In the field of power electronics, three-phase inverters serve as the core devices for DC-AC conversion and are widely deployed in smart grids, distributed generation, and renewable energy systems. Among the various types of solar inverters, such as string inverters, microinverters, central inverters, and multi-string inverters, the requirement for handling unbalanced loads and maintaining neutral-point voltage balance is critical. This paper focuses on a three-phase four-wire inverter topology with an independently controlled neutral leg, which is particularly suitable for types of solar inverters that need to operate under unbalanced grid conditions or supply mixed single-phase and three-phase loads. We propose a composite control strategy combining inner-loop state feedback (SF) and outer-loop proportional-integral (PI) control for neutral leg voltage regulation, along with an adaptive switching strategy to minimize losses by enabling the neutral leg only when necessary.
I. Topology and Modeling
The inverter topology under study consists of a three-phase full-bridge inverter and an independently controlled neutral leg module. The neutral leg is designed to stabilize the neutral-point voltage at half the DC bus voltage. To simplify analysis, the neutral line current is modeled as a current source load, and the neutral leg can be represented as a Buck converter equivalent circuit. The differential equations governing the system are:
$$L_f \frac{di_L}{dt} = u_M – i_L R_f – u_o$$
$$C_{eq} \frac{du_o}{dt} = i_L – i_{fn}$$
where \(i_L\) is the neutral inductor current, \(u_o\) is the neutral-point voltage, \(u_M\) is the bridge arm output voltage, \(i_{fn}\) is the neutral line current (disturbance), \(L_f\) and \(R_f\) are the filter inductor and its internal resistance, and \(C_{eq}=C_{bus1}+C_{bus2}\) is the equivalent split DC-link capacitance. Discretizing the continuous model with sampling period \(T_s\) and incorporating one-step computational delay yields an augmented third-order discrete state-space model:
$$\mathbf{x}_d(k+1) = \mathbf{F}_d \mathbf{x}_d(k) + \mathbf{H}_{ud} u_{M\_ref}(k) + \mathbf{H}_{id} i_{fn}(k)$$
$$u_o(k) = \mathbf{C}_d \mathbf{x}_d(k)$$
where \(\mathbf{x}_d = [i_L, u_o, u_M]^T\). This model forms the basis for controller design. The neutral leg topology is also commonly employed in hybrid types of solar inverters that combine battery storage and grid interaction, where frequent load imbalances occur.
II. Controller Design
The proposed control structure uses an inner-loop state feedback to actively damp the LC filter resonance and an outer-loop PI controller to achieve zero steady-state error for the DC reference. The control law is:
$$u_{M\_ref}(k) = u_i(k) – \mathbf{Kx}_d(k)$$
where \(\mathbf{K}=[k_{iL}, k_{uo}, k_{uM}]\) is the state feedback gain matrix. Substituting into the augmented model, the inner-loop transfer function from \(u_i\) to \(u_o\) is derived as:
$$P(z) = \frac{P_N(z)}{P_D(z)} = \mathbf{C}_d(z\mathbf{I} – \mathbf{F}_d + \mathbf{H}_{ud}\mathbf{K})^{-1}\mathbf{H}_{ud}$$
The PI controller in discrete form is \(G_{PI}(z)=k_p + k_i \frac{z^{-1}}{1-z^{-1}} = \frac{k_p(z-1)+k_i}{z-1}\). By pre-specifying all four closed-loop poles at \(p_c = e^{pT_s}\) with \(p=-2\pi/T_s\) (all poles coinciding with the zero \(L=1-k_i/k_p\)), the closed-loop transfer function becomes:
$$G_c(z)=\frac{k_p(z-L)P_N(z)}{(z-p_c)^4}$$
Enforcing \(G_c(1)=1\) yields the proportional gain:
$$k_p = \frac{(1-p_c)^4}{(1-L)P_N(1)}$$
The integral gain is then \(k_i = k_p(1-L)\). The state feedback gains are obtained by equating the denominators of (18) and (20) from the original analysis, which leads to a linear system \(\mathbf{UK} = \mathbf{V}\). The matrix \(\mathbf{U}\) and vector \(\mathbf{V}\) are functions of the discrete model coefficients and the chosen closed-loop poles. Detailed expressions were derived in the original work; here we present the final computed parameters for our prototype system in Table I.
Table I: Control Parameters for the Prototype
| Parameter | Symbol | Value |
|---|---|---|
| Proportional gain | \(k_p\) | 7.5490 |
| Integral gain | \(k_i\) | 7.5349 |
| State feedback gain for \(i_L\) | \(k_{iL}\) | 10.6810 |
| State feedback gain for \(u_o\) | \(k_{uo}\) | 4.6159 |
| State feedback gain for \(u_M\) | \(k_{uM}\) | 1.7278 |
Robustness analysis shows that when the neutral inductor \(L_f\) or the equivalent capacitor \(C_{eq}\) varies by ±30%, the control bandwidth remains above 4 kHz, confirming the strong robustness of the proposed method. This feature is desirable for types of solar inverters that may experience parameter drift due to temperature or aging.
