The utilization of solar energy through grid-tied photovoltaic (PV) power generation has witnessed rapid development. Among various applications, large-scale ground-mounted PV plants and distributed generation systems dominate the market. In these systems, three-phase single-stage centralized solar inverters are widely adopted due to their structural simplicity, cost-effectiveness, and ease of maintenance. To meet increasing demands for higher efficiency and power density, three-level inverter topologies have gradually replaced their two-level counterparts in high-power commercial solar inverters. Furthermore, to enhance overall power transmission efficiency, multiple inverter units are often connected in parallel and fed into the medium-voltage grid via a step-up transformer. A typical commercial configuration involves two 500 kW (or 630 kW) solar inverters operating in parallel, connected to a 10 kV or 35 kV grid through a 1 MVA (or 1.25 MVA) dual-winding transformer.
Given the indispensable role of the transformer in this parallel scheme, an innovative alternative can be explored: the Open-End Winding Transformer (OEWT) dual-inverter scheme. This topology, initially proposed for motor drive applications, connects two inverters to the two open ends of a transformer’s winding. Through appropriate control and modulation, two N-level inverters can synthesize an output equivalent to a (2N-1)-level inverter, resulting in lower harmonic distortion. Additionally, compared to a traditional (2N-1)-level inverter, the dual-N-level configuration offers more redundant voltage vectors, which can be strategically used to suppress common-mode voltage or reduce switching losses. It also provides higher DC voltage utilization, better redundancy, and improved fault tolerance. These advantages have led to its application in various fields, including active power filters, static synchronous compensators, dynamic voltage restorers, wind power generation, and PV grid-tied systems.
When applying the OEWT topology to PV systems, key research areas include the selection of the dual-inverter structure, the choice between independent or common DC buses (fed by one or two PV arrays), filter design, system control schemes, and modulation strategies. Existing literature presents several approaches but also reveals limitations. Some schemes use dual two-level solar inverters with a single PV array, limiting the system to only one Maximum Power Point Tracking (MPPT) channel and potentially reducing energy yield. Others employ independent PV arrays but enforce equal DC voltages across the inverters, preventing independent MPPT operation. Furthermore, many proposals utilize simple inductor filters, requiring large inductance values to meet grid harmonic standards, which increases cost, volume, and can degrade dynamic response. While LCL filters have been proposed for OEWT systems, their structures can be complex.
Therefore, significant room for improvement remains in both the power circuit and control strategy for OEWT-based PV systems. This paper proposes a novel grid-tied PV system structure based on an OEWT dual three-level inverter topology with independent DC buses. Starting from the widely used commercial parallel-inverter scheme, we detail the improvement process, ultimately presenting a topology that reduces filter volume and cost. We then develop a comprehensive mathematical model and propose a corresponding control strategy enabling independent MPPT operation for both solar inverters. Finally, simulation and experimental results validate the proposed scheme’s feasibility and correctness.
Topology of the Dual Three-Level Solar Inverter System
The conventional parallel scheme for PV systems is shown conceptually below. Two single-stage three-level solar inverters, each connected to an independent PV array, can perform independent MPPT. Their AC outputs are filtered by LC filters and connected in parallel before being fed to the medium-voltage grid via a dual-winding transformer. The transformer’s leakage inductance typically acts as the grid-side inductor, forming an LCL filter structure with the inverter-side LC filters. The leakage inductance \(L_t\) is related to the transformer’s impedance voltage \(V_k\):
$$L_t = \frac{3 v_g^2}{2\pi f_0 P_{\text{rated}}} V_k$$
where \(v_g\) is the transformer phase voltage (RMS), \(f_0\) is the fundamental frequency, and \(P_{\text{rated}}\) is the transformer’s rated capacity. For high-power PV step-up transformers, \(V_k\) is typically no less than 6%.
To transform this into an OEWT scheme, the neutral point of the transformer’s low-voltage (LV) winding is opened. The two ends of this winding are then connected to the outputs of two separate inverters. In this configuration, the inverter AC sides are connected in series through the transformer LV winding. The voltage across this winding is the difference between the two inverters’ output voltages. When the modulation waves of the two inverters are in phase opposition, the synthesized voltage across the transformer LV winding reaches its maximum, which is twice the output voltage of a single inverter. To minimize changes to the inverter modules (keeping their original power rating and nominal output current), the LV winding’s phase voltage rating must be doubled.
