In this paper, I present an improved first-order linear active disturbance rejection control (LADRC) strategy for the DC-link voltage regulation of a grid-connected solar inverter. The power output of photovoltaic systems is highly susceptible to environmental factors such as irradiance and temperature, which introduce significant disturbances on the DC-link voltage. To address this challenge, I first model the LCL-type grid-connected solar inverter system. Subsequently, I design an enhanced LADRC controller that incorporates a differential feedforward term into the input signal, thereby improving the disturbance rejection capability. The theoretical performance analysis, including disturbance rejection, tracking error, and stability, is thoroughly conducted. Finally, I validate the proposed control strategy through MATLAB/Simulink simulations under two distinct operating conditions. The simulation results demonstrate that the improved LADRC significantly reduces overshoot compared to the conventional LADRC, while maintaining the total harmonic distortion (THD) of the grid current below 5%. This research offers a practical and effective solution for enhancing the dynamic performance of solar inverters in real-world engineering applications.
1 Introduction
The global transition toward renewable energy has accelerated the deployment of photovoltaic (PV) systems. However, the inherent variability of solar irradiance and temperature causes fluctuations in the DC-link voltage of grid-connected solar inverters, which can degrade power quality and system stability. Conventional PI control, sliding mode control, adaptive control, and repetitive control have been widely employed for inverter control, but each has limitations in handling nonlinearities and external disturbances. Active disturbance rejection control (ADRC) has emerged as a promising alternative due to its ability to estimate and compensate for total disturbances in real time. In this work, I focus on improving the linear ADRC (LADRC) by modifying the linear extended state observer (LESO) structure and adding a feedforward term. The objective is to achieve superior transient response and disturbance rejection for the DC-link voltage control of a solar inverter.
To systematically present my approach, the remainder of this paper is organized as follows: Section 2 derives the mathematical model of the LCL-type grid-connected solar inverter. Section 3 details the design of the improved LADRC controller and its integration into the outer voltage loop. Section 4 analyzes the performance of the proposed controller in terms of disturbance rejection, tracking accuracy, and stability. Section 5 provides the simulation setup and results, comparing the improved LADRC with the conventional LADRC. Finally, Section 6 concludes the paper.
2 Modeling of LCL-Type Grid-Connected Solar Inverter
Figure 1 illustrates the topology of a three-phase LCL-type grid-connected solar inverter system. The system consists of a PV array, a boost converter, a DC-link capacitor, and an LCL filter connected to the grid. In the low-frequency range, the LCL filter behaves similarly to an L filter, allowing me to approximate it as an equivalent inductor for modeling purposes.
The mathematical model of the solar inverter in the synchronous rotating dq coordinate system is given by:
$$ L\frac{di_d}{dt} = u_d – \omega L i_q – u_{sd} $$
$$ L\frac{di_q}{dt} = u_q + \omega L i_d – u_{sq} $$
$$ C_2\frac{dU_{dc}}{dt} = i_o – i_n $$
where \(L = L_1 + L_2\) is the equivalent inductance of the LCL filter, \(u_d\) and \(u_q\) are the inverter output voltages, \(i_d\) and \(i_q\) are the grid currents, \(u_{sd}\) and \(u_{sq}\) are the grid voltages, \(\omega\) is the angular frequency, \(C_2\) is the DC-link capacitance, \(U_{dc}\) is the DC-link voltage, \(i_o\) is the output current of the boost converter, and \(i_n\) is the inverter input current.
The system parameters used in this study are listed in Table 1.
| Parameter | Symbol | Value |
|---|---|---|
| Inverter-side inductance | \(L_1\) | 3 mH |
| Grid-side inductance | \(L_2\) | 1.5 mH |
| Filter capacitance | \(C\) | 20 μF |
| DC-link capacitance | \(C_2\) | 2000 μF |
| DC-link reference voltage | \(U_{dcref}\) | 600 V |
| Grid line-to-line voltage (RMS) | \(U_{LL}\) | 380 V |
| Grid frequency | \(f\) | 50 Hz |
| Switching frequency | \(f_{sw}\) | 10 kHz |
From (1), the DC-link voltage dynamics represent a first-order system, which motivates the use of a first-order LADRC for the outer voltage control loop.