III. Adaptive Switching Strategy
In normal balanced operation, the neutral leg is unnecessary and its continuous operation increases losses. We propose an adaptive switching strategy that enables the neutral leg only when neutral-point voltage fluctuation exceeds a threshold. The switching conditions are:
Enable condition: \(|u_o – U_{dc}/2| \geq U_{dcTH}\), where \(U_{dcTH}\) is set slightly above the residual ripple caused by non-ideal factors such as dead time and capacitor mismatch.
Disable condition: The filtered square of the neutral inductor current falls below \(I_{LTH}^2\). The current is squared and processed through a notch filter tuned at twice the fundamental frequency to extract the DC component (which equals the square of the RMS value). To avoid chattering, a hysteresis band is created: when enabling, the voltage must exceed \(U_{dcTH}\); when disabling, the filtered current must stay below \(I_{LTH}^2\) for a hold time \(T_d\). This ensures stable switching. The disable threshold is chosen such that when the neutral leg is removed, the resulting voltage ripple \(|\Delta u_{oL}|\) is smaller than the enable threshold \(U_{dcTH}\), preventing immediate re-enablement.
The switching process is illustrated in the sequence diagram (not shown). In our implementation, the voltage threshold was set to 10 V and the current threshold to 2 A² (RMS²). Experimental measurements demonstrated that the neutral leg losses decreased by 53.9 W compared to continuous operation, validating the effectiveness of the strategy. Such adaptive operation is particularly beneficial for types of solar inverters that operate for long periods under balanced conditions, such as utility-scale photovoltaic plants.
IV. Experimental Results
We built a prototype using SiC MOSFETs (C3M0032120K) and a TMS320F28379D DSP. System parameters are listed in Table II. Experimental waveforms were captured under both steady-state and transient conditions to verify the proposed control and switching strategy.
Table II: System Parameters of the Prototype
| Parameter | Symbol | Value |
|---|---|---|
| DC bus voltage | \(U_{dc}\) | 750 V |
| Fundamental frequency | \(f\) | 50 Hz |
| Filter inductance | \(L_f\) | 1 mH |
| Filter capacitance | \(C_f\) | 30 μF |
| Inductor ESR | \(R_f\) | 0.01 Ω |
| Split capacitors | \(C_{bus1}=C_{bus2}\) | 50 μF |
| Switching frequency | \(f_{sw}\) | 50 kHz |
| Sampling frequency | \(f_s\) | 50 kHz |
A. Voltage Regulation Performance
When the load transitions from three-phase balanced (each phase full load) to unbalanced (A and B phases full load, C phase no load), the neutral-point voltage was suppressed within ±4 V while the output voltage THD remained at 1.00%. In contrast, conventional PI control exhibited a THD of 2.61% and voltage ripple of ±6 V. Deadbeat control produced excessive noise and ripple. These results confirm that the proposed SF+PI method offers superior dynamic and steady-state performance. For types of solar inverters that must comply with strict power quality standards, such low THD and tight voltage regulation are essential.
B. Parameter Variation Robustness
With the same controller parameters, we varied \(L_f\) and \(C_{eq}\) by ±30%. The output voltage THD remained around 1.01%–1.05%, and the neutral-point voltage ripple stayed within ±4 V, validating the robustness discussed earlier. Such robustness is critical for types of solar inverters that may operate under widely different ambient conditions.
C. Adaptive Switching
When the load was balanced, the neutral leg was disabled and the inductor current was zero. Upon switching to unbalanced load, the neutral-point voltage exceeded the 10 V threshold, immediately enabling the neutral leg. The zero-sequence current then flowed through the inductor, restoring voltage balance. When the load returned to balance, the filtered current squared dropped below the threshold (2 A²), and after a hold time \(T_d=100\) ms, the neutral leg was disabled. No false triggering occurred. The loss reduction of 53.9 W demonstrates a clear efficiency improvement. This adaptive feature is particularly valuable for types of solar inverters that frequently experience partial shading or unbalanced grid conditions but also have long balanced operating periods.
V. Conclusion
This paper presented a straightforward composite control method for neutral leg voltage regulation in three-phase four-wire inverters. The inner-loop state feedback provides active damping, while the outer-loop PI eliminates steady-state error. All controller parameters are directly determined from predefined closed-loop poles, simplifying the tuning process. Furthermore, an adaptive switching strategy based on neutral-point voltage ripple and inductor current RMS enables the neutral leg to be enabled only during unbalanced conditions, reducing losses by 53.9 W in the prototype. Experimental results confirmed the effectiveness of both the voltage regulation and switching strategy. The proposed approach can be applied to various types of solar inverters, including string, multi-string, and hybrid inverters, to enhance efficiency and reliability under unbalanced load scenarios.