Grid Current Distortion Suppression Based on Harmonic Voltage Feedforward for Grid-Forming Inverters

Abstract

A grid-forming converter (GFM) controls power output by adjusting the phase angle and amplitude of its output voltage, providing voltage and frequency support to the power system and effectively enhancing system stability. However, it has limitations in current control, influencing the current only indirectly through voltage regulation, which results in weaker control over current waveform quality. In the context of a large number of renewable energy generation units being connected to the grid, harmonics in the grid voltage can lead to excessively high harmonic content in the grid current, exceeding standard limits and causing oscillations. To solve this problem, this paper proposes a control strategy of harmonic voltage feedforward compensation to suppress grid current distortion. The proposed control strategy extracts harmonic voltages from the output port of the GFM converter through a harmonic extraction module, processes them via a feedforward factor, and introduces the resulting signals into the converter’s control loop as feedforward compensation terms. This allows the converter’s output voltage to compensate for the harmonic components in the grid, achieving the improvement of grid current and reducing the total harmonic distortion (THD) value. The effectiveness of the proposed control strategy is verified by simulation results.

1. Introduction

In recent years, the rapid integration of renewable energy sources, such as wind and photovoltaic power, into power systems has significantly transformed the energy landscape [1,2]. As most renewable energy generation requires long-distance transmission, the equivalent impedance of the lines is relatively high, leading to weak grid characteristics where line impedance cannot be ignored [3]. Furthermore, renewable energy generation is mostly integrated into the grid through power electronic converters. The presence of a large number of nonlinear loads in the grid, coupled with the increasingly severe distortion of grid harmonic voltages, will result in significant harmonic currents in the output current of the grid-connected converters, severely degrading the quality of the grid current.

Currently, the grid-connected control methods for power electronic converters mainly include grid-following (GFL) control and grid-forming (GFM) control. GFL converters operate as current sources, synchronizing with the grid voltage through phase-locked loops (PLLs). While this approach is widely adopted, GFL converters cannot provide voltage or frequency support in scenarios where grid stability is compromised [4,5,6]. To address this limitation, GFM converters have been developed to emulate the behavior of synchronous generators by incorporating virtual inertia and damping control. This enables GFM converters to autonomously establish and regulate grid voltage and frequency without relying on an external grid reference [7,8]. Common GFM control techniques include droop control, virtual synchronous generator (VSG), and virtual oscillator control (VOC). In the following text, droop control is taken as an example. Ref. [9] investigates the stability characteristics of GFM- and GFL-controlled converters under isolated microgrid conditions, providing theoretical support for capacity planning, parameter design, and controller optimization of these two types of inverters in isolated microgrids. However, it does not investigate the operational characteristics of GFM-controlled converters under grid-connected conditions. Refs. [10,11] propose GFM technology, and analyze its positioning and role in the new power system, but their research is based on ideal grid conditions.

Despite their advantages, GFM converters face a critical challenge: their voltage-source nature inherently limits their ability to directly control the output current. In grid-connected operation, when the grid voltage contains harmonic components, the output current of GFM converters can become severely distorted, significantly impacting power quality. While existing research has made strides in improving the voltage quality and stability of GFM converters, the issue of harmonic-induced current distortion remains largely unaddressed. For instance, ref. [12] proposed a virtual impedance-based loop gain reshaping strategy to enhance stability in weak grids, but this approach does not explicitly target harmonic current suppression. Similarly, ref. [13] introduced a dual-sequence control strategy in the dq rotating frame to mitigate unbalanced voltage conditions, yet its focus remains on voltage regulation rather than current quality. Other studies, such as [14], have explored unified droop control for harmonic current distribution among parallel units, but these methods are complex and do not directly address current distortion in GFM converters.

As summarized in

Table 1. Comparison of existing methods for improving GFM converter performance.