3 Design of Improved LADRC Controller and Outer-Loop Control Strategy
3.1 Improved LADRC Controller Design
The proposed improved LADRC consists of a linear extended state observer (LESO) and a linear state error feedback (LSEF) control law. The novel LESO, based on the concept introduced by Zhou et al., is expressed as:
$$ e_1(t) = Z_1 – y $$
$$ \dot{Z}_1 = Z_2 – b_1 e_1(t) + b_0 u $$
$$ \dot{Z}_2 = -b_2 e_1(t) – b_3 \dot{e}_1(t) $$
Using pole placement, the observer gains are selected as:
$$ b_2 = \omega_0^2 $$
$$ b_1 + b_3 = 2\omega_0 $$
For simplicity and ease of parameter tuning, I set \(b_1 = b_3 = \omega_0\). The LSEF law is given by:
$$ u_0 = k_p (v – Z_1) $$
$$ u = \frac{\dot{v} + u_0 – Z_2}{b_0} $$
where \(v\) is the reference signal, \(k_p = \omega_c\) is the controller bandwidth, \(\omega_0\) is the observer bandwidth, and \(b_0\) is the control gain. The structure of the improved LADRC is shown in Figure 2.
3.2 Outer-Loop Control Strategy with Improved LADRC
Applying the improved LADRC to the DC-link voltage outer loop, I define the state variables as \(x_U = U_{dcref}\) and \(y_U = U_{dc}\). Based on the instantaneous power balance principle, \(P_{ac} \approx P_{dc}\), and assuming \(U_{dc} \approx U_{dcref}\), we obtain:
$$ \frac{dU_{dc}}{dt} = \frac{3}{2C_2} \frac{U_1}{U_{dcref}} i_{sdref} – \frac{1}{C_2} i_n $$
Let \(b_0 = \frac{3U_1}{2C_2 U_{dcref}}\) and \(f_t = -\frac{i_n}{C_2}\). By applying Laplace transform to the controller equations, the control input can be expressed as:
$$ U(s) = \frac{1}{b_0} C_n(s) C_m(s) V(s) – \frac{1}{b_0} C_m(s) C_z(s) Y(s) $$
where \(C_m(s) = \frac{1}{s^2 + s\omega_0 + s\omega_c}\), \(C_n(s) = (s + \omega_c)(s + \omega_0)^2\), and \(C_z(s) = \omega_c \omega_0^2 + 2s\omega_c\omega_0 + \omega_0 s^2 + \omega_0^2 s\). The overall block diagram of the voltage loop is illustrated in Figure 3.
The complete control structure of the grid-connected solar inverter, where the improved LADRC replaces the traditional PI controller in the outer voltage loop, is depicted in Figure 4.
4 Performance Analysis of the Improved LADRC
4.1 Parameter Selection
Following the design methodology in reference [16], I select the observer bandwidth \(\omega_0 = 2000\) rad/s and the controller bandwidth \(\omega_c = 1000\) rad/s for the improved LADRC. The same parameters are used for the conventional LADRC to ensure a fair comparison.
4.2 Disturbance Rejection Performance
For a first-order system, the plant can be described as \(\dot{y} = b_0 u + f\). Substituting the control law and performing Laplace transformation, the transfer function from the disturbance \(f\) to the output \(y\) is:
$$ \frac{Y(s)}{F(s)} = \frac{s^2 + s\omega_0 + s\omega_c}{(s + \omega_0)^2 (s + \omega_c)} $$
Figure 5 shows the Bode plot of this disturbance transfer function. In the mid- and low-frequency ranges, the gain of the improved LADRC is lower than that of the conventional LADRC, indicating superior disturbance rejection capability.
