In recent years, the global energy sector has been grappling with the dual challenges of fossil fuel dependency and environmental degradation. As a researcher in power electronics, I have focused on advancing distributed generation systems, where photovoltaic and wind power integration is pivotal. However, the increased penetration of these resources introduces power quality concerns, necessitating robust power electronic interfaces. Three-level inverters, particularly the active neutral point clamped (ANPC) topology, have emerged as a preferred solution for medium- to high-power applications due to their superior harmonic performance and reduced voltage stress. These on-grid inverters serve as critical links between DC sources and AC grids, enabling efficient energy conversion. Yet, when multiple ANPC three-level on-grid inverters are paralleled to achieve higher power ratings, zero-sequence circulation currents arise, leading to unbalanced current stress, output distortion, and potential system instability. Addressing this issue is essential for the reliable operation of modern on-grid inverter systems.
In this article, I present a comprehensive study on a novel virtual large medium zero vectors modulation (VLMZVM) strategy designed to suppress low-frequency zero-sequence circulation currents in parallel ANPC three-level on-grid inverters. The approach builds upon existing modulation techniques but introduces dynamic virtual vector synthesis to mitigate circulation currents without compromising output voltage quality. Through detailed modeling, analysis, and experimental validation, I demonstrate the efficacy of this method under various non-ideal conditions, emphasizing its applicability in real-world on-grid inverter deployments. The content is structured as follows: first, I derive a zero-sequence circulation current model to identify influencing factors; second, I elaborate on the VLMZVM strategy, including optimal vector selection and timing calculations; third, I provide experimental results from a hardware-in-the-loop platform; and finally, I conclude with key findings and future directions.
The zero-sequence circulation current in parallel ANPC three-level on-grid inverters can be modeled using fundamental circuit theory. For the j-th inverter in a system with common DC and AC buses, the three-phase voltage equations are expressed as:
$$ U_{O_jN} + u_{aj} – L_{j1} \frac{di_{aj}}{dt} – L_{j2} \frac{di_{agj}}{dt} = e_a + u_{N’N} $$
$$ U_{O_jN} + u_{bj} – L_{j1} \frac{di_{bj}}{dt} – L_{j2} \frac{di_{bgj}}{dt} = e_b + u_{N’N} $$
$$ U_{O_jN} + u_{cj} – L_{j1} \frac{di_{cj}}{dt} – L_{j2} \frac{di_{cgj}}{dt} = e_c + u_{N’N} $$
Here, \( U_{O_jN} \) denotes the voltage from the inverter’s neutral point \( O_j \) to the DC bus negative terminal, \( u_{kj} \) represents the output voltage of phase k (where k = a, b, c), \( i_{kj} \) is the inverter-side current, \( i_{kgj} \) is the grid-side current, and \( u_{N’N} \) is the potential difference between the grid neutral point N’ and the DC bus midpoint N. The zero-sequence circulation current for inverter j is defined as the average of the three-phase grid-side currents:
$$ i_{zj} = \frac{1}{3} \sum_{k=a,b,c} i_{kgj} = \frac{1}{3} \sum_{k=a,b,c} i_{kj} $$
By summing the three-phase equations and assuming a symmetrical grid (i.e., \( e_a + e_b + e_c = 0 \)), we obtain:
$$ U_{O_jN} + \frac{1}{3} \sum_{k=a,b,c} u_{kj} – (L_{j1} + L_{j2}) \frac{di_{zj}}{dt} = u_{N’N} $$
For a system with two parallel on-grid inverters, the zero-sequence circulation current \( i_z = i_{z1} = -i_{z2} \) can be represented by the transfer function:
$$ i_z(s) = \frac{ \frac{1}{3} \sum_{k=a,b,c} [u_{k1}(s) – u_{k2}(s)] + [U_{O_1N}(s) – U_{O_2N}(s)] }{(L_{11} + L_{12} + L_{21} + L_{22}) s } $$
This model reveals that circulation currents depend on differences in neutral point potentials and switching states, as well as the filter inductances. To delve deeper, the output voltage of an ANPC on-grid inverter can be related to its switching states:
$$ u_{kj} = \frac{U_{dc}}{2} S_{kj} + \frac{\Delta U_j}{2} S_{kj}^2 $$
$$ \Delta U_j = U_{PO_j} – U_{O_jN} $$
where \( S_{kj} \) takes values 1, 0, or -1 corresponding to switching states P, O, or N, and \( \Delta U_j \) is the neutral point potential difference. Substituting into the circulation current expression for two inverters yields:
$$ i_{z1}(s) = \frac{ -\frac{1}{2}(\Delta U_1 – \Delta U_2) + \frac{1}{6} U_{dc} \sum_{k=a,b,c} (S_{k1} – S_{k2}) + \frac{1}{6} \sum_{k=a,b,c} (\Delta U_1 S_{k1}^2 – \Delta U_2 S_{k2}^2) }{ (L_{11} + L_{12} + L_{21} + L_{22}) s } $$
From this equation, three primary contributors to circulation currents are identified: (1) neutral point potential differences, (2) switching state differences, and (3) mixed terms involving both. Conventional space vector pulse width modulation (SVPWM) strategies often employ small vectors that can cause neutral point voltage偏移, exacerbating circulation currents. The large medium zero vectors modulation (LMZVM) strategy avoids small vectors, thus mitigating neutral point偏移 but still fails to address switching state-induced circulation currents. Therefore, I propose a novel VLMZVM strategy that incorporates virtual large vectors to comprehensively suppress circulation currents in parallel ANPC three-level on-grid inverters.
