I present a detailed investigation of a high-voltage, high-power photovoltaic grid-connected generation system based on an open-end winding dual solar inverter topology. My main objective is to explain how two independent photovoltaic arrays can each operate at their own maximum power point while the overall solar inverter system remains stable, grid-compatible, and free from destructive overmodulation. I focus on a voltage space vector strategy with a 180° decoupling principle, and I develop a reactive power compensation method that extends the maximum power point tracking range when the two photovoltaic arrays produce strongly unbalanced power. Throughout this article, I use first-person reasoning to connect the mathematical model, the modulation strategy, the control loops, the overmodulation mechanism, the compensation design, and the simulation and experimental validation.
1. Motivation and System Topology
I begin with the motivation for the open-end winding dual solar inverter. In conventional high-power photovoltaic plants, multilevel solar inverter topologies are widely used because they reduce harmonic distortion, lower dv/dt stress, and improve efficiency. Diode-clamped, flying-capacitor, cascaded H-bridge, and open-end winding dual solar inverter structures are common candidates. Among them, the open-end winding dual solar inverter offers a distinctive advantage: two two-level solar inverters can be combined so that the equivalent output behaves like a three-level solar inverter. This gives more voltage levels without adding clamping diodes or flying capacitors.
In the topology I study, the two solar inverters have separate DC sides fed by two independent photovoltaic arrays. The AC sides are connected through a three-phase open-end winding transformer, and the secondary side of the transformer is connected to the grid. Because the two arrays are separate, each array can be controlled independently for maximum power point tracking. This independent control improves the energy yield of the photovoltaic system, especially under partial shading, module mismatch, or uneven soiling.
However, the same independence introduces a serious challenge. The AC currents flowing through the two solar inverters are equal because the two inverters share the same grid current path. If one photovoltaic array produces much less power than the other, the solar inverter connected to the stronger array must generate a larger voltage vector to push the same current. That solar inverter can enter overmodulation, causing distorted grid current, increased harmonic content, and possible instability. I therefore design a reactive power compensation scheme that keeps both solar inverters in the linear modulation region while preserving independent maximum power point operation.
| Feature | Conventional Three-Level Solar Inverter | Open-End Winding Dual Solar Inverter |
|---|---|---|
| Number of voltage levels | Three | Equivalent three-level or higher |
| Clamping diodes | Required | Not required |
| Flying capacitors | Often required | Not required |
| Neutral-point balancing | Necessary | Not necessary |
| Independent array MPPT | Difficult in many topologies | Natural with two DC links |
| Filter sharing | Usually separate or complex | One shared filter possible |
| Transformer leakage utilization | Limited | Can be used effectively |
2. Mathematical Model of the Open-End Winding Dual Solar Inverter
I now derive the mathematical model that I use for control and compensation. Let the three phase legs of the first solar inverter be controlled by switching functions \(s_{a1}, s_{b1}, s_{c1}\), and let the three phase legs of the second solar inverter be controlled by \(s_{a2}, s_{b2}, s_{c2}\). Each switching function is either one or zero. The DC-link voltages are \(V_{dc1}\) and \(V_{dc2}\). The grid voltages are \(E_a, E_b, E_c\), the phase currents are \(i_a, i_b, i_c\), the filter inductance is \(L\), and the line resistance is \(R\).
In the three-phase stationary frame, the equivalent output voltage of each phase is the difference between the two inverter pole voltages:
$$
\begin{aligned}
V_a &= E_a + L\frac{di_a}{dt} + R i_a = s_{a1}V_{dc1} – s_{a2}V_{dc2}, \\
V_b &= E_b + L\frac{di_b}{dt} + R i_b = s_{b1}V_{dc1} – s_{b2}V_{dc2}, \\
V_c &= E_c + L\frac{di_c}{dt} + R i_c = s_{c1}V_{dc1} – s_{c2}V_{dc2}.
