In the context of global energy transition, the utilization of renewable energy sources has become a pivotal strategy to address energy crises and reduce carbon emissions. In recent years, wind and solar power generation systems have been widely promoted worldwide. As the primary interface between renewable energy systems and the grid, the utility interactive inverter has garnered extensive application and research attention. Traditional three-phase utility interactive inverters require AC side voltage sensors for control, which not only increases cost but also compromises system reliability. This paper investigates a control strategy for utility interactive inverters that eliminates the need for AC side voltage sensors, thereby enhancing economic efficiency and robustness. The proposed method integrates a grid voltage observer based on a second-order generalized integrator (SOGI) with a quasi-proportional resonant (QPR) control algorithm employing capacitor current feedback active damping, achieving precise control of grid-connected current. Simulation results validate the effectiveness of this approach, demonstrating its potential for practical implementation in modern power systems.
The utility interactive inverter is a critical component in renewable energy integration, converting DC power from sources like photovoltaic panels or wind turbines into AC power synchronized with the grid. Conventional control schemes, such as grid voltage-oriented vector control, rely on measurements of AC grid voltage, grid current, and DC bus voltage, necessitating multiple sensors. This increases system complexity, cost, and failure points. To address these issues, sensorless control techniques have been developed, but challenges like integrator saturation or noise amplification persist. This research focuses on a sensorless solution for a three-phase LCL-filter-based utility interactive inverter, leveraging advanced observers and controllers to maintain high performance without voltage sensors.
The topology of a three-phase LCL-filter-based utility interactive inverter is illustrated in the figure above. It consists of a DC voltage source, a three-phase inverter bridge, an LCL filter, and the grid. The LCL filter, comprising inverter-side inductors, grid-side inductors, and filter capacitors, offers superior high-frequency harmonic attenuation compared to single-inductor filters. However, it introduces resonance issues that must be damped actively or passively. In this study, active damping via capacitor current feedback is adopted to stabilize the system without additional passive components. The mathematical model of the utility interactive inverter is derived in the stationary reference frame (αβ) to facilitate control design.
The three-phase utility interactive inverter with an LCL filter can be modeled using Kirchhoff’s laws. Assuming symmetrical components, the parameters are defined as follows: inverter-side inductance \(L_i\) and resistance \(R_i\), grid-side inductance \(L_g\) and resistance \(R_g\), and filter capacitance \(C_f\). The DC bus voltage is \(V_{dc}\), and the inverter output voltages are \(V_{i\alpha}\) and \(V_{i\beta}\) after Clark transformation. The inverter-side currents are \(i_{L\alpha}\) and \(i_{L\beta}\), grid currents are \(i_{g\alpha}\) and \(i_{g\beta}\), and capacitor currents are \(i_{c\alpha}\) and \(i_{c\beta}\). The system equations in the αβ frame are:
$$ \begin{aligned} V_{g\alpha} &= V_{c\alpha} – L_g \frac{di_{g\alpha}}{dt} – R_g i_{g\alpha} \\ V_{g\beta} &= V_{c\beta} – L_g \frac{di_{g\beta}}{dt} – R_g i_{g\beta} \\ i_{c\alpha} &= C_f \frac{dV_{c\alpha}}{dt} = i_{L\alpha} – i_{g\alpha} \\ i_{c\beta} &= C_f \frac{dV_{c\beta}}{dt} = i_{L\beta} – i_{g\beta} \\ V_{i\alpha} &= V_{c\alpha} + L_i \frac{di_{L\alpha}}{dt} + R_i i_{L\alpha} \\ V_{i\beta} &= V_{c\beta} + L_i \frac{di_{L\beta}}{dt} + R_i i_{L\beta} \end{aligned} $$
