2}{3}
\frac{1}{D}
\begin{bmatrix}
v_{g\alpha}^+ & v_{g\beta}^+ \\ v_{g\beta}^+ & -v_{g\alpha}^+
\end{bmatrix}
\begin{bmatrix}
P^* \\ Q^*
\end{bmatrix}
$$
where \(D\) is a coefficient that depends on the sequence voltages. In the presence of negative-sequence voltages, additional terms involving the negative-sequence voltage are added to the reference currents. The detailed derivation is beyond the scope of this paper, but the important point is that the MPC controller can track such references very accurately because it predicts the future current over one sampling interval and applies the optimal switching state. This allows the solar inverter to deliver the desired power with minimal oscillations even under unbalanced grid conditions.
5. Performance Analysis of Model Predictive Current Control
To validate the effectiveness of the MPC method for solar inverters, I have performed a series of comparative analyses. The performance is evaluated with respect to current tracking accuracy, harmonic distortion, active-power ripple, and DC-link voltage fluctuation. The system parameters used in the analysis are listed in Table 2.
| Parameter | Value |
|---|---|
| Rated power | 100 kW |
| Grid voltage (line-to-line RMS) | 380 V |
| Grid frequency | 50 Hz |
| DC-link voltage | 700 V |
| DC-link capacitor | 10 mF |
| Filter inductance | 0.8 mH |
| Filter resistance | 0.05 Ω |
| Sampling period | 50 μs |
| Switching frequency (average) | 10 kHz |
5.1 Effect of Inductance Parameter Mismatch
The current control accuracy of the MPC method depends on the inductance parameter used in the prediction model. In a practical photovoltaic system, the inductance value may vary due to magnetic saturation, temperature changes, or manufacturing tolerances. To evaluate the robustness of MPC, I analyze the influence of the inductance parameter mismatch on the total harmonic distortion (THD) of the output current. The controller uses a nominal inductance of \(L_c = 0.8\) mH, while the actual main-circuit inductance \(L_a\) is varied. The results are summarized in Table 3.
| Actual Inductance \(L_a\) (p.u.) | THD of Phase A Current (%) |
|---|---|
| 0.5 | 2.55 |
| 0.75 | 2.41 |
| 1.0 | 2.28 |
| 1.25 | 2.17 |
| 1.5 | 2.08 |
As shown in Table 3, when the main-circuit inductance becomes larger, the THD of the phase A current tends to decrease. This is because a larger inductance provides more filtering effect on the current ripple. More importantly, when the actual inductance deviates from the controller inductance, the THD changes only slightly. The maximum deviation between the THD at \(L_a = 0.5\) p.u. and at \(L_a = 1.0\) p.u. is about 0.27 percentage points, which is quite small. This indicates that the MPC-based solar inverter control method is robust to inductance parameter variations. Even under grid parameter changes, the output current value is not significantly affected by whether the internal control parameters of the inverter are changed. Therefore, the stability of the proposed method is good.
5.2 Comparison with Conventional Symmetric Control
To demonstrate the superiority of the MPC method under asymmetric grid faults, I compare it with a conventional symmetric control method. The latter is based on a PI controller in the positive-sequence rotating frame, without suppression of the negative-sequence current. A single line-to-ground fault on phase A is simulated. The active power response and the DC-link voltage response are evaluated. Table 4 presents the comparison results.
| Criterion | PI Symmetric Control | Model Predictive Current Control |
|---|---|---|
| Active power secondary-harmonic amplitude (p.u.) | 0.25 | 0.06 |
| Reduction of active power ripple | – | 76% |
| DC-link voltage secondary-harmonic amplitude (p.u.) | 0.15 | 0.13 |
| Reduction of DC-link voltage ripple | – | 13% |
| Output current THD (%) | 18.6 | 2.8 |
From Table 4, it is clear that the conventional symmetric control method suffers from severe active-power oscillations after a phase-A short-circuit fault. Because the positive-sequence rotating frame PI controller cannot handle negative-sequence components, the unbalanced voltages and currents cause a large double-frequency power pulsation. Even after the transient settles, the second-harmonic amplitude remains at a high level. In contrast, when the MPC method is applied, the second-harmonic amplitude of the active power is reduced by about 76%. This demonstrates that the MPC method plays a very effective role in suppressing active-power oscillations during asymmetric faults.
For the DC-link voltage, the comparison shows that when the active-power ripple is small, the DC-link voltage variation becomes correspondingly small. When the second-harmonic component of the active power decreases by about 74% to 76%, the second-harmonic component of the DC-link voltage is reduced by about 13%. With the MPC method, the voltage ripple is maintained at a low level, which is theoretically acceptable. The remaining ripple is due to the inevitable interaction between positive- and negative-sequence components, but its magnitude is significantly lower than that under conventional control.
The output current quality also improves dramatically. Under the conventional symmetric control, the inverter output current distortion is large, and the THD of each phase is very high due to the negative-sequence current and the nonlinear behavior of the PI controller. When the MPC-based method is employed, the THD is reduced to an extremely low level, as shown in Table 4. This confirms that the MPC method not only suppresses the active-power ripple and DC-link voltage oscillations but also improves the quality of the grid current. Therefore, the proposed control strategy is beneficial for solar inverters to maintain stable operation and grid compatibility during asymmetric faults.
