In the context of China’s ‘dual carbon’ strategy, new energy power generation systems have been widely researched and applied. Grid-connected inverters serve as a critical bridge between distributed power sources and the main grid, and their performance directly impacts system power quality. Among various types of solar inverters, the diode neutral-point-clamped (NPC) three-level grid-connected inverter has gained significant attention in the field of new energy generation due to its advantages such as lower output harmonics at the same switching frequency, reduced device voltage stress, and strong fault tolerance compared to two-level inverters.
With the rapid advancement of microcontroller technology, model predictive control (MPC) has received widespread attention. In particular, finite control set model predictive control (FCS-MPC) is widely applied in grid-connected inverter control due to its multi-objective control capability, fast dynamic response, and flexible control features. However, traditional three-level FCS-MPC must traverse all 27 switching states of the three-level three-phase inverter in each sampling period for optimization. Additionally, three-level inverters must consider neutral-point potential balance. As the control set and control objectives increase, the computational load grows exponentially.
To address the issues of large online computational burden and variable switching frequency in FCS-MPC for multi-level inverters, this paper proposes a low-complexity fixed-frequency model predictive control method for NPC-type three-level grid-connected inverters—one of the key types of solar inverters. First, leveraging the mechanism of redundant small vectors on the neutral-point potential, a single-objective reference current tracking cost function is constructed. Then, a voltage middle-axis vector is defined as the axis of the optimization sector. The first rolling optimization using the middle-axis vector determines the optimization sector. Combined with the q-axis component of the target prediction error, the core optimization region is further located. After a second rolling optimization, the optimal three vectors are determined. Finally, by combining the error values generated in the evaluation of the target cost function for the selected voltage vectors, the vector action times are optimally allocated. The influence of model parameter mismatch on the control method is also analyzed. The proposed method reduces computational effort while enabling the inverter to output a fixed switching frequency.
To verify the effectiveness and feasibility of the proposed low-complexity fixed-frequency three-level FCS-MPC method, simulation models based on Matlab/Simulink and an experimental platform for the 3L-NPC grid-connected inverter were established. Under the same conditions, comparative studies among traditional single-vector FCS-MPC, modulation model predictive control (M-MPC), and the proposed control strategy (improved FCS-MPC) were conducted from the aspects of steady-state current harmonic distribution and dynamic current tracking.
The main circuit parameters are shown in the table below.
| Parameter | Value |
|---|---|
| Grid voltage (RMS) | E = 380 V |
| Grid frequency | f = 50 Hz |
| DC bus voltage | Udc = 680 V |
| Filter inductor | L = 1.5 mH |
| DC bus capacitance | C1 = C2 = C = 2400 μF |
| Sampling frequency | fs = 10 kHz |
Mathematical Model and Traditional MPC
The dynamic model of the 3L-NPC grid-connected inverter in the synchronous rotating dq coordinate system, oriented along the grid voltage vector, is given by:
$$ \begin{cases}
L \frac{di_{dq}}{dt} = u_{dq} – Ri_{dq} – j\omega L i_{dq} – e_{dq} \\
C \left( \frac{du_{C1}}{dt} – \frac{du_{C2}}{dt} \right) = \sum_{x=a,b,c} i_x (S_x == 0)
\end{cases} $$
Where \(i_{abc}\) are the three-phase output currents of the inverter, and \(u_{C1}\), \(u_{C2}\) are the upper and lower DC bus capacitor voltages. Using forward Euler discretization:
$$ i_{dq}(k+1) = \frac{T_s}{L} (u_{dq}(k) – e_{dq}(k) – R i_{dq}(k)) + i_{dq}(k)(1 – j\omega) $$
$$ \Delta u_C(k+1) = \Delta u_C(k) + \frac{1}{C} \sum_{x=a,b,c} i_x(k)(S_x == 0) $$
The conventional FCS-MPC cost function for this type of solar inverter is:
$$ J(k) = ||i_d^* – i_d(k+1)|| + ||i_q^* – i_q(k+1)|| + \sigma ||u_{C1}(k+1) – u_{C2}(k+1)|| $$
Proposed Low Complexity Fixed Frequency MPC
The proposed method selects three vectors per control cycle. First, six middle vectors \(V_M \in \{V_{M1}[PON], V_{M2}[OPN], V_{M3}[NOP], V_{M4}[NOP], V_{M5}[ONP], V_{M6}[NOP]\}\) are substituted into the current prediction model and the single-objective cost function:
$$ J(k) = ||i_d^* – i_d(k+1)|| + ||i_q^* – i_q(k+1)|| $$
The middle vector that minimizes the cost function is selected as the axis vector of the secondary optimization sector. This divides the vector plane into 6 sectors (S1 to S6). For example, with current vector I in sector S1, the first rolling optimization result might be as shown in the table below.