\end{aligned}
$$
After applying the Clarke transformation and then the Park transformation, I obtain the synchronous rotating frame model:
$$
\begin{aligned}
V_d &= E_d – \omega L i_q + L\frac{di_d}{dt} + R i_d = V_{d1} – V_{d2}, \\
V_q &= E_q + \omega L i_d + L\frac{di_q}{dt} + R i_q = V_{q1} – V_{q2}.
\end{aligned}
$$
Here, \(\omega\) is the grid angular frequency. The terms \(V_{d1}, V_{q1}\) are the dq-axis components produced by the first solar inverter, and \(V_{d2}, V_{q2}\) are the dq-axis components produced by the second solar inverter. The total equivalent voltage vector of the open-end winding dual solar inverter is therefore the vector difference of the two individual solar inverter voltage vectors:
$$
\vec{V} = \vec{V}_1 – \vec{V}_2.
$$
This vector difference is the foundation of the 180° decoupled space vector modulation strategy. I can independently shape \(\vec{V}_1\) and \(\vec{V}_2\), but the grid current is shared. Therefore, the power-sharing ratio between the two solar inverters is controlled by the relative magnitudes and phase angles of \(\vec{V}_1\) and \(\vec{V}_2\).
| Symbol | Meaning | Role in My Model |
|---|---|---|
| \(V_{dc1}, V_{dc2}\) | DC-link voltages of the two arrays | Determine maximum linear modulation amplitude |
| \(i_a, i_b, i_c\) | Grid currents | Shared by both solar inverters |
| \(L\) | Filter inductance | Limits current ripple and stores reactive energy |
| \(R\) | Line resistance | Represents conduction and transformer losses |
| \(\vec{V}_1, \vec{V}_2\) | Voltage vectors of the two solar inverters | Combined by vector subtraction |
| \(\vec{V}\) | Equivalent total voltage vector | Synthesized for grid current control |
3. Voltage Space Vector 180° Decoupling Modulation
The space vector diagram of a three-phase two-level solar inverter contains eight switching states: six active vectors and two zero vectors. When I combine two such solar inverters in an open-end winding configuration, the total number of switching combinations is \(8 \times 8 = 64\). After eliminating redundant combinations, 19 distinct voltage space vectors appear. This redundancy is valuable because it allows flexible modulation and improves the effective voltage resolution.
For the first solar inverter, I define the voltage space vector as:
$$
\vec{V}_1 = \frac{2}{3}\left(s_{a1} + a s_{b1} + a^2 s_{c1}\right)V_{dc1},
$$
and for the second solar inverter:
$$
\vec{V}_2 = \frac{2}{3}\left(s_{a2} + a s_{b2} + a^2 s_{c2}\right)V_{dc2},
$$
where \(a = e^{j2\pi/3}\). The resulting total voltage vector is:
$$
\vec{V} = \vec{V}_1 – \vec{V}_2.
$$
In the 180° decoupled modulation strategy, I force the two solar inverter reference vectors to be approximately opposite in phase. I define the total reference vector \(\vec{V}^*\), and I allocate it to the two solar inverters through a power-sharing coefficient \(k\):
$$
\vec{V}_1^* = k \vec{V}^*, \qquad \vec{V}_2^* = -(1-k)\vec{V}^*.
$$
Then the vector difference is automatically correct:
$$
\vec{V}_1^* – \vec{V}_2^* = k\vec{V}^* + (1-k)\vec{V}^* = \vec{V}^*.
$$
When \(k = 0.5\), the two solar inverters share the voltage equally. When \(k\) deviates from 0.5, one solar inverter produces a larger voltage vector than the other. This is exactly the mechanism I use to handle unequal photovoltaic power. The stronger array must receive a larger voltage vector share, while the weaker array receives a smaller share. If the required share exceeds the linear modulation limit, overmodulation occurs, and I then activate reactive power compensation.