The VLMZVM strategy enhances the LMZVM approach by dynamically replacing actual large vectors with virtual ones when they would amplify circulation currents. LMZVM utilizes only large vectors, medium vectors, and zero vectors for synthesis. For example, in sector 1 of the space vector diagram, the vectors \( V_{L1} \) (PNN), \( V_{M1} \) (PON), and \( V_Z \) (OOO) are used with a switching sequence OOO-PON-PNN-PON-OOO. However, switching state differences between parallel on-grid inverters can still generate circulation currents. Analysis shows that P-type large vectors (e.g., \( V_{L2} \), \( V_{L4} \), \( V_{L6} \)) tend to enhance circulation currents flowing out of an inverter, while N-type large vectors (e.g., \( V_{L1} \), \( V_{L3} \), \( V_{L5} \)) have the opposite effect. To suppress circulation currents without altering the synthesized reference voltage vector \( V_{ref} \), I introduce virtual large vectors synthesized from nearby circulation-suppressing vectors.
Consider sector 1 where \( V_{ref} \) is located. If the measured zero-sequence circulation current \( i_z \) is negative, the required large vector \( V_{L1} \) (an N-type vector) would further enhance this negative current. Instead, a virtual \( V_{L1} \) can be synthesized using P-type large vectors, medium vectors, and zero vectors. Three candidate methods are evaluated:
- Method a: Direct synthesis using \( V_{L2} \) and \( V_{L6} \).
- Method b: Synthesis using \( (V_Z + V_{L2})/2 \) and \( V_{M6} \).
- Method c: Synthesis using \( (V_Z + V_{L6})/2 \) and \( V_{M1} \).
I assess these methods based on the number of participating vectors, switching state transitions per cycle, and circulation current suppression capability. Table 3 summarizes the comparison for sector 1.
| Method | Participating Vectors | Switching Transitions per Cycle | Circulation Suppression Efficacy |
|---|---|---|---|
| a | \( V_{L2}, V_{L6}, V_{M1}, V_Z \) | 12 | Moderate |
| b | \( V_{L2}, V_{M6}, V_{M1}, V_Z \) | 10 | Lower due to additional medium vector |
| c | \( V_{L6}, V_{M1}, V_Z \) | 10 | Highest, as virtual large vector dominates |
Method c emerges as optimal due to fewer vectors, reasonable switching transitions, and superior circulation suppression. In this method, the virtual \( V_{L1} \) is effectively synthesized by combining \( V_{L6} \), \( V_{M1} \), and \( V_Z \), with the switching sequence PNP-OOO-PON-OOO-PNP. The influence of medium vectors on circulation currents is secondary, as their impact (with three-phase switch state differences of ±1) is overshadowed by the virtual large vector’s effect (difference of +2).