Method	Characteristics	Advantages	Disadvantages
Virtual Impedance [12]	Reshapes loop gain to improve stability	Enhances weak-grid stability	Limited effectiveness in suppressing harmonic currents
Dual-Sequence Control [13]	Suppresses negative-sequence voltage components	Effective under unbalanced grids	Does not address harmonic current distortion
Unified Droop Control [14]	Distributes harmonic currents based on unit capacities	Improves PCC voltage quality	Complex implementation, limited focus on current quality
Auxiliary Current Loop [15]	Limits overcurrent during faults using low-pass filters	Prevents overcurrent during faults	Limited applicability to harmonic suppression in normal operation
Auxiliary Harmonic Elimination Unit [16]	Cancels ripple components via symmetric current generation	Reduces harmonic distortion	Untested for GFM architectures

, existing methods primarily focus on voltage regulation, fault resilience, or harmonic current distribution, with limited attention to direct harmonic current suppression in GFM converters. This gap is particularly critical in grid-connected operation, where harmonic pollution can severely degrade current quality.

To solve this issue, this paper proposes a harmonic voltage feedforward compensation control strategy to suppress the current distortion of the grid. The remaining sections of this paper are organized as follows. The grid current distortion problem in the system studied is first described in Section 2, and the proposed control scheme is proposed in Section 3. In Section 4, the simulation results verify the effectiveness of the proposed control scheme. The conclusion and future work are given in Section 5.

2. Mechanism of GFM Grid Current Distortion Under Distorted Grid Conditions

Figure 1 presents the topology and control block diagram of a GFM converter based on droop control. In the diagram, U_dc represents the DC-side battery voltage, while u_abc and i_abc represent the output voltage and grid current of the converter, respectively.

The control of GFM converters adopts a typical dual-loop droop structure for voltage and current, and the droop controller can be mathematically expressed as

$$\left\{\begin{array}{c}\omega ={\omega }_0+K_p\left(P_{ref}-P\right)\\ E=E_0+K_q\left(Q_{ref}-Q\right)\\ \theta ={\displaystyle \int \omega \mathrm{d}t}\end{array}\right.$$

(1)

For the grid-connected system shown in Figure 1, based on circuit principles, the mathematical model of the inverter in the three-phase stationary coordinate system can be derived as shown in Equation (2).

$$\left\{\begin{array}{c}{e}_a-u_a=L_f{\displaystyle \frac{d{i}_{La}}{dt}}+R_f{i}_{La}\\ e_b-u_b=L_f{\displaystyle \frac{d{i}_{Lb}}{dt}}+R_f{i}_{Lb}\\ e_c-u_c=L_f{\displaystyle \frac{d{i}_{Lc}}{dt}}+R_f{i}_{Lc}\\ i_{La}-i_a=C_f{\displaystyle \frac{d{u}_a}{dt}}\\ i_{Lb}-i_b=C_f{\displaystyle \frac{d{u}_b}{dt}}\\ i_{Lc}-i_c=C_f{\displaystyle \frac{d{u}_c}{dt}}\end{array}\right.$$

(2)

The differential equations in the dq two-phase rotating coordinate system are as follows:

$$\left\{\begin{array}{c}{L}_f{\displaystyle \frac{d{i}_{Ld}}{dt}}=e_d-u_d+\omega L_f{i}_{Lq}-R_f{i}_{Ld}\\ L_f{\displaystyle \frac{d{i}_{Lq}}{dt}}=e_q-u_q-\omega L_f{i}_{Ld}-R_f{i}_{Lq}\\ C_f{\displaystyle \frac{d{u}_d}{dt}}=i_{Ld}-i_d+\omega C_f{u}_q\\ C_f{\displaystyle \frac{d{u}_d}{dt}}=i_{Ld}-i_d+\omega C_f{u}_q\end{array}\right.$$

(3)

It can be seen from the above equations that the system in the dq coordinate system is a coupled system, and the decoupling control of voltage and current is required. Decoupling control can be achieved in a dual-loop control of the voltage and current. Figure 2 illustrates the simplified control structure of the dual closed-loop system for the voltage and current, where G_v(s) = K_vp + K_vi/s and G_i(s) = K_ip + K_ii/s. Z_f(s) = sL_f + R_f and Z_C(s) = 1/(sC_f), where L_f is the filter inductance, R_f is the equivalent internal resistance of the filter inductance, and C_f is the filter capacitance. U_ref stands for the reference input voltage for the voltage loop load, and K_pwm represents the equivalent gain of the inverter’s SPWM (sinusoidal pulse width modulation).