| Modulation Quantity | Expression | Condition for Linear Operation |
|---|---|---|
| First solar inverter modulation index | \(m_1 = \frac{2|V_1^*|}{V_{dc1}}\) | \(m_1 \le 1\) |
| Second solar inverter modulation index | \(m_2 = \frac{2|V_2^*|}{V_{dc2}}\) | \(m_2 \le 1\) |
| Total voltage vector | \(\vec{V}^* = \vec{V}_1^* – \vec{V}_2^*\) | Must be synthesizable by available vectors |
| Power-sharing coefficient | \(k \in [0,1]\) | Controls voltage distribution between solar inverters |
4. Independent MPPT Control of the Two Photovoltaic Arrays
My control architecture uses two voltage control loops: a sum loop and a difference loop. The sum of the DC-link voltage errors generates the active current reference for the total solar inverter system. The difference of the DC-link voltage errors generates the power-sharing coefficient \(k\). This allows both arrays to track their own maximum power points without requiring a central MPPT compromise.
I define the voltage errors as:
$$
e_1 = V_{dc1}^* – V_{dc1}, \qquad e_2 = V_{dc2}^* – V_{dc2}.
$$
The sum error is processed by a voltage regulator \(G_{\Sigma V}\), and the difference error is processed by a difference regulator \(G_{\Delta V}\). The d-axis current reference is produced from the sum loop:
$$
I_d^* = G_{\Sigma V}(e_1 + e_2).
$$
The power-sharing coefficient is produced from the difference loop:
$$
k = \frac{1}{2} + G_{\Delta V}(e_1 – e_2),
$$
with \(k\) limited to the interval \(0 \le k \le 1\). When both arrays are balanced, \(e_1 \approx e_2\), so \(k \approx 0.5\). When one array has a higher maximum power point voltage, the difference loop adjusts \(k\) so that the corresponding solar inverter takes a larger voltage share.
I then rotate the total dq voltage references into a coordinate frame aligned with the grid current. I define \(V_d’^*\) as the active voltage component and \(V_q’^*\) as the reactive voltage component:
$$
\begin{bmatrix}
V_d’^* \\
V_q’^*
\end{bmatrix}
=
\begin{bmatrix}
\cos\phi & \sin\phi \\
-\sin\phi & \cos\phi
\end{bmatrix}
\begin{bmatrix}
V_d^* \\
V_q^*
\end{bmatrix}.
$$
Here, \(\phi\) is the angle between the grid voltage vector and the grid current vector. The active and reactive components are distributed between the two solar inverters as:
$$
V_{1d}’^* = k V_d’^*, \qquad V_{2d}’^* = -(1-k)V_d’^*,
$$
$$
V_{1q}’^* = k V_q’^*, \qquad V_{2q}’^* = -(1-k)V_q’^*.
$$
Under normal balanced operation, I set \(I_q^* = 0\) so that the solar inverter system operates at unity power factor. When overmodulation is detected, I modify \(I_q^*\) using my reactive compensation design.
| Control Loop | Input | Output | Purpose |
|---|---|---|---|
| Sum voltage loop | \(e_1 + e_2\) | \(I_d^*\) | Regulates total active power and grid current |
| Difference voltage loop | \(e_1 – e_2\) | \(k\) | Balances voltage shares between two solar inverters |
| Current inner loop | \(I_d^*, I_q^*, I_d, I_q\) | \(V_d^*, V_q^*\) | Tracks current references with decoupling and feedforward |
| Reactive compensation | Overmodulation flag | \(I_q^*\) | Prevents modulation saturation |
5. Overmodulation Mechanism
I now explain the overmodulation mechanism in detail. The two solar inverters carry the same AC current \(I_g\), but their DC-link voltages and powers may differ. For the first array, the power balance is approximately:
$$
P_1 = V_{dc1} I_{dc1} = \frac{3}{2} V_1^* I_g \cos\delta \approx \frac{3}{2} V_1^* I_g.
$$
For the second array, I write:
$$
P_2 = V_{dc2} I_{dc2} = \frac{3}{2} V_2^* I_g \cos\delta \approx \frac{3}{2} V_2^* I_g.
