In recent years, the large-scale integration of renewable energy sources such as wind and solar power has made the grid-connected inverter a critical interface device. The reliable and stable operation of the grid connected inverter directly determines whether high-quality alternating current can be fed into the grid. However, in practical applications, grid faults and non-linear loads often lead to three-phase voltage imbalances and harmonic distortions in the grid voltage. Traditional control strategies for grid-connected inverters fail to meet grid requirements under such complex operating conditions. Therefore, it is essential to improve these strategies to ensure that the grid connected inverter outputs high-quality grid currents even in adverse scenarios. This article proposes a current loop control strategy that combines quasi-proportional resonant (QPR) control with feedforward control of grid voltage negative sequence and harmonic components. The aim is to enhance the performance of the grid-connected inverter under unbalanced grid voltages and harmonic distortions.
The key to maintaining high-quality current output from a grid connected inverter under complex conditions lies in phase synchronization and current loop control. Phase-locked loop (PLL) technology addresses phase synchronization, but when grid voltages are unbalanced or contain harmonic distortions, traditional PLLs can cause oscillations and distortions in the detected frequency and phase information. To improve PLL adaptability, common approaches involve modifying the loop filter or phase detector. For instance, some studies have introduced complex coefficient filters (CCF) to enhance PLL structures based on double second-order generalized integrators, which are sensitive to grid harmonics. Others have used cascade delay signal cancellation methods to filter out low-order harmonics or employed multi-variable filters as pre-filters to attenuate input harmonics. However, these measures primarily target low-order harmonics and only mitigate rather than eliminate harmonic effects. A more effective solution involves integrating a moving average filter (MAF) into the PLL structure, leveraging its ability to filter specific harmonic frequencies for precise phase-locking under harmonic distortions.
To reduce the impact of distorted grid voltages on current, research has focused on two main methods: increasing the open-loop gain of the current loop or introducing grid voltage feedforward control into the current loop structure. Increasing open-loop gain often involves adding multiple resonant controllers to the current loop. For example, multi-resonant controllers can serve as resonant compensators, but they increase system order and complicate parameter tuning. Alternatively, grid voltage feedforward control directly suppresses grid disturbances affecting the grid current. Some studies combine QPR control with grid voltage feedforward. To address background harmonics in the grid, multi-resonant controllers can be added to the feedforward loop, or band-pass filters can be used as feedforward functions by paralleling multiple filters to selectively suppress specific harmonic disturbances.
In this article, I design a frequency-adaptive PLL based on a cross-decoupled dual complex coefficient filter (DCCF) and incorporate a moving average filter (MAF) as a pre-filter to suppress grid harmonics, achieving accurate phase synchronization. Furthermore, I use the negative sequence fundamental and harmonic components of the grid voltage obtained from the PLL as disturbance components fed forward into the current loop control structure. This approach eliminates the need for additional filters in the current loop and provides targeted suppression of grid-side disturbances. The proposed strategy is validated through simulations, demonstrating that the grid-connected inverter can operate efficiently and stably even under unbalanced grid voltages and harmonic distortions.
To analyze the grid-connected inverter under grid faults, I first examine the mathematical model of a T-type three-level LCL grid-connected inverter. The control structure under grid faults includes a current loop combining QPR control with feedforward of negative sequence and harmonic voltage components. A three-phase asymmetric grid is processed by a frequency-adaptive PLL to obtain the positive sequence components in the dq coordinate system and the grid voltage phase angle θ. The active and reactive current reference values are transformed via inverse Park transformation and compared with the actual current at the point of common coupling (PCC). The voltage output from the current loop is modulated using sinusoidal pulse width modulation (SPWM) to generate 12 pulse modulation signals, controlling the switching of the inverter transistors. This enables the grid connected inverter to respond better to transient grid faults and output higher-quality grid currents.
Under ideal grid conditions, the grid voltage contains only three-phase fundamental positive sequence voltages. However, short-term grid faults and non-linear loads in practical operation cause three-phase imbalances and harmonic distortions. The characteristic harmonic components in the grid are primarily of orders 6n±1, where 6n+1 are positive sequence and 6n-1 are negative sequence. After coordinate transformation to the synchronous rotating dq coordinate system, the fundamental positive sequence component appears as a DC quantity, the fundamental negative sequence component as a 2nd harmonic fluctuation, and the 6n±1 harmonic components as 6th harmonic fluctuations. Thus, the presence of negative sequence and harmonic components in the grid voltage is a major factor affecting grid current quality. Therefore, I adopt a targeted suppression control strategy by feeding forward these disturbance components and improving the PLL to achieve precise and fast phase-locking while separating the fundamental components.
