In recent years, the rapid adoption of distributed generation systems has been driven by growing environmental concerns and the need for sustainable energy solutions. Among these, photovoltaic (PV) systems have gained significant traction, particularly in residential applications. As a critical interface between PV arrays and the grid, the solar inverter plays a pivotal role in determining power quality, system reliability, and grid stability. Traditional control strategies for solar inverters often face limitations in terms of dynamic response, robustness to disturbances, and seamless transition between grid-connected and islanded modes. This paper addresses these challenges by proposing a novel sliding mode voltage control scheme that enhances the schedulability of solar inverters, enabling precise tracking of active and reactive power dispatch commands while ensuring smooth mode transitions. We present a comprehensive analysis, supported by mathematical derivations, simulation results, and comparative insights, to demonstrate the efficacy of our approach.
The integration of solar inverters into modern power systems requires advanced control techniques to manage power flow, mitigate grid disturbances, and support grid services. Conventional methods such as PI control, proportional-resonant control, repetitive control, and deadbeat control have been widely studied. However, each has inherent drawbacks: PI control suffers from steady-state errors and limited dynamic performance; proportional-resonant control is constrained by bandwidth limitations; repetitive control is effective only for periodic disturbances; and deadbeat control demands high computational accuracy and system model precision. Moreover, dual-mode solar inverters typically employ hybrid voltage-current control, necessitating complex switching between control modes during grid-tied and stand-alone operation, which can lead to power quality issues and transient surges. Our work eliminates these complexities by maintaining voltage control across both modes, leveraging sliding mode control for its fast response, insensitivity to parameter variations, and robustness against load and grid perturbations.
To contextualize our research, we first describe the structure of a schedulable single-phase solar inverter system. The system comprises a DC source representing the PV array with maximum power point tracking and energy storage, a full-bridge inverter, an LC filter, cable impedance, local load, and grid connection points. The solar inverter is connected via switches that facilitate mode transitions: S1 for grid connection, S2 for local load selection, and S3 for system isolation. In grid-tied mode, the solar inverter delivers power to the grid and local load, while in islanded mode, it solely supplies the local load. The control objective varies with mode: in grid-tied operation, the solar inverter tracks active and reactive power dispatch commands; in stand-alone operation, it maintains high-quality voltage for the load. Our proposed control scheme unifies these objectives through a voltage-based approach, eliminating mode-switching complexities and enhancing system reliability.
The core of our methodology lies in the sliding mode voltage control for the solar inverter. We begin by deriving the reference voltage generation strategy for both operational modes. In grid-tied mode, the reference voltage is computed based on power dispatch instructions to achieve decoupled control of active and reactive power. Let \( P_{\text{ref}} \) and \( Q_{\text{ref}} \) denote the active and reactive power commands, respectively, and \( U_s \) represent the grid voltage. The reference current components are given by:
$$ I_p = \frac{P_{\text{ref}}}{U_s}, \quad I_q = \frac{Q_{\text{ref}}}{U_s} $$
These currents flow through the cable impedance \( R + jX \), producing voltage drops \( U_p \) and \( U_q \):
$$ U_p = I_p (R + jX), \quad U_q = I_q (R + jX) $$
Thus, the reference voltage for the solar inverter output is:
$$ U_{\text{cref}} = U_s + U_p + U_q = U_s + \frac{P_{\text{ref}} R + Q_{\text{ref}} X}{U_s} + j \frac{P_{\text{ref}} X – Q_{\text{ref}} R}{U_s} $$
This formulation allows independent adjustment of active and reactive power by modifying the magnitude and phase of the solar inverter’s output voltage. In stand-alone mode, the reference voltage is set according to user-defined specifications, such as amplitude and frequency, to ensure load power quality. The solar inverter’s control system then tracks this reference using sliding mode techniques, ensuring consistent performance across modes.
Next, we design the sliding mode voltage controller for the solar inverter. The state-space model of the inverter system is developed using the filter capacitor voltage \( u_c \) and its derivative as state variables. The system dynamics are described by:
$$ \frac{d}{dt} \begin{bmatrix} u_c \\ \dot{u}_c \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -\frac{1}{L_f C_f} & -\frac{1}{R_o C_f} \end{bmatrix} \begin{bmatrix} u_c \\ \dot{u}_c \end{bmatrix} + \begin{bmatrix} 0 \\ \frac{U_{\text{dc}}}{L_f C_f} \end{bmatrix} u $$
where \( L_f \) and \( C_f \) are the filter inductance and capacitance, \( R_o \) is the equivalent impedance (combining cable, load, and grid parameters), \( U_{\text{dc}} \) is the DC input voltage, and \( u \) represents the switching function of the inverter bridge, defined as \( u = 1 \) for upper switches on and \( u = -1 \) for lower switches on. To achieve voltage tracking, we define the error \( e = u_c – u_{\text{cref}} \) and construct a sliding surface \( s = c e + \dot{e} \), where \( c > 0 \) is a design constant. Using an exponential reaching law:
$$ \dot{s} = -\epsilon \operatorname{sign}(s) – k s $$
with \( \epsilon > 0 \) and \( k > 0 \), we derive the equivalent control signal \( u_{\text{eq}} \):
$$ u_{\text{eq}} = \frac{L_f C_f}{U_{\text{dc}}} \left( -\epsilon \operatorname{sign}(s) – k s + \ddot{u}_{\text{cref}} + c (\dot{u}_{\text{cref}} – \dot{u}_c) + \frac{u_c}{L_f C_f} + \frac{\dot{u}_c}{R_o C_f} \right) $$
This control law ensures that the solar inverter’s output voltage rapidly converges to the reference, with robustness against DC voltage fluctuations and load disturbances. The stability of the sliding mode control is verified by satisfying the condition \( s \dot{s} < 0 \), which guarantees finite-time convergence to the sliding surface. The inclusion of \( U_{\text{dc}} \) in the denominator provides inherent adaptability to variations in the solar inverter’s DC input, a common issue in PV systems due to changing irradiance levels.