$$
Here, \(\delta\) is the small angle between the grid voltage vector and the grid current vector when operating near unity power factor. If the first array produces much more power than the second, then \(V_1^*\) must be much larger than \(V_2^*\). With sinusoidal pulse-width modulation, the maximum linear AC voltage amplitude that a two-level solar inverter can produce is \(V_{dc}/2\). Therefore, I require:
$$
V_1^* \le \frac{V_{dc1}}{2}, \qquad V_2^* \le \frac{V_{dc2}}{2}.
$$
Using the power balance equations, I obtain the minimum grid current magnitude needed to avoid overmodulation:
$$
I_g \ge \frac{4}{3} I_{dc1}, \qquad I_g \ge \frac{4}{3} I_{dc2}.
$$
Thus, the critical minimum current is:
$$
I_{\min} = \max\left\{\frac{4}{3} I_{dc1}, \frac{4}{3} I_{dc2}\right\}.
$$
For unity power factor operation, the actual grid current magnitude is determined by the total power:
$$
I_{gd} = \frac{P_1 + P_2}{\frac{3}{2} V_g}.
$$
If \(I_{gd} \le I_{\min}\), the stronger solar inverter cannot synthesize the required voltage without entering overmodulation. This is the exact condition I use to trigger reactive power compensation.
| Condition | Interpretation | Consequence |
|---|---|---|
| \(P_1 \approx P_2\) | Two arrays produce similar power | \(k \approx 0.5\), linear modulation, unity power factor possible |
| \(P_1 > P_2\) but \(I_{gd} > I_{\min}\) | Moderate power imbalance | Both solar inverters remain linear, no compensation needed |
| \(P_1 \gg P_2\) and \(I_{gd} \le I_{\min}\) | Severe power imbalance | Overmodulation occurs, grid current distortion increases |
| Reactive compensation active | Additional current magnitude is injected | Required voltage vector is reduced, overmodulation is avoided |
6. Reactive Power Compensation Design
When I detect \(I_{gd} \le I_{\min}\), I inject reactive current to increase the total current magnitude. This may seem counterintuitive because a larger current usually requires a larger voltage. However, the active power that each solar inverter must transfer is fixed by the photovoltaic array. If I increase the current magnitude while keeping active power constant, the active voltage component can decrease. The solar inverter voltage vector therefore becomes smaller, and the stronger solar inverter moves out of overmodulation.
I define \(\phi\) as the angle between the grid voltage vector and the grid current vector, and \(\phi_1\) as the angle between the first solar inverter voltage vector and the grid current vector. I set the first solar inverter voltage magnitude to its linear limit:
$$
V_1^* = \frac{V_{dc1}}{2}.
$$
I then solve the following three power-balance equations:
$$
\begin{aligned}
\frac{3}{2} V_1^* I_g \cos\phi_1 &= P_1, \\
\frac{3}{2} V_g I_g \cos\phi &= P_1 + P_2, \\
V_g I_g \sin\phi &= \omega L I_g^2 + \frac{V_1^* I_g (P_1 + P_2)\sin\phi_1}{P_1}.
\end{aligned}
$$
The unknowns are \(\phi\), \(\phi_1\), and \(I_g\). Because the third equation is nonlinear, I solve the set numerically. Once I obtain \(I_g\) and \(\phi\), I compute the reactive current reference:
$$
I_q^* = I_g \sin\phi.
$$
I keep the active current reference generated by the maximum power point control loops, and I add \(I_q^*\) as the quadrature-axis current reference. The solar inverter then injects a controlled amount of reactive power. From the grid point of view, the plant can still appear close to unity power factor if an external reactive compensation device absorbs or supplies the corresponding reactive power. The important point is that the open-end winding dual solar inverter remains in the linear modulation region and both photovoltaic arrays continue to operate at their own maximum power points.