From an energy yield perspective, connecting each inverter to an independent PV array (enabling two MPPT channels) is superior to sharing a single array. However, with conventional framed PV modules, the panels have a significant parasitic capacitance to ground. This creates a conductive path between the DC sides of the two inverters, and the common-mode voltage difference between them can drive a circulating current. While modulation techniques like 120° decoupled space vector modulation can suppress this voltage difference, they also reduce the maximum synthesized voltage to \(\sqrt{3}\) times a single inverter’s voltage. If the transformer LV voltage is doubled, the inverter’s MPPT lower voltage limit must increase proportionally, reducing the MPPT operating range and potentially harming energy yield.
An alternative solution is to attack the circulating current path itself by reducing the PV panel’s ground capacitance. The capacitance in conventional modules primarily exists between the cell strings and the grounded aluminum frame. Using frameless double-glass PV modules can drastically reduce this parasitic capacitance, effectively mitigating the circulating current issue in OEWT systems with independent DC buses.
Regarding filter design for the OEWT dual-inverter, the shared filtering characteristic must be considered. A promising approach is for each inverter to be connected to one side of a common filter capacitor via its bridge arm inductor, with the other side of the capacitor connected to the grid via the transformer leakage inductance. Combining this filter structure with the aforementioned insights leads to the proposed system topology, as shown in the figure below.
The single-phase equivalent circuit of the inverter and filter is derived as shown. Here, \(v_{\text{inv1}}\), \(i_{\text{inv1}}\) and \(v_{\text{inv2}}\), \(i_{\text{inv2}}\) are the phase voltages and currents of inverter 1 and 2, respectively; \(L_1\) is the bridge arm inductance; \(C_f\) is the filter capacitance; \(L_2\) is the grid-side inductance (the transformer leakage inductance referred to the LV side); \(e_g\) is the transformer LV phase voltage; and \(i_2\) is the transformer LV current. Observing the equivalent circuit, the two bridge arm inductors are in series and can be combined into a single inductor, saving a magnetic core and further reducing the filter’s volume and cost. This is simpler than using magnetic integration techniques for two separate inductors.
Compared to the conventional parallel scheme, the proposed OEWT dual-inverter scheme offers advantages in reducing filter size and cost. First, the synthesized output line voltage has more levels, leading to lower voltage harmonics and relaxed filtering requirements. Second, apart from the transformer, it requires only one set of bridge arm inductors and filter capacitors, reducing the number of passive components. Finally, with the LV winding voltage doubled and the impedance voltage unchanged, the referred leakage inductance \(L_2\) becomes four times larger according to the formula, allowing for further reduction in the size of other filter components.
| Feature | Conventional Parallel Scheme | Proposed OEWT Scheme |
|---|---|---|
| Transformer | Dual-Winding | Open-End Winding |
| LV Winding Voltage | V | 2V |
| MPPT Channels | 2 (Independent) | 2 (Independent) |
| Synthesized Line Voltage Levels | 5 (per inverter) | 9 (equivalent) |
| Filter Structure | Two independent LCL | One shared LCL |
| Passive Component Count | Higher | Lower |
Mathematical Modeling of the Dual-Inverter System
To achieve independent DC voltage control for MPPT while maintaining a maximum synthesized output voltage, a control-oriented model of the system is essential. The system parameters are referred to the transformer’s LV side, and parasitic resistances are neglected for clarity.
In steady state, the modulation wave \(m_{xk}\) for phase \(x\) (\(x = a, b, c\)) of inverter \(k\) (\(k = 1, 2\)) is defined as:
$$m_{xk} = \frac{v_{xk}}{V_{\text{dc}k} / 2}$$
where \(v_{xk}\) is the fundamental component of the AC output voltage and \(V_{\text{dc}k}\) is the DC-link voltage.
The AC voltage equations in the three-phase stationary frame are:
$$
\begin{aligned}
v_a &= e_a + L \frac{di_a}{dt} = v_{a1} – v_{a2} = m_{a1}\frac{V_{\text{dc}1}}{2} – m_{a2}\frac{V_{\text{dc}2}}{2} \\
v_b &= e_b + L \frac{di_b}{dt} = v_{b1} – v_{b2} = m_{b1}\frac{V_{\text{dc}1}}{2} – m_{b2}\frac{V_{\text{dc}2}}{2} \\
v_c &= e_c + L \frac{di_c}{dt} = v_{c1} – v_{c2} = m_{c1}\frac{V_{\text{dc}1}}{2} – m_{c2}\frac{V_{\text{dc}2}}{2}
\end{aligned}
$$
where \(L = 2L_1 + L_2\) is the total AC side inductance, \(v_a, v_b, v_c\) are the synthesized phase voltages, and \(i_a, i_b, i_c\) are the grid currents.