These equations form the basis for designing the voltage observer and current controller. To eliminate the AC voltage sensor, a grid voltage observer based on a second-order generalized integrator (SOGI) is proposed. The SOGI is an adaptive filter that tracks sinusoidal signals at a specified frequency, providing in-phase and quadrature outputs. Its transfer functions are:
$$ H_d(s) = \frac{v^{\wedge}(s)}{v(s)} = \frac{k\omega s}{s^2 + k\omega s + \omega^2} $$
$$ H_q(s) = \frac{qv^{\wedge}(s)}{v(s)} = \frac{k\omega^2}{s^2 + k\omega s + \omega^2} $$
where \(v\) is the input signal, \(v^{\wedge}\) and \(qv^{\wedge}\) are the filtered in-phase and quadrature outputs, \(\omega\) is the target frequency (e.g., 314 rad/s for 50 Hz), and \(k\) is a gain coefficient optimized for damping. For this utility interactive inverter, the observer estimates grid voltage by processing known quantities. The inverter output voltages \(V_{i\alpha}\) and \(V_{i\beta}\) are computed from the switching states and DC bus voltage:
$$ V_{ix} = S_{ix} \cdot V_{dc}, \quad x \in \{a, b, c\} $$
where \(S_{ix}\) is the switching function. After Clark transformation, \(V_{i\alpha}\) and \(V_{i\beta}\) are obtained. Using measured inverter-side currents \(i_{L\alpha}\) and \(i_{L\beta}\), the capacitor voltages are estimated via SOGI:
$$ \begin{aligned} V_{c\alpha}^{\wedge} + j qV_{c\alpha}^{\wedge} &= \text{SOGI} \left( V_{i\alpha} – L_i \frac{di_{L\alpha}}{dt} – R_i i_{L\alpha} \right) \\ V_{c\beta}^{\wedge} + j qV_{c\beta}^{\wedge} &= \text{SOGI} \left( V_{i\beta} – L_i \frac{di_{L\beta}}{dt} – R_i i_{L\beta} \right) \end{aligned} $$
Subsequently, with measured grid currents \(i_{g\alpha}\) and \(i_{g\beta}\), the grid voltages are estimated as:
$$ \begin{aligned} V_{g\alpha}^{\wedge} + j qV_{g\alpha}^{\wedge} &= \text{SOGI} \left( V_{c\alpha}^{\wedge} – L_g \frac{di_{g\alpha}}{dt} – R_g i_{g\alpha} \right) \\ V_{g\beta}^{\wedge} + j qV_{g\beta}^{\wedge} &= \text{SOGI} \left( V_{c\beta}^{\wedge} – L_g \frac{di_{g\beta}}{dt} – R_g i_{g\beta} \right) \end{aligned} $$
This observer provides accurate grid voltage estimates without physical sensors, crucial for the utility interactive inverter’s control. The estimated grid voltage is then used for synchronization via a software phase-locked loop (PLL), generating reference currents for power control.
For current control, a quasi-proportional resonant (QPR) controller is employed in the stationary frame to achieve zero steady-state error for sinusoidal references. The QPR controller transfer function is:
$$ G_{\text{QPR}}(s) = K_p + \frac{2K_r \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$
where \(K_p\) is the proportional gain, \(K_r\) is the resonant gain, \(\omega_0\) is the fundamental frequency, and \(\omega_c\) is a cutoff frequency that broadens the resonant peak for robustness against frequency variations. To damp LCL resonance, capacitor current feedback active damping is integrated, equivalent to a virtual resistor in parallel with the filter capacitor. The control block diagram for the α-axis is shown below (similar for β-axis):
The control loop includes the QPR controller, inverter gain \(G_{\text{pwm}}\), and plant model. The capacitor current feedback coefficient \(k_c\) is designed to stabilize the system. Based on system specifications like steady-state error, phase margin, and gain margin, parameters are tuned. For instance, with the utility interactive inverter parameters listed in Table 1, typical values are \(K_p = 0.4\), \(K_r = 100\), \(\omega_c = 5\) rad/s, and \(k_c = 30\).
