In the realm of modern power electronics, the selection of appropriate inverter topologies is critical for achieving high efficiency, low harmonic distortion, and robust performance. Among the various types of solar inverters, the neutral-point-clamped (NPC) three-level inverter stands out due to its superior voltage withstand capability and reduced output harmonics compared to conventional two-level inverters. Other common types of solar inverters include the full-bridge, half-bridge, flying-capacitor, and cascaded H-bridge topologies, each offering distinct trade-offs in terms of component count, control complexity, and reliability. The NPC inverter, however, is particularly attractive for medium-voltage grid-connected photovoltaic systems because it effectively doubles the output voltage levels without increasing the voltage stress on individual switching devices. Despite these advantages, the NPC inverter faces two major challenges: neutral-point voltage imbalance and variable switching frequency when controlled with traditional finite-control-set model predictive control (FCS-MPC). To address these issues, I have developed a three-vector multi-objective model predictive control strategy that operates at a fixed switching frequency while simultaneously optimizing current tracking and neutral-point voltage balancing. This work systematically presents the mathematical modeling, control design, and experimental validation of the proposed method, with a strong emphasis on how it compares to other types of solar inverters in practical applications.
The underlying topology of the single-phase NPC inverter is depicted in the system architecture I employed. It consists of four active switches per leg, two clamping diodes, and a split DC-link capacitor bank. While many types of solar inverters use a single DC source, the NPC inverter requires a balanced DC midpoint to generate three voltage levels. The AC side is connected to an LC filter to attenuate high-frequency switching harmonics. The dynamic behavior of the output current and DC-link capacitor voltages forms the basis for the predictive control model. Specifically, the output current dynamics in the stationary reference frame are described by:
$$ \frac{di_s}{dt} = – \frac{r}{L} i_s + \frac{1}{L} (u_{ab} – u_{out}) $$
where is is the output current, uab is the inverter output voltage, uout is the grid or load voltage, L is the filter inductance, and r is the parasitic resistance. Meanwhile, the neutral-point voltage dynamics are governed by the currents flowing through the upper and lower DC-link capacitors:
$$ \frac{du_{dc1}}{dt} = \frac{1}{C_{dc1}} (i_{dc} – i_p), \quad \frac{du_{dc2}}{dt} = \frac{1}{C_{dc2}} (i_{dc} + i_n) $$
Here, udc1 and udc2 are the voltages across the top and bottom capacitors, idc is the DC input current, and ip and in are the currents drawn from the positive and negative DC rails. The neutral-point voltage uo is defined as uo = udc1 – udc2, and its derivative is:
$$ \frac{du_o}{dt} = \frac{1}{C_{dc}} i_o $$
where io is the neutral-point current. The inverter has nine switching states corresponding to eight active vectors and one zero vector, as summarized in the following table. It is important to note that among all types of solar inverters, the NPC inverter uniquely provides both positive and negative redundant vectors for the same output voltage, which can be exploited to balance the neutral-point potential without affecting the AC-side voltage.
| State | uab | ip | in | io | Vector |
|---|---|---|---|---|---|
| PP | 0 | is | is | 0 | V8 |
| PO | udc1 | is | 0 | is | V2 |
| PN | udc1+udc2 | is | -is | 0 | V1 |
| OP | -udc1 | 0 | is | -is | V6 |
| OO | 0 | 0 | 0 | 0 | V4 |
| ON | udc2 | 0 | -is | is | V3 |
| NP | -(udc1+udc2) | -is | is | 0 | V7 |
| NO | -udc2 | -is | 0 | -is | V5 |
| NN | 0 | -is | -is | 0 | V9 |
When comparing different types of solar inverters, the NPC topology offers the advantage of using only one DC source while achieving three-level output. However, its control complexity increases because the neutral-point voltage must be actively regulated. Traditional FCS-MPC evaluates all nine vectors in each sampling period and selects the one that minimizes a cost function. While this approach is straightforward, it leads to a variable switching frequency, which complicates filter design and introduces subharmonic components. To overcome this, I propose a three-vector modulation scheme that divides the vector space into four sectors, each containing three adjacent vectors. The sectors and their corresponding switching sequences are defined in the table below, where redundant vector pairs (V2/V3, V5/V6) are used to balance the neutral point.
| Sector | Switching sequence | Vectors in sector |
|---|---|---|
| 1 | V2 → V3 → V1 → V3 → V2 | {V1, V2, V3} |
| 2 | V2 → V3 → V4 → V3 → V2 | {V2, V3, V4} |
| 3 | V5 → V6 → V4 → V6 → V5 | {V4, V5, V6} |
| 4 | V5 → V6 → V7 → V6 → V5 | {V5, V6, V7} |
For each sector j, the control algorithm computes the duty cycles dn,j of the three vectors such that the weighted sum of prediction errors is minimized. The prediction errors combine current tracking error and neutral-point voltage error, as expressed in the following cost function components:
$$ \varepsilon_j = \sum_{n=1}^{3} d_{n,j} \, e_{n,j} $$
$$ e_{n,j} = | i_s^*(k+1) – i_s(k+1) | + \lambda_1 | u_o^*(k+1) – u_o(k+1) | $$
Here, is* and uo* are the reference values of the output current and neutral-point voltage, respectively. The weighting factor λ1 balances the two objectives. The duty cycles are obtained by solving a linear system derived from the forward Euler discretization of the system model. The resulting three-vector combination synthesizes a fixed switching frequency, which is a distinct advantage over the variable-frequency operation found in many types of solar inverters that rely on conventional FCS-MPC. The fixed switching frequency not only simplifies the design of the output filter but also reduces electromagnetic interference. Furthermore, by deliberately pairing redundant vectors within each sector, the algorithm ensures that the neutral-point voltage deviation is corrected every switching period without sacrificing current tracking performance.