Applying Clark and Park transformations to synchronize with the grid voltage vector (with \(e_q = 0\)), the equations in the synchronous rotating \(dq\)-frame become:
$$
\begin{aligned}
v_d &= e_d – \omega L i_q + L \frac{di_d}{dt} = v_{d1} – v_{d2} = m_{d1}\frac{V_{\text{dc}1}}{2} – m_{d2}\frac{V_{\text{dc}2}}{2} \\
v_q &= \omega L i_d + L \frac{di_q}{dt} = v_{q1} – v_{q2} = m_{q1}\frac{V_{\text{dc}1}}{2} – m_{q2}\frac{V_{\text{dc}2}}{2}
\end{aligned}
$$
Here, the synthesized voltage vector is \(\mathbf{v} = v_d + jv_q\), and the individual inverter voltage vectors are \(\mathbf{v_1} = v_{d1} + jv_{q1}\) and \(\mathbf{v_2} = v_{d2} + jv_{q2}\), with \(\mathbf{v} = \mathbf{v_1} – \mathbf{v_2}\). To maximize the synthesized output, \(\mathbf{v_1}\) and \(-\mathbf{v_2}\) must be aligned. From the vector diagram, this alignment implies:
$$\frac{v_{d1}}{-v_{d2}} = \frac{v_{q1}}{-v_{q2}}$$
To find the proportion of each inverter’s voltage contribution relative to the total synthesized voltage, the power balance is considered. Assuming lossless inverters, the input DC power equals the output AC power for each unit:
$$
\begin{aligned}
P_{\text{dc}1} &= V_{\text{dc}1} I_{\text{dc}1} = \frac{3}{2}(v_{d1} i_d + v_{q1} i_q) \\
P_{\text{dc}2} &= V_{\text{dc}2} I_{\text{dc}2} = \frac{3}{2}(-v_{d2} i_d – v_{q2} i_q)
\end{aligned}
$$
Combining the power equations with the voltage alignment condition yields the expressions for the individual inverter voltage components:
$$
\begin{aligned}
v_{d1} &= v_d \frac{P_{\text{dc}1}}{P_{\text{dc}1} + P_{\text{dc}2}}, \quad &v_{q1} &= v_q \frac{P_{\text{dc}1}}{P_{\text{dc}1} + P_{\text{dc}2}} \\
v_{d2} &= -v_d \frac{P_{\text{dc}2}}{P_{\text{dc}1} + P_{\text{dc}2}}, \quad &v_{q2} &= -v_q \frac{P_{\text{dc}2}}{P_{\text{dc}1} + P_{\text{dc}2}}
\end{aligned}
$$
Finally, the \(dq\)-axis modulation signals for each solar inverter are derived:
$$
\begin{aligned}
m_{d1} &= \frac{2 v_d P_{\text{dc}1}}{(P_{\text{dc}1} + P_{\text{dc}2}) V_{\text{dc}1}}, \quad &m_{q1} &= \frac{2 v_q P_{\text{dc}1}}{(P_{\text{dc}1} + P_{\text{dc}2}) V_{\text{dc}1}} \\
m_{d2} &= \frac{-2 v_d P_{\text{dc}2}}{(P_{\text{dc}1} + P_{\text{dc}2}) V_{\text{dc}2}}, \quad &m_{q2} &= \frac{-2 v_q P_{\text{dc}2}}{(P_{\text{dc}1} + P_{\text{dc}2}) V_{\text{dc}2}}
\end{aligned}
$$
Applying the inverse Park and Clark transformations to these modulation signals produces the three-phase modulation waves for each inverter’s pulse-width modulation (PWM) stage.
| Description | Equation |
|---|---|
| Modulation Wave Definition | $$m_{xk} = \frac{2 v_{xk}}{V_{\text{dc}k}}$$ |
| AC Voltage in dq-Frame | $$\begin{aligned} v_d &= m_{d1}\frac{V_{\text{dc}1}}{2} – m_{d2}\frac{V_{\text{dc}2}}{2} \\ v_q &= m_{q1}\frac{V_{\text{dc}1}}{2} – m_{q2}\frac{V_{\text{dc}2}}{2} \end{aligned}$$ |
| Voltage Alignment Condition | $$\frac{v_{d1}}{-v_{d2}} = \frac{v_{q1}}{-v_{q2}}$$ |
| Power Balance | $$P_{\text{dc}k} = \frac{3}{2}(v_{dk} i_d + v_{qk} i_q)$$ |
| Final Modulation Signals | $$\begin{aligned} m_{d1} &= \frac{2 v_d P_1}{P_{\Sigma} V_{\text{dc}1}}, \quad &m_{d2} &= \frac{-2 v_d P_2}{P_{\Sigma} V_{\text{dc}2}} \\ m_{q1} &= \frac{2 v_q P_1}{P_{\Sigma} V_{\text{dc}1}}, \quad &m_{q2} &= \frac{-2 v_q P_2}{P_{\Sigma} V_{\text{dc}2}} \end{aligned}$$ where \(P_{\Sigma}=P_1+P_2\). |
Proposed Control Strategy for Independent MPPT
Based on the derived mathematical model, a control strategy is proposed to achieve independent MPPT for the two solar inverters while maintaining high-quality grid current injection. The strategy comprises three main parts: the DC voltage loop, the grid current loop, and the modulation strategy, as illustrated in the control block diagram.