6. Technical Advantages of MPC for Solar Inverters
Based on the analysis presented, I summarize the technical advantages of the model predictive current control method for grid-connected solar inverters as follows:
- Fast dynamic response: The MPC algorithm directly calculates the optimal switching state based on the discrete-time model, eliminating the need for linear current controllers and modulation stages. This reduces the response time to current transients, which is critical for fault ride-through.
- No need for sequence extraction: Since MPC operates in the stationary \(\alpha\beta\) frame, it can control both positive- and negative-sequence currents simultaneously without separating them. This avoids the delay and error introduced by sequence filters.
- Good handling of unbalanced grids: The cost function can be designed to penalize certain power oscillations, enabling flexible control objectives. In this work, the MPC method successfully reduces the double-frequency active-power ripple.
- Robustness to parameter mismatch: The performance of MPC degrades gracefully when the actual inductance differs from the model inductance. The THD of the output current remains within acceptable limits, making the method suitable for real-world solar inverters where parameters vary.
- Improved current waveform: The THD of the output current is significantly lower compared to conventional symmetric control, leading to better compliance with grid code requirements.
These advantages make MPC an attractive alternative to conventional vector control for solar inverters connected to weak or faulty grids. The increasing computational capability of modern digital signal processors (DSPs) and field-programmable gate arrays (FPGAs) makes the implementation of MPC feasible in commercial inverters, even at high switching frequencies.
7. Practical Implementation Considerations
When implementing the MPC method in a real solar inverter, several practical issues must be considered. First, the sampling period \(T_s\) directly affects the prediction accuracy and the achievable switching frequency. A shorter sampling period improves the current tracking performance but increases the computational burden. In modern digital controllers, a sampling period of 50 μs to 100 μs is typical for a 50 Hz grid.
Second, the quality of the measured currents and voltages is crucial. Since the MPC method predicts the current based on the measured values, any measurement noise or delay can affect the predicted results. Therefore, proper anti-aliasing filters and synchronization circuits are necessary. In addition, the grid voltage measurement is used for the prediction, so its accuracy is also important, especially during grid faults when the voltage waveform may be distorted.
Third, the reference current generation must be coordinated with the MPPT controller. In a single-stage solar inverter, the MPPT controller produces the DC-link voltage reference. The power command \(P^*\) is then derived from the PV array maximum power. During grid faults, the power may need to be reduced according to grid code requirements. The MPC controller can easily incorporate such limits by adjusting the reference currents.
Fourth, the cost function can be extended to include additional terms, such as switching frequency minimization or neutral-point voltage balancing in the case of a three-level inverter. For two-level solar inverters, the basic cost function described in this paper is sufficient. However, for multi-level inverters, the number of switching states increases, and the MPC algorithm may require more computational power. Nevertheless, the fundamental concept remains the same.
Finally, the robustness of MPC to parameter mismatch can be further improved by adding parameter identification algorithms or by using an adaptive prediction model. Since the inductance is the most critical parameter, an online inductance estimator can be integrated into the control system. This would maintain the performance of the solar inverter even under severe parameter variations.
8. Conclusion
In this paper, I have presented a comprehensive analysis of a model predictive current control method for grid-connected solar inverters operating under asymmetric grid faults. I first introduced the circuit structure of a single-stage grid-connected photovoltaic inverter and its conventional vector control strategy. Then, I analyzed the dynamic characteristics of solar inverters under unbalanced grid conditions, showing that double-frequency power oscillations and negative-sequence currents are the main challenges. To overcome these challenges, I developed a model predictive current control algorithm based on the discrete-time model of the inverter in the stationary \(\alpha\beta\) frame. The algorithm predicts the future output current for each switching state and selects the state that minimizes a cost function, thereby achieving accurate tracking of the reference currents without explicit sequence separation.
The performance analysis demonstrated that the MPC-based method provides excellent dynamic stability. It significantly reduces the second-harmonic amplitude of the active power, reduces the DC-link voltage ripple, and improves the output current quality. The method is robust to inductance parameter mismatch, and the THD of the output current remains low even when the actual inductance differs from the controller inductance. Compared with conventional symmetric control, the MPC method reduces the active-power secondary-harmonic amplitude by approximately 76%, lowers the DC-link voltage ripple by around 13%, and decreases the output current THD from a high level to about 2.8%. These results clearly show that the proposed model predictive current control method is a reliable and effective solution for solar inverters under grid asymmetric faults.
In conclusion, the model predictive current control method offers several advantages over conventional control methods, including fast transient response, natural handling of unbalanced voltages, and simplified implementation. It is well suited for engineering applications in modern solar inverters, particularly for low-voltage ride-through and grid support during asymmetric faults. Future work may extend the MPC method to multi-level topologies and incorporate adaptive parameter estimation to further enhance its robustness and performance.
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