In the field of solar energy conversion, solar inverters play a pivotal role in transforming DC power from photovoltaic panels into AC power for grid integration or local consumption. The performance of solar inverters directly impacts the efficiency, stability, and power quality of renewable energy systems. Traditional control methods, such as proportional-integral (PI) control, are widely used in dual closed-loop structures (voltage outer loop and current inner loop) due to their simplicity. However, these linear approaches often fail to account for the nonlinear dynamics inherent in solar inverter systems, leading to suboptimal transient response, steady-state accuracy, and robustness against disturbances. To address these limitations, this paper proposes an improved dual closed-loop control strategy that combines a modified linear active disturbance rejection controller (LADRC) for the voltage outer loop with a PI controller for the current inner loop. The enhanced LADRC incorporates an output error compensation term into the linear state error feedback (LSEF) law, mitigating oscillations and improving stability. Through comprehensive parameter tuning, performance analysis, and simulation in Matlab/Simulink, the proposed method demonstrates superior dynamic and static performance compared to conventional PI-based dual closed-loop control for a 1.2 kW single-phase solar inverter system.
The dual closed-loop control structure for single-phase solar inverters typically consists of an outer voltage loop and an inner current loop. This configuration enhances dynamic response and steady-state precision by regulating output voltage and inductor current simultaneously. The system’s mathematical model is derived from Kirchhoff’s laws and state-space averaging techniques. For a single-phase full-bridge solar inverter with LCL filter, the output voltage \( V_o \) and inductor current \( i_L \) are governed by the following equations:
$$ V_{ab} = L \frac{di_L}{dt} + R i_L + V_o $$
$$ i_L = C \frac{dV_o}{dt} + i_o $$
where \( V_{ab} \) is the voltage difference between the bridge legs, \( L \) is the filter inductance, \( R \) is the equivalent resistance, \( C \) is the filter capacitance, and \( i_o \) is the output current. Applying Laplace transform, the transfer function between output voltage and input reference is expressed as:
$$ G_{PV}(s) = \frac{V_o(s)}{V_{ab}(s)} = \frac{1}{LCs^2 + RCs + 1} $$
To account for internal and external disturbances (e.g., parameter variations, load changes, and switching noise), the system is reformulated into a state-space model. Defining state variables as \( x_1 = V_o \), \( x_2 = \dot{V}_o \), and \( x_3 = f \) (lumped disturbance), the state equation becomes:
$$ \dot{\mathbf{x}}_m = \mathbf{N}_m \mathbf{x}_m + \mathbf{P}_m u + \mathbf{E}_n f $$
$$ y = \mathbf{C}_m \mathbf{x}_m $$
where \( \mathbf{x}_m = [x_1, x_2, x_3]^T \), \( u \) is the control input, and matrices \( \mathbf{N}_m \), \( \mathbf{P}_m \), \( \mathbf{E}_n \), and \( \mathbf{C}_m \) are derived from system parameters. This model forms the basis for designing the improved LADRC.
The improved LADRC comprises a linear extended state observer (LESO) and a modified LSEF law. The LESO estimates system states and disturbances in real-time, while the LSEF generates control signals with added output error compensation. For a second-order solar inverter system, a third-order LESO is designed as:
$$ \dot{\hat{\mathbf{z}}}_m = \mathbf{N}_m \hat{\mathbf{z}}_m + \mathbf{P}_m u + \mathbf{\beta}_m (y – \hat{y}) $$
$$ \hat{y} = \mathbf{C}_m \hat{\mathbf{z}}_m $$
where \( \hat{\mathbf{z}}_m = [z_1, z_2, z_3]^T \) represents estimated states, and \( \mathbf{\beta}_m = [\beta_1, \beta_2, \beta_3]^T \) is the observer gain matrix. Using pole placement, gains are parameterized as \( \beta_1 = 3\omega_o \), \( \beta_2 = 3\omega_o^2 \), and \( \beta_3 = \omega_o^3 \), where \( \omega_o \) is the observer bandwidth. The modified LSEF includes an output error compensation term \( T = \beta_2 (V_{ref} – z_1) \), resulting in the control law:
$$ u = \frac{u_c – z_3 – T}{b_0} $$
$$ u_c = k_p (V_{ref} – z_1) + k_d (-z_2) $$
Here, \( b_0 \) is a compensation factor, and \( k_p \), \( k_d \) are feedback gains set as \( k_p = \omega_c^2 \) and \( k_d = 2\omega_c \), where \( \omega_c \) is the controller bandwidth. This structure enhances disturbance rejection and reduces overshoot in solar inverters.