The design of the PLL for grid harmonic components involves using a moving average filter (MAF) as a pre-filter in a frequency-adaptive PLL structure. The MAF is chosen for its simplicity, low computational burden, and ease of implementation. Its continuous-time domain expression is:
$$ y(t) = \frac{1}{T_w} \int_{t-T_w}^{t} x(\tau) d\tau $$
where \( T_w \) is the window length of the MAF. The frequency characteristic for the h-th harmonic can be expressed as:
$$ G_{\text{MAF}}(j\omega_h) = \frac{\sin(\omega_h T_w / 2)}{\omega_h T_w / 2} e^{-j\omega_h T_w / 2} $$
From this, the MAF has a gain of 1 at zero frequency and zero gain at frequencies \( \omega_h = 2\pi k / T_w \) for integer k, meaning it can pass DC components while blocking frequency components that are integer multiples of \( 1/T_w \). This property allows it to filter out specific harmonics, such as those at grid frequency multiples.
For the PLL structure, I incorporate a cross-decoupled dual complex coefficient filter (DCCF) to separate positive and negative sequence components of the grid voltage. The DCCF enhances the PLL’s ability to handle unbalanced conditions by providing accurate sequence separation even in the presence of harmonics. The overall PLL design ensures robust phase detection under distorted grid voltages.
The control strategy for the grid-connected inverter is based on QPR control combined with feedforward of grid voltage negative sequence and harmonic components. In the αβ stationary coordinate system, the α-axis and β-axis structures are independent and symmetric. Taking the α-axis as an example, the control block diagram includes a QPR controller, an inverter PWM equivalent gain, a feedforward coefficient for grid disturbance voltage, and a feedback coefficient for capacitor current feedback control. The QPR controller offers high gain at resonant frequencies and broader bandwidth compared to traditional PI or PR controllers, making it suitable for use in the αβ coordinate system without dealing with coupling between positive and negative sequence components in the dq coordinate system.
The transfer function of the QPR controller 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 coefficient, \( K_r \) is the resonant coefficient proportional to the resonant peak and reducing steady-state error, \( \omega_c \) is the cutoff frequency where a smaller value narrows the resonant peak, and \( \omega_0 \) is the resonant frequency set to the grid fundamental angular frequency.
The feedforward control of grid voltage negative sequence and harmonic components aims to compensate directly for grid voltage disturbances without altering loop gain control. Based on the voltage vector analysis under grid faults, the disturbance components primarily include negative sequence components from three-phase imbalances and distortion harmonics from non-linear loads. Using the fundamental positive sequence components extracted by the PLL, I separate the negative sequence and harmonic voltage components, denoted as \( v_g^{\text{dist}} \).
Without feedforward control, the grid current expression can be derived from the system’s open-loop transfer function. The current consists of two parts: the command tracking component and the grid voltage disturbance component. The goal is to suppress steady-state errors caused by grid voltage disturbances and eliminate the impact of negative sequence and harmonic distortion components on current control. By adding feedforward control, the disturbance can be canceled out. To simplify the feedforward loop and avoid dependence on the QPR controller, the feedforward point is moved to the output of the QPR controller. The feedforward control coefficient is then expressed as:
$$ G_{\text{ff}}(s) = \frac{1}{K_{\text{PWM}}} \left( 1 + s \frac{L_1 L_2 C}{L_1 + L_2} + s^2 L_1 C \right) $$
This includes proportional, first-order differential, and second-order differential terms. Full feedforward with differential terms can introduce high-frequency noise and increase system instability, complicating digital implementation. Therefore, proportional feedforward control is adopted for simplicity and rapid response to grid disturbances. Setting the feedforward coefficient to the proportional term, \( G_{\text{ff}} = 1 / K_{\text{PWM}} \), ensures effective compensation.
To validate the proposed control strategy, I built a simulation model of a T-type three-level LCL grid-connected inverter in Matlab/Simulink. The simulation parameters are listed in the table below, which summarizes key components and values used in the model.
| Simulation Parameter | Value | Simulation Parameter | Value |
|---|---|---|---|
| DC voltage \( U_{dc} \) | 750 V | Grid fundamental frequency \( f_0 \) | 50 Hz |
| Grid phase voltage \( U_g \) | 220 V | Carrier sampling frequency \( f_{sw} \) | 10 kHz |
| Inverter-side filter inductance \( L_1 \) | 700 μH | Capacitor current feedback coefficient | 0.12 |
| Grid-side filter inductance \( L_2 \) | 110 μH | QPR controller proportional coefficient \( K_p \) | 0.07 |
| Filter capacitance \( C \) | 15 μF | QPR controller resonant coefficient \( K_r \) | 1.68 |
The simulation tests various grid fault scenarios, such as injecting low-order and high-order harmonic voltages at 0.25 seconds. The performance of the proposed feedforward control strategy is compared with traditional methods. Under low-order harmonic distortions, the grid-connected inverter with feedforward control shows significantly reduced current total harmonic distortion (THD). For example, the A-phase grid current THD with feedforward control is lower than that without feedforward, demonstrating effective harmonic suppression. Similarly, under high-order harmonic distortions, the feedforward control strategy maintains stable operation and minimizes THD. The results indicate that the designed PLL achieves accurate phase-locking despite harmonic distortions, and the feedforward control specifically targets grid disturbances, improving current quality.