To generalize across all sectors, I propose a vector allocation scheme that distinguishes between odd and even sectors. For odd sectors (1, 3, 5, 7, 9, 11), the virtual large vector is synthesized using a large vector that lags the medium vector by 90°; for even sectors (2, 4, 6, 8, 10, 12), a large vector leading by 90° is used. This leads to a systematic allocation, as detailed in Table 4.
| Sector | Vectors for \( i_z < 0 \) | Vectors for \( i_z > 0 \) |
|---|---|---|
| 1 | \( V_{L6}, V_{M1}, V_Z \) | \( V_{L1}, V_{M1}, V_Z \) |
| 2 | \( V_{L2}, V_{M1}, V_Z \) | \( V_{L3}, V_{M1}, V_Z \) |
| 3 | \( V_{L2}, V_{M2}, V_Z \) | \( V_{L1}, V_{M2}, V_Z \) |
| 4 | \( V_{L4}, V_{M2}, V_Z \) | \( V_{L3}, V_{M2}, V_Z \) |
| 5 | \( V_{L2}, V_{M3}, V_Z \) | \( V_{L3}, V_{M3}, V_Z \) |
| 6 | \( V_{L4}, V_{M3}, V_Z \) | \( V_{L5}, V_{M3}, V_Z \) |
| 7 | \( V_{L4}, V_{M4}, V_Z \) | \( V_{L3}, V_{M4}, V_Z \) |
| 8 | \( V_{L6}, V_{M4}, V_Z \) | \( V_{L5}, V_{M4}, V_Z \) |
| 9 | \( V_{L4}, V_{M5}, V_Z \) | \( V_{L5}, V_{M5}, V_Z \) |
| 10 | \( V_{L6}, V_{M5}, V_Z \) | \( V_{L1}, V_{M5}, V_Z \) |
| 11 | \( V_{L6}, V_{M6}, V_Z \) | \( V_{L5}, V_{M6}, V_Z \) |
| 12 | \( V_{L6}, V_{M6}, V_Z \) | \( V_{L1}, V_{M6}, V_Z \) |
The vector作用时间 calculation is derived from the reference vector synthesis. For sector 1, without virtual vectors, the dwell times for \( V_{L1} \), \( V_{M1} \), and \( V_Z \) are given by:
$$ T_{L1}’ = \sqrt{3} m T_S \sin\left(\frac{\pi}{6} – \theta\right) $$
$$ T_{M1}’ = 2 m T_S \sin \theta $$
$$ T_Z’ = T_S – T_{L1}’ – T_{M1}’ $$
where \( m = \sqrt{3} |V_{ref}| / U_{dc} \) is the modulation index, \( T_S \) is the switching period, and \( \theta \) is the angle of \( V_{ref} \). The linear modulation constraint \( T_{L1}’ + T_{M1}’ \leq T_S \) implies \( m \leq 1 / \cos(\theta – \pi/6) \), ensuring a maximum voltage utilization factor of 1, comparable to traditional SVPWM.
With virtual vector synthesis using method c, the times become:
$$ T_{L6} = 2 \times \frac{1}{2} \times T_{L1}’ = \sqrt{3} m T_S \sin\left(\frac{\pi}{6} – \theta\right) $$
$$ T_{M1} = T_{M1}’ + \frac{3}{2} T_{L1}’ = m T_S \left[ 2 \sin \theta + \frac{3}{2} \sin\left(\frac{\pi}{6} – \theta\right) \right] $$
$$ T_Z = T_S – T_{L6} – T_{M1} $$
Thus, the large vector changes from \( V_{L1} \) to \( V_{L6} \) but retains the same dwell time, while the medium vector’s time increases and the zero vector’s time decreases. This adjustment ensures that the synthesized \( V_{ref} \) remains unchanged, but the switching states are altered to suppress circulation currents.
For systems with more than two parallel on-grid inverters, the circulation current model can be extended. The zero-sequence circulation current for the j-th inverter, \( i_{zj} \), represents the net current flowing into other inverters. By equivalencing all other inverters into a single equivalent circuit, the VLMZVM strategy can be applied to each on-grid inverter independently based on its own measured circulation current direction, without requiring complex modeling of interactions among all units. This scalability is crucial for practical deployments where multiple on-grid inverters operate in parallel.