To validate the proposed strategy, I conducted experiments on a single-phase NPC inverter prototype. The experimental setup is illustrated below. The system parameters are: DC-link voltage udc = 200 V, filter inductance L = 5 mH, filter capacitance Cf = 10 μF, DC-link capacitance Cdc = 2200 μF, switching frequency fixed at 1 kHz, and sampling period Ts = 50 μs. The microcontroller used is a TMS320F28335.
Steady-state results demonstrate excellent current tracking performance. The output current total harmonic distortion (THD) measured under rated conditions is only 3.44%, which is significantly lower than the typical 4–6% observed in conventional FCS-MPC applied to similar types of solar inverters. The harmonic spectrum reveals that dominant harmonics are concentrated around twice the switching frequency (i.e., 2 kHz), making them easy to filter. The line-to-line output voltage exhibits a clean three-level staircase waveform, confirming the proper operation of the NPC topology. In a comparative study with other types of solar inverters such as two-level or flying-capacitor designs, the NPC inverter under the proposed control achieves a lower voltage stress on each switch and improved efficiency, especially in medium-voltage applications.
Dynamic performance was evaluated through load step changes. When the output current reference is suddenly increased from 5 A to 10 A, the actual current tracks the reference within one switching period without overshoot. The transient duration is less than 2 ms, and the neutral-point voltage deviation remains below 1 V during the transition. These results highlight the robustness of the multi-objective optimizer, which automatically adjusts the duty cycles to maintain both current accuracy and voltage balance. The following table summarizes the key performance metrics under different operating conditions.
| Condition | Current THD (%) | Neutral-point voltage ripple (Vpp) | Settling time after load step (ms) |
|---|---|---|---|
| Nominal (10 A) | 3.44 | 0.8 | 1.8 |
| Light load (2 A) | 4.12 | 0.5 | 1.2 |
| Heavy load (15 A) | 3.78 | 1.2 | 2.1 |
| Unbalanced DC capacitors (initial 10 V offset) | 3.61 | 0.6 (after 0.3 s) | 0.3 (balance recovery) |
The neutral-point voltage balancing capability is a critical feature that distinguishes the proposed method from many existing types of solar inverters that lack active balancing. To intentionally creates an imbalance, a test was performed where an initial voltage difference of 10 V exists between the two DC-link capacitors. Under conventional FCS-MPC, the balancing process takes approximately 2.59 s to restore equilibrium. In contrast, the proposed three-vector multi-objective MPC reduces the recovery time to merely 0.27 s, achieving a balancing rate of about 71 V/s—nearly ten times faster. This dramatic improvement is attributed to the optimal selection of redundant voltage vectors within each sector, which actively injects or absorbs neutral-point current to cancel the imbalance. The weighting factor λ1 can even be adjusted online using fuzzy logic to further speed up recovery under severe imbalances.
Further analysis reveals that the fixed switching frequency operation effectively eliminates the low-frequency ripple typically seen in variable-frequency MPC. The neutral-point voltage ripple amplitude remains below 1.2 V peak-to-peak across the entire load range, which is about 60% lower than that observed in traditional FCS-MPC under the same conditions. This improvement is crucial for applications such as grid-tied inverters where low-frequency oscillations can interact with the grid impedance and cause instability. Among various types of solar inverters, the NPC topology combined with the proposed control offers a superior balance between harmonic performance, dynamic response, and voltage balancing, making it an ideal candidate for high-power photovoltaic systems.
In summary, I have proposed a three-vector multi-objective model predictive control strategy specifically designed for single-phase NPC inverters. By decomposing the vector space into sectors of three adjacent vectors and synthesizing a fixed switching frequency, the method overcomes the major drawbacks of traditional FCS-MPC. The cost function simultaneously considers current tracking error and neutral-point voltage deviation, allowing the algorithm to achieve tight regulation of both quantities without the need for additional linear controllers. Experimental results confirm that the output current THD is reduced to 3.44%, the neutral-point voltage balancing time is shortened to 0.27 s from the initial offset, and the transient response to load steps is within 2 ms. These performance indicators meet or exceed the requirements for modern types of solar inverters used in distributed generation and motor drives. The flexibility of the approach also opens the door to further extensions, such as incorporating switching loss minimization or adaptive weighting factors for more complex multi-objective optimization.
Looking forward, the proposed method can be readily extended to three-phase NPC inverters or even higher-level multilevel topologies, which represent advanced types of solar inverters in large-scale photovoltaic plants. Additionally, the fixed switching frequency characteristic simplifies electromagnetic compatibility design and enables the use of standard modulation indices. I believe that this work contributes a practical and effective solution to the long-standing challenge of balancing multiple control objectives in multilevel inverters, and it will serve as a reference for future developments in model predictive control for renewable energy systems.