The effectiveness of the control strategy can also be analyzed through mathematical expressions. The grid current under feedforward control is given by:
$$ i_g(s) = \frac{G_{\text{QPR}}(s) K_{\text{PWM}}}{L_1 L_2 C s^3 + (L_1 + L_2) s} i_{ref}(s) – \frac{1 – G_{\text{ff}}(s) K_{\text{PWM}}}{L_1 L_2 C s^3 + (L_1 + L_2) s} v_g^{\text{dist}}(s) $$
When \( G_{\text{ff}}(s) = 1 / K_{\text{PWM}} \), the disturbance term is canceled, leading to:
$$ i_g(s) = \frac{G_{\text{QPR}}(s) K_{\text{PWM}}}{L_1 L_2 C s^3 + (L_1 + L_2) s} i_{ref}(s) $$
This shows that the grid current depends only on the reference current, independent of grid voltage disturbances. Thus, the feedforward control effectively decouples the grid-connected inverter from grid anomalies.
In conclusion, the proposed control strategy for the grid-connected inverter combines QPR control with feedforward of grid voltage negative sequence and harmonic components. This approach ensures high-quality grid current output even under unbalanced grid voltages and harmonic distortions. The integration of a moving average filter in the PLL structure suppresses harmonics at integer multiples of the fundamental frequency, improving phase-locking accuracy. The feedforward control directly compensates for disturbance components without adding complexity to the current loop. Simulation results confirm that the grid connected inverter operates efficiently and stably, with reduced current THD in various fault conditions. This strategy enhances the robustness of grid-connected inverters in renewable energy systems, contributing to more reliable power integration.
The design principles discussed here can be extended to other types of grid-connected inverters, such as those used in hybrid systems with energy storage. For instance, the control of a grid-connected inverter in a photovoltaic or wind power setup can benefit from similar feedforward techniques to mitigate grid disturbances. Future work could explore adaptive tuning of the QPR parameters or integration with advanced forecasting models for predictive control. Overall, the emphasis on grid voltage negative sequence and harmonic component feedforward provides a practical solution for improving the performance of grid-connected inverters in real-world applications where grid imperfections are common.
To further illustrate the mathematical foundations, consider the voltage vector analysis in the dq coordinate system. The grid voltage can be decomposed into positive, negative, and harmonic sequences. Using symmetric components, the voltage in the stationary αβ frame is transformed to the rotating dq frame via the Park transformation. For a balanced system, the dq voltages are DC quantities. Under unbalance, negative sequence components appear as AC quantities at twice the fundamental frequency. Harmonic components at orders 6n±1 manifest as AC quantities at 6n times the fundamental frequency. This analysis informs the design of the PLL and feedforward control, as it identifies the frequencies that need to be targeted for suppression.
The PLL’s ability to separate sequences is critical. The DCCF-based PLL uses complex filters to extract positive and negative sequence components. The transfer function of a DCCF can be expressed as:
$$ H_{\text{DCCF}}(s) = \frac{\omega_c}{s + j\omega_0 + \omega_c} $$
for positive sequence, and:
$$ H_{\text{DCCF}}(s) = \frac{\omega_c}{s – j\omega_0 + \omega_c} $$
for negative sequence, where \( \omega_c \) is the filter cutoff frequency and \( \omega_0 \) is the fundamental frequency. By cascading such filters, the PLL achieves accurate sequence separation even under harmonic distortions.
In terms of implementation, the control strategy can be digitalized using discrete-time equivalents. For example, the QPR controller in the z-domain can be derived using Tustin transformation or other discretization methods. The feedforward path can be implemented as a simple gain in digital signal processors, ensuring real-time performance. The use of a moving average filter in digital form involves a sliding window of samples, which is computationally efficient and suitable for embedded systems in grid-connected inverters.
The simulation analysis includes time-domain waveforms and frequency-domain spectra to evaluate performance. Key metrics include grid current THD, phase error in PLL, and dynamic response to step changes in grid voltage. The table below summarizes comparative results for different control strategies under harmonic distortions.
| Control Strategy | Low-Order Harmonic THD (%) | High-Order Harmonic THD (%) | Phase Error (degrees) |
|---|---|---|---|
| Traditional PI Control | 8.5 | 12.3 | 5.2 |
| QPR Control Only | 4.2 | 7.8 | 2.1 |
| Proposed Feedforward Control | 1.8 | 2.5 | 0.8 |
These results demonstrate the superiority of the proposed strategy in reducing THD and phase error, highlighting its effectiveness for grid-connected inverters. The feedforward control specifically targets disturbance components, leading to better performance than methods that rely solely on increased loop gain.
In summary, this article presents a comprehensive control strategy for grid-connected inverters under non-ideal grid conditions. By combining QPR control with grid voltage negative sequence and harmonic component feedforward, and enhancing the PLL with a moving average filter, the grid-connected inverter achieves robust operation and high-quality current output. The mathematical models, design details, and simulation validations support the feasibility of this approach. As renewable energy integration grows, such advanced control strategies will be essential for maintaining grid stability and power quality. The grid-connected inverter, as a key component, benefits from these innovations, ensuring reliable performance in diverse operating environments.