To validate our proposed control scheme, we conducted extensive simulations in MATLAB/Simulink. The solar inverter parameters are summarized in Table 1, reflecting typical residential PV system configurations. We considered various scenarios to test the solar inverter’s performance under dynamic conditions, including power dispatch changes, DC voltage variations, mode transitions, and load perturbations. Each scenario was designed to stress the solar inverter’s schedulability and robustness, with results analyzed in terms of tracking accuracy, transient response, and power quality metrics.
| Parameter | Symbol | Value |
|---|---|---|
| Filter Inductance | \( L_f \) | 5 mH |
| Filter Capacitance | \( C_f \) | 10 μF |
| Cable Resistance | \( R \) | 0.5 Ω |
| Cable Reactance | \( X \) | 0.3 Ω |
| Switching Frequency | \( f_{\text{sw}} \) | 10 kHz |
| Sliding Surface Coefficient | \( c \) | 3000 |
| Reaching Law Coefficient | \( \epsilon \) | 5 |
| Reaching Law Coefficient | \( k \) | 2500 |
| DC Voltage Range | \( U_{\text{dc}} \) | 450–550 V |
The simulation timeline spanned 1 second, with the solar inverter operating in grid-tied mode from 0.125 s to 0.935 s, and in stand-alone mode otherwise. Active and reactive power dispatch commands were varied periodically to assess tracking performance, as shown in Figure 1 (simulated data). The solar inverter demonstrated rapid tracking with settling times under 0.02 s, negligible overshoot, and minimal cross-coupling between active and reactive power. This highlights the solar inverter’s ability to follow dynamic dispatch instructions, a key requirement for participative grid services. Moreover, the solar inverter maintained stable operation despite DC input voltage fluctuations between 450 V and 550 V, confirming the controller’s robustness to source variations common in solar energy systems.
Mode transition performance was evaluated during grid connection and disconnection events. The solar inverter seamlessly switched between modes without control reconfiguration, as evidenced by smooth voltage and current waveforms at the point of common coupling. Local load voltage remained stable during transitions, with total harmonic distortion (THD) below 0.5%, meeting power quality standards. The grid current THD was approximately 1%, within acceptable limits for solar inverter integration. These results underscore the advantage of voltage control over traditional hybrid approaches, eliminating transient surges and ensuring uninterrupted power supply to critical loads. A comparative analysis of control strategies is presented in Table 2, emphasizing the solar inverter’s superior performance under our sliding mode voltage control.
| Control Method | Tracking Speed | Robustness to Disturbances | Mode Transition Smoothness | Implementation Complexity |
|---|---|---|---|---|
| PI Control | Moderate | Low | Poor | Low |
| Proportional-Resonant | Fast | Moderate | Moderate | Medium |
| Repetitive Control | Slow | High (periodic only) | Poor | High |
| Deadbeat Control | Very Fast | Low | Moderate | Very High |
| Proposed Sliding Mode Voltage Control | Very Fast | Very High | Excellent | Medium |
Further analysis involved subjecting the solar inverter to sudden load changes, simulating real-world residential scenarios. At 0.54 s, the local load impedance shifted from \( 10 + j9.4 \, \Omega \) to \( 20 + j15.7 \, \Omega \). The solar inverter’s output voltage remained unaffected, with rapid adjustment of current to maintain power balance. The control system’s insensitivity to load variations is attributed to the sliding mode design, which enforces invariance to matched disturbances. This capability is crucial for solar inverters in isolated microgrids or during grid outages, where load dynamics can be unpredictable. Mathematical analysis of disturbance rejection can be expressed using the Lyapunov function \( V = \frac{1}{2} s^2 \), yielding:
$$ \dot{V} = s \dot{s} = s(-\epsilon \operatorname{sign}(s) – k s) = -\epsilon |s| – k s^2 < 0 $$
ensuring global asymptotic stability regardless of parameter uncertainties or external perturbations affecting the solar inverter.
The economic and operational benefits of our control scheme extend beyond technical performance. By enabling precise power scheduling, the solar inverter can participate in demand response programs, ancillary service markets, and voltage regulation initiatives. This enhances the value proposition of residential PV systems, potentially accelerating adoption. Additionally, the reduced need for mode-switching logic simplifies hardware and software design, lowering manufacturing costs for solar inverter manufacturers. Future work could explore extensions to three-phase solar inverters, integration with energy management systems, and experimental validation using hardware-in-the-loop platforms. We also plan to investigate adaptive sliding mode techniques to further optimize performance under varying environmental conditions.
In conclusion, we have presented a comprehensive sliding mode voltage control strategy for schedulable solar inverters. Our approach addresses key limitations of existing methods by providing decoupled active and reactive power control, seamless mode transitions, and robust operation against disturbances. The solar inverter’s performance, validated through detailed simulations, demonstrates fast tracking of dispatch commands, high power quality, and resilience to DC voltage and load variations. This research contributes to the advancement of distributed generation technologies, offering a practical solution for enhancing grid integration of solar energy. As the penetration of solar inverters continues to grow, such control innovations will be vital for building sustainable, reliable, and smart power systems.