| Parameter | Value |
|---|---|
| DC Bus Voltage | 600 V |
| Grid Voltage | 380 V (line-to-line RMS) |
| Grid Frequency | 50 Hz |
| Switching Frequency | 10 kHz |
| Inverter-Side Inductance | 2 mH |
| Grid-Side Inductance | 150 μH |
| Filter Capacitance | 10 μF |
| Inverter-Side Resistance | 0.1 Ω |
| Grid-Side Resistance | 0.05 Ω |
The overall control structure for the sensorless utility interactive inverter combines the SOGI-based voltage observer and QPR current controller. The grid voltage phase from the PLL is used to generate reference currents based on active and reactive power commands. The current controller then drives the inverter to track these references accurately. This approach reduces cost and enhances reliability by eliminating voltage sensors, making the utility interactive inverter more suitable for large-scale renewable energy systems.
Simulation studies were conducted in MATLAB/Simulink to validate the proposed method. The utility interactive inverter was tested under steady-state and dynamic conditions. The grid voltage observer performance is shown in Figure 1, comparing estimated and actual grid voltages. The observer tracks the voltage accurately with minimal phase delay, demonstrating its feasibility for sensorless operation. The utility interactive inverter’s output current and voltage waveforms are presented in Figure 2, showing a sinusoidal grid current with low distortion. The total harmonic distortion (THD) of the grid current is measured at 0.87%, meeting grid standards. The system maintains stable operation even under parameter variations, highlighting the robustness of the QPR controller and active damping.
Further analysis includes dynamic response tests, such as step changes in power reference. The utility interactive inverter responds quickly with minimal overshoot, confirming effective current control. The absence of voltage sensors does not degrade performance, as the observer provides reliable estimates. Comparative studies with traditional PI-based controllers show superior tracking accuracy and harmonic rejection for the QPR-based utility interactive inverter. Additionally, the sensorless approach reduces hardware complexity, which is beneficial for maintenance and scalability in field installations.
The utility interactive inverter’s efficiency and power quality are critical for grid integration. The proposed control strategy ensures high efficiency by minimizing switching losses and optimizing current waveforms. The use of an LCL filter with active damping reduces filter size and cost compared to passive solutions. The sensorless technique further enhances the utility interactive inverter’s appeal for commercial applications, where cost-effectiveness and reliability are paramount. Future work could explore adaptive observers for non-ideal grid conditions, such as voltage dips or harmonics, to improve the utility interactive inverter’s resilience.
In conclusion, this research presents a comprehensive control solution for a three-phase utility interactive inverter without AC side voltage sensors. The SOGI-based grid voltage observer accurately estimates grid voltages, eliminating the need for physical sensors. Combined with a QPR controller and capacitor current feedback active damping, the system achieves precise current control and LCL resonance damping. Simulation results validate the method’s effectiveness, showing low THD and stable operation. This approach reduces cost and improves reliability, making it a promising technology for modern renewable energy systems. The utility interactive inverter thus becomes more competitive and adaptable, supporting global efforts toward sustainable energy.
The implications of this study extend beyond theoretical insights. Practical implementation of the sensorless utility interactive inverter can lead to significant cost savings in solar and wind farms. By reducing sensor count, system failure rates are lowered, and maintenance becomes simpler. Moreover, the control algorithms are computationally efficient, suitable for digital signal processors (DSPs) or microcontrollers. As renewable energy penetration grows, advanced utility interactive inverters will play a crucial role in grid stability and power quality. This research contributes to that goal by offering a robust, sensorless control framework that can be extended to other power converter topologies.
To summarize, the key contributions of this paper are: (1) development of a SOGI-based voltage observer for sensorless operation of utility interactive inverters; (2) integration of QPR control with active damping for high-performance current regulation; and (3) demonstration via simulation of the system’s efficacy. The utility interactive inverter, as a core element in renewable energy systems, benefits from these innovations, paving the way for wider adoption of clean energy technologies.