1. DC Voltage Loop: This loop processes the measured DC voltages \(V_{\text{dc}1}, V_{\text{dc}2}\) and currents \(I_{\text{dc}1}, I_{\text{dc}2}\) from each inverter. An MPPT algorithm (e.g., Perturb and Observe) generates the DC voltage references \(V_{\text{ref1}}\) and \(V_{\text{ref2}}\) for each array. The errors between the references and the actual voltages are fed into proportional-integral (PI) regulators, which output the corresponding DC current references \(I_{\text{ref1}}\) and \(I_{\text{ref2}}\). Multiplying these current references by their respective DC voltages yields the individual DC power references \(P_{\text{ref1}}\) and \(P_{\text{ref2}}\). The total active power reference for the system is \(P_{\text{ref_tot}} = P_{\text{ref1}} + P_{\text{ref2}}\). Assuming power balance between the DC and AC sides, the reference for the active current component \(i_d\) is derived as \(i_{d\_ref} = P_{\text{ref_tot}} / (1.5 e_d)\), where \(e_d\) is the d-axis grid voltage.
2. Grid Current Loop: This loop regulates the grid current. The inputs are the active current reference \(i_{d\_ref}\) from the DC loop, the reactive current reference \(i_{q\_ref}\) (set to zero for unity power factor, or to compensate for filter capacitor current if needed), and the measured dq-axis grid currents \(i_d, i_q\). The current errors pass through PI regulators and are compensated with standard cross-coupling and grid voltage feedforward terms to generate the dq-axis references for the total synthesized inverter voltage: \(v_{d\_ref}\) and \(v_{q\_ref}\).
3. Modulation Strategy: For dual-inverter systems where DC voltages and power levels may differ, a decoupled modulation approach is necessary. Using the derived formulas, the total voltage reference \(\mathbf{v_{ref}} = v_{d\_ref} + j v_{q\_ref}\) is decomposed into individual modulation signals for each solar inverter based on their instantaneous power references:
$$
\begin{aligned}
m_{d1\_ref} &= \frac{2 v_{d\_ref} P_{\text{ref1}}}{P_{\text{ref_tot}} V_{\text{dc}1}}, \quad &m_{q1\_ref} &= \frac{2 v_{q\_ref} P_{\text{ref1}}}{P_{\text{ref_tot}} V_{\text{dc}1}} \\
m_{d2\_ref} &= \frac{-2 v_{d\_ref} P_{\text{ref2}}}{P_{\text{ref_tot}} V_{\text{dc}2}}, \quad &m_{q2\_ref} &= \frac{-2 v_{q\_ref} P_{\text{ref2}}}{P_{\text{ref_tot}} V_{\text{dc}2}}
\end{aligned}
$$
These dq-axis modulation signals are then transformed back to the three-phase stationary frame \((m_{a1}, m_{b1}, m_{c1})\) and \((m_{a2}, m_{b2}, m_{c2})\). Each set of three-phase modulation waves is independently processed by a three-level Space Vector PWM (SVPWM) algorithm to generate the gate signals for its respective inverter. This strategy ensures that the two solar inverters operate cooperatively to produce the desired grid current while independently tracking their own maximum power points.
Simulation Analysis
A simulation model of the proposed OEWT dual three-level solar inverter system was built in Matlab/Simulink to validate the theoretical analysis. To align with practical experimental conditions, PV arrays were simulated as DC voltage sources in series with resistors. Key system parameters are summarized in the table below.
| Parameter | Value |
|---|---|
| Total System Power | 30 kW |
| Individual Inverter Power | 15 kW |
| Switching Frequency | 5 kHz |
| DC Source Voltage (per inverter) | 660 V |
| DC Series Resistance | 1.6 Ω |
| Bridge Arm Inductance \(L_1\) | 2.4 mH |
| Filter Capacitance \(C_f\) | 5 μF |
| Transformer Ratio (LV/Grid) | 364 V / 380 V |
| Grid Line Voltage | 380 V |
First, the system was operated with both inverters sharing power equally (balanced mode). The line-to-line voltage waveforms were analyzed. The line voltage of a single three-level inverter (\(v_{A1B1}\) or \(v_{A2B2}\)) exhibits five distinct voltage levels. Crucially, the synthesized line voltage (\(v_{A1B1} – v_{A2B2}\)) displays nine voltage levels, which is characteristic of a traditional five-level inverter. This confirms the topology’s inherent advantage of generating a higher-quality voltage waveform with lower harmonic content using two standard three-level solar inverter modules, thereby relaxing the filter requirements.