| Design Step | Action | Equation or Condition |
|---|---|---|
| 1 | Compute actual unity-power-factor current | \(I_{gd} = \frac{P_1+P_2}{1.5 V_g}\) |
| 2 | Compute minimum current limit | \(I_{\min} = \max\left\{\frac{4}{3}I_{dc1}, \frac{4}{3}I_{dc2}\right\}\) |
| 3 | Detect overmodulation | If \(I_{gd} \le I_{\min}\), enable compensation |
| 4 | Set stronger solar inverter voltage limit | \(V_1^* = V_{dc1}/2\) |
| 5 | Solve power balance equations | Obtain \(I_g\), \(\phi\), and \(\phi_1\) |
| 6 | Generate reactive current reference | \(I_q^* = I_g \sin\phi\) |
| 7 | Resume independent MPPT | Both arrays remain at their own maximum power points |
7. Simulation Studies
I validated the proposed control and compensation method using a detailed simulation model. The photovoltaic arrays were represented by a DC voltage source in series with a resistor, which is sufficient to emulate the maximum power point behavior for control verification. The open-end winding transformer secondary was connected in delta. I used the following parameters.
| Parameter | Value |
|---|---|
| DC source voltage | 656 V |
| Series resistance | 1.6 Ω |
| DC-link capacitance | 3.36 mF |
| Filter inductance | 3.5 mH |
| Open-end transformer ratio | 364/380 |
| Switching frequency | 5 kHz |
| Rated power | 40 kW |
| Grid line voltage RMS | 396 V |
In the balanced case, I set \(V_{dc1} = V_{dc2} = 615\) V and \(P_1 = P_2 = 15.76\) kW. The two photovoltaic arrays produce equal power. The solar inverter system operates at unity power factor. The combined line voltage of the open-end winding dual solar inverter is equivalent to the line voltage of a single three-level solar inverter. This confirms that the dual two-level solar inverter can behave as an equivalent three-level solar inverter when the DC links are balanced.
In the lightly unbalanced case, I set \(V_{dc1} = 615\) V, \(V_{dc2} = 625\) V, \(P_1 = 15.76\) kW, and \(P_2 = 12.11\) kW. The power difference is modest, and the actual grid current remains above the minimum current limit. Therefore, no overmodulation occurs. The grid current amplitude decreases slightly, but the waveform remains nearly sinusoidal. The solar inverter system continues to operate at unity power factor. When the second array returns to normal power, the system smoothly returns to the balanced state.
In the heavily unbalanced case, I set \(V_{dc1} = 615\) V, \(V_{dc2} = 629\) V, \(P_1 = 15.76\) kW, and \(P_2 = 10.61\) kW. The power difference is large, and the unity-power-factor grid current falls below the minimum current limit. The first solar inverter enters overmodulation. The grid current waveform becomes visibly distorted, and the total harmonic distortion rises to 5.53%. The modulation wave of the stronger solar inverter exceeds the triangular carrier amplitude of 0.5. After I activate the reactive compensation at 0.4 s, the grid current distortion decreases, and the THD falls to 3.72%. The modulation wave of the first solar inverter is restored to the linear boundary. When the second array recovers at 0.6 s, the system returns to balanced operation.
| Simulation Case | \(V_{dc1}\) | \(V_{dc2}\) | \(P_1\) | \(P_2\) | Overmodulation | THD Before | THD After Compensation |
|---|---|---|---|---|---|---|---|
| Balanced | 615 V | 615 V | 15.76 kW | 15.76 kW | No | Low | Not needed |
| Light unbalance | 615 V | 625 V | 15.76 kW | 12.11 kW | No | Acceptable | Not needed |
| Heavy unbalance | 615 V | 629 V | 15.76 kW | 10.61 kW | Yes | 5.53% | 3.72% |
8. Experimental Validation
I also built an experimental platform to confirm the simulation results. The DC side used two 20 kW rectifiers in series with resistors to emulate the photovoltaic arrays. The controller was based on a TMS320F28335 digital signal processor. I used an oscilloscope, high-voltage probes, current clamps, and a power analyzer to capture the voltage and current waveforms. The experimental parameters and operating conditions were kept consistent with the simulation cases.