To validate the proposed VLMZVM strategy, I conducted extensive experiments using a hardware-in-the-loop (HIL) platform based on StarSim, with STM32F28335 microcontrollers as core controllers. The main circuit comprised three ANPC three-level on-grid inverters connected in parallel with common DC and AC buses, simulating a typical distributed generation setup. The system parameters are listed in Table 5.
| Parameter | Value |
|---|---|
| Grid frequency \( f_g \) | 50 Hz |
| Filter capacitor \( C_i \) | 40 μF |
| DC-side capacitors \( C_{i1}, C_{i2} \) | 8000 μF each |
| Inverter-side inductance \( L_{i1} \) | 1 mH (default, varied in tests) |
| Grid-side inductance \( L_{i2} \) | 0.5 mH |
| Grid line voltage (RMS) \( e_a, e_b, e_c \) | 690 V |
| d-axis reference current \( i_{gdref1}, i_{gdref2}, i_{gdref3} \) | 200 A (baseline, varied) |
| q-axis reference current \( i_{gqref1}, i_{gqref2}, i_{gqref3} \) | 0 A (baseline, varied) |
| PI controller proportional gain \( K_P \) | 2 |
| PI controller integral gain \( K_I \) | 200 |
| Switching frequency \( f_s \) | 10 kHz |
| Sampling period \( T_s \) | 100 μs |
| DC-side voltage \( U_{dc} \) | 1500 V |
The experiments evaluated circulation current suppression under various non-ideal scenarios common in on-grid inverter systems. First, the line voltage \( u_{ab1} \) of inverter 1 was measured under both conventional LMZVM and proposed VLMZVM strategies. The waveforms confirmed that the output voltage synthesis was unaffected by the virtual vector modulation, maintaining the desired reference vector.
Next, circulation currents were assessed under reference current mismatches. With \( i_{gdref1} = i_{gdref2} = 200 \) A and \( i_{gdref3} \) stepped from 200 A to 150 A, the conventional LMZVM resulted in circulation currents peaking at ±20 A and noticeable current distortion. In contrast, the VLMZVM strategy suppressed circulation currents to within ±2 A. When \( i_{gdref3} \) was reduced further to 100 A, LMZVM produced circulation currents of ±40 A, while VLMZVM limited them to ±4 A. Table 6 summarizes these results.
| Condition (\( i_{gdref3} \)) | LMZVM Circulation Current | VLMZVM Circulation Current | Reduction |
|---|---|---|---|
| 150 A | ±20 A | ±2 A | ~90% |
| 100 A | ±40 A | ±4 A | ~90% |
Similarly, with consistent reference currents but filter parameter inconsistencies (e.g., \( L_{11} = L_{21} = 1 \) mH, \( L_{31} = 2 \) mH), LMZVM generated circulation currents of ±30 A, whereas VLMZVM reduced them to ±3 A. This demonstrates the strategy’s robustness against parameter variations in on-grid inverters.
Fast Fourier transform (FFT) analysis of the grid-side current \( i_{ag3} \) for inverter 3 under the worst-case scenario (\( i_{gdref3} = 100 \) A) revealed that with LMZVM, the total harmonic distortion (THD) was 6%, with a dominant 3rd harmonic at 5.1%. With VLMZVM, THD dropped to 1.2%, and the 3rd harmonic decreased to 0.8%. This significant improvement underscores the enhanced power quality offered by the proposed modulation for on-grid inverter applications.
Furthermore, the VLMZVM strategy was tested across a full range of power factors to ensure compatibility with various grid conditions. When the power factor changed from 1 to 0.707 (by introducing reactive current), from 0.707 to 0.5, and from 0.5 to 0 (purely reactive operation), the VLMZVM strategy consistently maintained low circulation currents, while LMZVM exhibited substantial fluctuations. These results validate the method’s effectiveness in diverse operating regimes of on-grid inverters.
In conclusion, I have developed and validated a novel VLMZVM-based circulation current suppression method for parallel ANPC three-level on-grid inverters. The approach leverages virtual large vector synthesis to dynamically counteract switching state-induced circulation currents, without altering the output voltage synthesis. A systematic vector allocation scheme based on odd and even sectors simplifies implementation, and the strategy is scalable to multiple on-grid inverters. Experimental results from a hardware-in-the-loop platform demonstrate a circulation current reduction of approximately 90% and a THD improvement of 4.8% under various non-ideal conditions, including reference current mismatches, filter parameter inconsistencies, and full power factor variations. By eliminating small vectors, the method also inherently addresses neutral point voltage balancing, further enhancing the reliability of on-grid inverter systems. Future work will explore integrated control schemes that combine circulation current suppression with advanced neutral point balancing and fault tolerance, paving the way for more resilient and efficient distributed generation networks.