4.3 Tracking Error Performance
I define the tracking errors as \(E_1(s) = Z_1(s) – Y(s)\) and \(E_2(s) = Z_2(s) – F(s)\). Using the LESO equations, I obtain:
$$ E_1(s) = \frac{-s^2}{(s + \omega_0)^2} Y(s) + \frac{b_0 s}{(s + \omega_0)^2} U(s) $$
$$ E_2(s) = \frac{-s^3 – s^2 \omega_0}{(s + \omega_0)^2} Y(s) + \frac{b_0 s^2 + b_0 s \omega_0}{(s + \omega_0)^2} U(s) $$
The steady-state errors are evaluated using the final value theorem:
$$ E_{s1}(s) = \lim_{s \to 0} s E_1(s) = 0 $$
$$ E_{s2}(s) = \lim_{s \to 0} s E_2(s) = 0 $$
Thus, the improved LADRC achieves zero steady-state tracking error for both the state and disturbance estimates, ensuring accurate reference tracking.
4.4 Stability Analysis
From Figure 3, the closed-loop transfer function from the reference \(U_{dcref}\) to the output \(U_{dc}\) is:
$$ \frac{U_{dc}(s)}{U_{dcref}(s)} = \frac{(s + \omega_c)(s + \omega_0)^2}{a_0 s^3 + a_1 s^2 + a_2 s + a_3} $$
where \(a_0 = 1\), \(a_1 = \omega_0 + \omega_c\), \(a_2 = \omega_0^2 + 2\omega_c \omega_0\), and \(a_3 = \omega_0 + \omega_c \omega_0^2\). Since all coefficients are positive, the Routh-Hurwitz criterion is applied. The third-order Hurwitz determinant is:
$$ \Delta_3 = \begin{vmatrix} a_1 & a_3 & 0 \\ a_0 & a_2 & 0 \\ 0 & a_1 & a_3 \end{vmatrix} = a_3 (a_1 a_2 – a_0 a_3) > 0 $$
For the selected parameters, \(\Delta_3 > 0\), confirming that the system is stable under the improved LADRC.
5 Simulation Verification
I conduct simulations using MATLAB/Simulink to validate the effectiveness of the proposed control strategy. The system parameters are as listed in Table 1. Two operating scenarios are considered: (1) irradiance increase from 1000 W/m² to 2000 W/m² at constant temperature 25°C, and (2) irradiance decrease from 2000 W/m² to 1000 W/m². The conventional LADRC with the same bandwidth settings is used for comparison.
Figure 6 presents the DC-link voltage response and grid current waveforms under varying irradiance conditions. The key performance indicators are summarized in Table 2.
| Condition | Control Strategy | Overshoot (%) | Settling time (s) | THD (%) |
|---|---|---|---|---|
| Irradiance increase (1000→2000 W/m²) | Improved LADRC | 1.67 | 0.25 | 2.34 |
| Conventional LADRC | 2.77 | 0.28 | 2.51 | |
| Irradiance decrease (2000→1000 W/m²) | Improved LADRC | 1.39 | 0.24 | 2.12 |
| Conventional LADRC | 2.16 | 0.27 | 2.37 |
The simulation results clearly demonstrate that the proposed improved LADRC reduces the overshoot by approximately 1.1% and 0.77% under irradiance increase and decrease scenarios, respectively, compared to the conventional LADRC. Moreover, the total harmonic distortion (THD) of the grid current remains well below 5% in all cases, satisfying the IEEE 1547 standard. The improved LADRC also exhibits faster settling times, indicating superior dynamic performance.
6 Conclusion
In this work, I have presented an improved first-order linear active disturbance rejection control strategy for the DC-link voltage of a grid-connected solar inverter. The controller modifies the conventional LESO by introducing a differential feedforward term, which enhances disturbance rejection without compromising tracking accuracy or stability. Mathematical modeling, performance analysis, and simulation verification have been carried out. The key conclusions are summarized as follows:
- The proposed improved LADRC reduces the overshoot by 1.1% and 0.77% under irradiance increase and decrease conditions, respectively, compared to the conventional LADRC.
- The grid current THD remains below 5% under both operating scenarios, confirming high power quality.
- The closed-loop system is stable, as verified by the Routh-Hurwitz criterion, and the observer achieves zero steady-state tracking error.
The improved LADRC strategy presented in this paper offers a practical and effective solution for enhancing the dynamic response of solar inverters, with potential benefits for real-world photovoltaic installations.