Subsequently, the dynamic performance of the independent MPPT control was tested. Initially, both inverters operated at their MPP with a DC voltage reference of 621 V, each delivering approximately 15.14 kW of power. At t=0.05 s, the DC voltage reference for Inverter 1 was stepped to 640 V. The simulation results show that Inverter 1’s DC voltage quickly tracked the new reference, and its power output decreased to about 8 kW as expected from the PV source characteristic. The total system power dropped to approximately 23.14 kW, and the amplitude of the three-phase grid current reduced correspondingly. At t=0.1 s, the DC voltage reference for Inverter 2 was also stepped to 640 V. Similarly, its power decreased to about 8 kW, bringing the total system power to 16 kW and further reducing the grid current amplitude. The grid current remained sinusoidal and well-controlled throughout the transients. These results successfully demonstrate that the proposed control strategy enables fully independent DC voltage control for the two solar inverters, allowing them to track different maximum power points independently.
Experimental Verification
A 30 kW laboratory-scale prototype of the independent DC bus OEWT dual three-level inverter system was constructed for experimental validation. The setup used two 15 kW rectifiers with series resistors to emulate PV arrays. The control algorithms were implemented on a DSP TMS320F28377. Voltage and current waveforms were captured using appropriate probes and an oscilloscope. The system parameters matched those used in the simulation.
The voltage waveforms under balanced power operation were measured. The experimental line voltage of a single inverter clearly shows the five-level pattern. The synthesized line voltage (\(v_{A1B1} – v_{A2B2}\)) distinctly exhibits nine voltage levels, experimentally corroborating the simulation findings and the topology’s enhanced harmonic performance.
The independent MPPT capability was tested dynamically. Initially, both inverters operated at full load (15 kW each) with DC voltages around 621 V, and the grid current amplitude was approximately 39 A. At time \(t_1\), the DC voltage reference for Inverter 1 was changed to 640 V. The DC voltage responded swiftly, and its power output dropped to about 8 kW. The total system power decreased, leading to a reduction in grid current amplitude to around 30 A. At time \(t_2\), the DC voltage reference for Inverter 2 was also changed to 640 V. Its DC voltage tracked the reference, its power fell to about 8 kW, and the grid current amplitude further decreased to about 20 A. The grid currents remained stable and sinusoidal during these changes. These experimental results conclusively validate the effectiveness of both the proposed OEWT dual-inverter topology and its associated control strategy in achieving independent voltage and power control for two solar inverters.
Conclusion
This paper has presented a comprehensive study on the application of the open-end winding transformer topology in grid-connected PV systems, focusing on a dual three-level inverter structure. Beginning with an analysis of existing schemes, we identified areas for improvement and systematically developed a novel system architecture based on the widely used commercial parallel-inverter configuration.
The proposed OEWT dual three-level solar inverter system offers a significant advantage in reducing the volume and cost of the output filter. This is achieved through multiple factors: the inherent generation of a higher-level output voltage waveform (equivalent to a nine-level line voltage) which reduces harmonic content; the use of a shared LCL filter structure with fewer passive components; and the increased referred leakage inductance of the transformer due to its doubled LV winding voltage.
A detailed mathematical model of the system was derived, leading to the formulation of key relationships that govern the voltage sharing between the two inverters based on their instantaneous power outputs. Based on this model, a decoupled control strategy was proposed. This strategy features independent outer DC voltage loops for MPPT and a common inner grid current control loop. The modulation signals are decomposed according to the instantaneous power ratio of the two solar inverters, enabling them to operate with independent DC voltages and power levels while cooperating to inject high-quality current into the grid.
The feasibility and performance of the proposed topology and control strategy were successfully verified through both simulation and experimental results from a 30 kW prototype. The results confirmed the generation of a nine-level line voltage and, more importantly, demonstrated the system’s capability to perform fully independent Maximum Power Point Tracking for two separate PV sources, a critical feature for maximizing energy yield in practical installations. Future work will focus on the detailed design methodology for the filter parameters and a quantitative techno-economic comparison with conventional parallel solar inverter schemes.