| Vector V | VM1 | VM2 | VM3 | VM4 | VM5 | VM6 |
|---|---|---|---|---|---|---|
| id*/A | 40 | 40 | 40 | 40 | 40 | 40 |
| id(k+1)/A | 34.36 | 49.11 | 45.72 | 86.56 | 71.82 | 75.21 |
| iq*/A | 0 | 0 | 0 | 0 | 0 | 0 |
| iq(k+1)/A | -1.96 | -23.58 | 21.63 | 1.95 | 23.58 | -21.62 |
| Cost J | 10.11 | 41.49 | 20.43 | 61.39 | 51.81 | 51.08 |
The q-axis component of the prediction error, \(\Delta i_q(k) = i_q^*(k+1) – i_q(k+1)\), is used to further locate the secondary optimization area. The vector action time allocation is proportional to the inverse of their cost function values:
$$ \begin{cases}
t_1 = T_s \cdot \frac{1/J_{①}}{1/J_{①} + 1/J_{③} + 1/J_{\min(②,④)}} \\
t_2 = T_s \cdot \frac{1/J_{③}}{1/J_{①} + 1/J_{③} + 1/J_{\min(②,④)}} \\
t_3 = T_s – t_1 – t_2
\end{cases} $$
This method compresses the traditional 27-step optimization to 9 steps (6 initial + 3 secondary).
Influence of Model Parameter Mismatch
The prediction error due to model parameter mismatch is:
$$ \Delta i_{dq}(k+1) = \hat{i}_{qd}(k+1) – i_{dq}(k+1) = -\frac{\Delta L \cdot T_s}{L(L+\Delta L)} [u_{dq}(k) – e_{dq}(k)] $$
Simulation results for different inductor values are summarized in the table below.
| Actual Inductance Lr | THD (%) |
|---|---|
| 0.75 mH (50% of L) | 6.85 |
| 1.5 mH (100% of L, matched) | 2.64 |
| 2.25 mH (150% of L) | 3.38 |
The results show that the proposed method maintains stability under limited parameter mismatch, with a slight degradation in THD.
Comparative Simulation Results
The steady-state performance of three control methods for types of solar inverters is compared in the table below.
| Control Method | Current THD (%) | Neutral-point voltage ripple (V) |
|---|---|---|
| Traditional 1-Vector FCS-MPC | 6.71 | 5.6 |
| M-MPC [16] | 3.11 | 8.0 |
| Proposed Improved FCS-MPC | 2.64 | 5.8 |
The dynamic response times are compared below.
| Control Method | Response Time (ms) |
|---|---|
| Traditional 1-Vector FCS-MPC | 0.88 |
| M-MPC [16] | 0.89 |
| Proposed Improved FCS-MPC | 0.56 |
Experimental Verification
The execution time of the algorithm on a TMS320F28335 DSP was measured.
| Control Method | Time (μs) |
|---|---|
| Traditional 1-Vector FCS-MPC | 63.6 |
| M-MPC [16] | 49.3 |
| Proposed Improved FCS-MPC | 36.2 |
Experimental steady-state and transient waveforms confirm the effectiveness of the proposed strategy for various types of solar inverters. The proposed improved FCS-MPC achieves a 43% reduction in execution time compared to the traditional method while providing better steady-state and dynamic performance, along with fixed switching frequency operation.
Conclusion
To optimize the FCS-MPC control for 3L-NPC grid-connected inverters—a critical class of types of solar inverters—this paper proposes a low-complexity fixed-switching-frequency model predictive control strategy based on multi-stage optimization of current tracking error. The following main conclusions are drawn:
- A system discrete model for the 3L-NPC grid-connected inverter was established. By utilizing the mechanism of redundant small vectors on neutral-point potential, a single-objective reference current tracking cost function was constructed. This reduces the computational load of the cost function evaluation and avoids the difficulty of selecting weighting factors, simplifying the control algorithm complexity.
- A voltage middle-axis vector was defined. The first rolling optimization using middle vectors determines the optimization sector. Combined with the q-axis component of the target prediction error, the core optimization region is identified. After a second rolling optimization, the optimal three vectors are determined. An in-depth analysis of the influence of the AC/DC bus voltage ratio on the output current total harmonic distortion (THD) confirmed the validity of the algorithm’s operating range for different types of solar inverters.
- By optimally allocating the vector action times based on the error values generated in the cost function evaluation, a fixed switching frequency output is achieved. Under the same filter parameters, a lower system current THD is obtained.
- The impact of model parameter mismatch on the proposed method was analyzed. By alternately using voltage vectors that force polarity changes in the predicted current error within a single control cycle, the adverse effects of parameter mismatch are mitigated to some extent.
This study focuses on reducing the rolling optimization computational load and achieving fixed switching frequency vector output for three-level inverters used in types of solar inverters. Experimental results confirm that the proposed method reduces computational intensity and algorithmic complexity without affecting system control performance. Further research will focus on optimizing output for high AC/DC bus voltage ratio conditions to improve the control effect of the system.