Parameter tuning is critical for optimal performance. The observer bandwidth \( \omega_o \) and controller bandwidth \( \omega_c \) are selected based on frequency response analysis. For the 1.2 kW solar inverter system with parameters listed in Table 1, \( \omega_o \) is set to 14,000 rad/s, and \( \omega_c \) to 6,000 rad/s through Bode plot analysis. The current inner loop PI controller gains are \( k_{pi} = 24 \) and \( k_{ii} = 7 \), while voltage outer loop PI gains (for comparison) are \( k_{pv} = 0.02 \) and \( k_{iv} = 21 \).
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| DC Input Voltage \( V_{dc} \) (V) | 400 | Filter Inductance \( L \) (mH) | 4.06 |
| Switching Frequency (kHz) | 10 | Filter Capacitance \( C \) (μF) | 6.23 |
| Grid Frequency (Hz) | 50 | Equivalent Resistance \( R \) (Ω) | 0.1 |
Controller performance is evaluated through disturbance rejection, tracking capability, and stability analysis. The transfer function from disturbance \( f \) to estimation error \( z_{e3} \) is derived as:
$$ \frac{z_{e3}(s)}{f(s)} = -\frac{s^3 + a_1 s^2 + (a_1 \beta_1 – \beta_2 – a_0) s}{ (s + \omega_o)^3 } $$
Bode plots of this transfer function for varying \( \omega_o \) indicate that \( \omega_o = 14,000 \) rad/s offers balanced steady-state accuracy and noise immunity. Similarly, the input-output transfer function of the improved LADRC is:
$$ \frac{y(s)}{V(s)} = \frac{ k_p (s^3 + \beta_1 s^2 + \beta_2 s + \beta_3 ) G_{PV}(s) }{ b_0 s (s + \omega_o)^3 + M_1 G_{PV}(s) (s^2 + M_2 s + M_3) } $$
where \( M_1 \), \( M_2 \), and \( M_3 \) are coefficients derived from controller gains. Comparative Bode plots with conventional PI control show that the improved LADRC-PI strategy achieves higher bandwidth and faster response, essential for solar inverters operating under varying conditions.
Stability is assessed using the Routh-Hurwitz criterion. The characteristic equation of the closed-loop system is:
$$ D(s) = s^5 + \phi_4 s^4 + \phi_3 s^3 + \phi_2 s^2 + \phi_1 s + \phi_0 = 0 $$
With parameters from Table 1, all coefficients \( \phi_i > 0 \), and the Routh array’s first column elements are positive, confirming system stability.
Simulations in Matlab/Simulink compare the improved LADRC-PI control with traditional dual-loop PI control under steady-state and dynamic conditions. For steady-state performance with resistive load, the output voltage and current waveforms are analyzed. The improved LADRC-PI control reduces voltage overshoot to 0.28% (0.85 V) and THD to 0.28%, compared to 4.23% overshoot (12.7 V) and 2.54% THD for PI control. This demonstrates enhanced steady-state precision and power quality for solar inverters.
| Metric | Dual-Loop PI Control | Improved LADRC-PI Control |
|---|---|---|
| Voltage Overshoot (%) | 4.23 | 0.28 |
| Maximum Overshoot (V) | 18.9 | 2.01 |
| THD (%) | 2.54 | 0.28 |
| Fundamental Amplitude (V) | 309.8 | 300.7 |
Under dynamic conditions, load transitions between resistive, inductive, and resistive-inductive loads are tested. The improved LADRC-PI control achieves near-instantaneous response with zero settling time and no waveform distortion during switches, whereas PI control exhibits 1–1.6 ms settling times and transient distortions. This highlights the superior robustness and transient capability of the proposed strategy for solar inverters facing real-world operational variations.
In conclusion, the improved LADRC-PI dual closed-loop control strategy significantly enhances the performance of single-phase solar inverters. By integrating an output error compensation term into LSEF, the method reduces oscillations and improves stability. Extensive simulations validate its advantages over conventional PI control, including lower overshoot, reduced THD, faster dynamic response, and better disturbance rejection. These attributes make it highly suitable for modern solar energy systems, ensuring reliable and efficient power conversion. Future work will focus on hardware implementation and optimization for grid-connected solar inverters under unbalanced conditions.