In the balanced experimental case, the two photovoltaic arrays produced equal power. The solar inverter system operated at unity power factor. The combined line voltage of the open-end winding dual solar inverter matched the expected three-level waveform. These results confirmed that the two two-level solar inverters form an equivalent three-level solar inverter when the DC links are balanced and the 180° decoupled modulation is used.
In the lightly unbalanced experimental case, the second array power dropped by a modest amount. The grid current amplitude decreased, but the waveform remained acceptable. The THD was 4.08%, and the system continued to operate at unity power factor. No reactive compensation was required because the current remained above the minimum limit.
In the heavily unbalanced experimental case, the second array power dropped severely. The grid current waveform became distorted, and the THD reached 6.47%. This confirmed that the first solar inverter was entering overmodulation. After I enabled the reactive compensation, the grid current waveform improved significantly, and the THD decreased to 3.93%. The experimental results therefore agree with the simulation and validate the proposed reactive compensation strategy.
| Experimental Case | Array 1 Power | Array 2 Power | Overmodulation | THD Before | THD After Compensation |
|---|---|---|---|---|---|
| Balanced | 15.76 kW | 15.76 kW | No | Low | Not needed |
| Light unbalance | 15.76 kW | 12.11 kW | No | 4.08% | Not needed |
| Heavy unbalance | 15.76 kW | 10.61 kW | Yes | 6.47% | 3.93% |
9. Why This Matters for Solar Inverter Systems
The proposed method is important for solar inverter systems because it preserves independent maximum power point tracking without sacrificing grid current quality. In a large photovoltaic plant, partial shading or module damage can create severe power mismatch between arrays. If the solar inverter system simply forces equal power sharing, the stronger array cannot operate at its true maximum power point. If the solar inverter system allows full independent operation without reactive compensation, the stronger solar inverter may overmodulate. My method solves both problems at the same time.
I also note that the open-end winding dual solar inverter has practical advantages for high-power photovoltaic applications. It can reduce the number of clamping devices, share a single filter, utilize transformer leakage inductance, and avoid neutral-point voltage balancing. These features lower cost and simplify control. At the same time, the 180° decoupled space vector modulation makes full use of the available voltage vectors and improves DC-link voltage utilization.
The reactive compensation strategy is simple to implement. It requires only the DC-link currents and voltages, the grid voltage, the grid current, and the filter inductance. The compensation current reference is calculated from a small set of power balance equations. The method does not require complex optimization or random phase allocation. Therefore, it is suitable for engineering application in solar inverter systems that must operate under unequal photovoltaic array conditions.
| Benefit | How It Is Achieved | Effect on Solar Inverter Operation |
|---|---|---|
| Independent MPPT | Two separate DC links and sum/difference voltage control | Each array can reach its own maximum power point |
| High voltage utilization | 180° decoupled space vector modulation | Uses the outer hexagon vectors effectively |
| Reduced hardware cost | No clamping diodes or flying capacitors | Lower component count and simpler structure |
| Improved grid current quality | Reactive compensation during severe imbalance | Prevents overmodulation and reduces THD |
| Wider MPPT range | Controlled reactive current injection | Maintains operation under large power mismatch |
10. Additional Analytical Considerations
I further examine the sensitivity of the compensation method. The most important variable is the ratio between the stronger array power and the weaker array power. When this ratio is close to one, the power-sharing coefficient \(k\) remains near 0.5, and the modulation indices of both solar inverters stay well below one. As the ratio increases, \(k\) moves away from 0.5. The stronger solar inverter receives a larger voltage vector, and its modulation index approaches the linear limit.
I define the power imbalance ratio as:
$$
r = \frac{P_1}{P_2}.
$$
When \(r\) is moderate, the minimum current condition \(I_{gd} > I_{\min}\) is satisfied, and no compensation is needed. When \(r\) becomes large, \(I_{gd}\) falls below \(I_{\min}\), and the compensation algorithm activates. The compensation current \(I_q^*\) increases the total current magnitude, which reduces the required active voltage component. The stronger solar inverter voltage magnitude is then held at its linear limit, preventing overmodulation while the weaker solar inverter continues to operate within its own linear range.
The compensation also affects the reactive power flow. The open-end winding dual solar inverter injects reactive power into the grid. This reactive power can be absorbed by a plant-level reactive compensation device, so the overall photovoltaic plant can still meet grid-code requirements for power factor. The key advantage is that the internal solar inverter modulation remains linear and the two arrays remain independently controlled.
| Power Imbalance Ratio | Expected \(k\) | Overmodulation Risk | Compensation Action |
|---|---|---|---|
| \(r \approx 1\) | Near 0.5 | Very low | None |
| \(1 < r < 1.5\) | Slightly above 0.5 | Low | Usually none |
| \(1.5 \le r < 2\) | Moderately above 0.5 | Medium | Compensation may activate |
| \(r \ge 2\) | Close to 1 | High | Compensation strongly required |
11. Control Implementation Details
In my implementation, I use a phase-locked loop to obtain the grid voltage angle and the grid current angle. I then compute the angle \(\phi\) for the coordinate rotation. The DC-link voltage controllers generate \(I_d^*\) and \(k\). The current controllers operate in the synchronous rotating frame with feedforward decoupling. The total voltage reference is rotated into the active and reactive axes, and then distributed between the two solar inverters using \(k\). Each solar inverter receives its own reference vector and uses space vector modulation or sinusoidal pulse-width modulation. When the overmodulation flag is set, the reactive current reference is calculated and added to the q-axis current command.
I use anti-windup limits in the voltage controllers and current controllers. I also limit \(k\) between zero and one. The reactive current reference is limited to a safe maximum value to avoid excessive current stress. The compensation is activated only when needed, so the solar inverter system operates at unity power factor whenever possible. This minimizes reactive current circulation and reduces losses.
| Implementation Block | Function | Key Limit |
|---|---|---|
| Phase-locked loop | Provides grid angle and synchronization | Bandwidth selected for stable grid tracking |
| DC voltage sum controller | Generates active current reference | Anti-windup and current limit |
| DC voltage difference controller | Generates power-sharing coefficient \(k\) | \(0 \le k \le 1\) |
| Current controller | Regulates dq currents | Voltage reference limit |
| Reactive compensation calculator | Computes \(I_q^*\) | Maximum reactive current limit |
| Modulation distributor | Splits total vector between two solar inverters | Linear modulation boundary |
12. Conclusion
I have presented a complete control and reactive compensation method for an open-end winding dual solar inverter photovoltaic generation system. The topology allows two photovoltaic arrays to operate at independent maximum power points, which improves energy harvesting. The 180° decoupled space vector modulation combines the two two-level solar inverters into an equivalent three-level solar inverter and provides high DC-link voltage utilization. The sum and difference voltage control loops regulate total power and power sharing between the two arrays. When the two arrays produce severely unbalanced power, the stronger solar inverter can enter overmodulation because the shared grid current forces a large voltage vector. I derived the minimum current condition and proposed a reactive power compensation method that increases the current magnitude, reduces the required active voltage component, and restores linear modulation. Simulation and experimental results show that the method reduces grid current THD in the heavy imbalance case and maintains independent maximum power point operation. The approach is simple, effective, and suitable for high-power solar inverter systems that must operate under partial shading, module mismatch, or uneven array conditions.
In my view, the most valuable contribution is the combination of independent maximum power point tracking and overmodulation avoidance. The open-end winding dual solar inverter can therefore achieve higher energy yield without sacrificing grid current quality. The method extends the maximum power point tracking range and supports the practical deployment of high-voltage, high-power photovoltaic plants.