According to Figure 2, when both U_ref(s) and I(s) are regarded as inputs, the transfer function of the inverter’s output voltage U(s) can be obtained as follows:

$$U\left(s\right)=G_u\left(s\right)U_{ref}\left(s\right)-Z\left(s\right)I\left(s\right)$$

(4)

where G_u(s) represents the voltage gain transfer function and Z(s) represents the equivalent output impedance of the inverter.

$$G_u(s)={\displaystyle \frac{K_{ip}{K}_{vp}{K}_{pwm}{s}^2+\left(K_{ip}{K}_{vi}+K_{ii}{K}_{vp}\right)K_{pwm}s+K_{ii}{K}_{vi}{K}_{pwm}}{L_f{C}_f{s}^4+\left(R_f+K_{ip}{K}_{pwm}\right)C_f{s}^3+\left(1+C_f{K}_{ii}{K}_{pwm}+K_{ip}{K}_{vp}{K}_{pwm}\right)s^2+\left(K_{ip}{K}_{vi}+K_{ii}{K}_{vp}\right)K_{pwm}s+K_{ii}{K}_{vi}{K}_{pwm}}}$$

(5)

$$Z(s)={\displaystyle \frac{L_f{s}^3+\left(R_f+K_{ip}{K}_{pwm}\right)s^2+K_{ii}{K}_{pwm}s}{L_f{C}_f{s}^4+\left(R_f+K_{ip}{K}_{pwm}\right)C_f{s}^3+\left(1+C_f{K}_{ii}{K}_{pwm}+K_{ip}{K}_{vp}{K}_{pwm}\right)s^2+\left(K_{ip}{K}_{vi}+K_{ii}{K}_{vp}\right)K_{pwm}s+K_{ii}{K}_{vi}{K}_{pwm}}}$$

(6)

Combined with voltage–current dual-loop control, the GFM inverter based on droop control can be regarded as a controlled voltage source in a series with an equivalent impedance, so that the equivalent circuit is like two voltage sources working in parallel through two impedances, as shown in Figure 3.

The grid current I(s) can be expressed as

$$I(s)={\displaystyle \frac{U_{ref}\left(s\right)}{Z_{inv}\left(s\right)}}-{\displaystyle \frac{U_g\left(s\right)}{Z_{grid}\left(s\right)}}$$

(7)

where Z_inv(s) is denoted as the impedance at the inverter side, and Z_grid(s) is denoted as the impedance at the grid side, which can be expressed as

$$Z_{inv}\left(s\right)={\displaystyle \frac{Z\left(s\right)+Z_g\left(s\right)}{G_u\left(s\right)}}$$

(8)

$$Z_{grid}\left(s\right)=Z\left(s\right)+Z_g\left(s\right)$$

(9)

According to (7), the grid current of the inverter partly depends on the voltage and impedance of the grid side, and partly depends on the output voltage and impedance of the inverter side. Therefore, when the grid voltage contains harmonics, harmonic current will be generated through the impedance of the grid side and injected into the grid, causing distortion of the grid current.

3. Proposed Scheme for Improving Grid Current Quality Control

In order to suppress the harmonic current generated by grid voltage distortion, this paper proposes a control strategy using harmonic voltage feedforward compensation. The proposed control structure is shown in Figure 4.

3.1. Analysis of Harmonic Current Suppression Principles

The main power circuit employs a three-phase full-bridge design, and its control loop architecture encompasses an outer power loop, a voltage–current loop, a harmonic extraction module, and a feedforward coefficient module. In scenarios where the grid voltage contains harmonic components, the output current of the inverter is inevitably perturbed by the harmonic voltage on the grid side, leading to a significant increase in harmonic content. Given the difficulty of directly measuring the grid voltage u_gabc, this study opted to indirectly extract harmonic voltage information by monitoring the inverter output port voltage u_abc. Subsequently, these extracted harmonic voltage components undergo coordinate transformation processing and are superimposed with the output signals of the voltage–current loop to generate six PWM drive signals, which precisely control the switching state of the inverter’s bridge arms. Building upon this foundation, when harmonic components of the same frequency as the grid voltage are incorporated into the inverter’s output voltage, the harmonic pollution in the inverter’s output current is effectively suppressed, thereby achieving optimization of the grid-connected current.

To facilitate the analysis of the effectiveness of the strategy proposed in this paper, we initially set the feedforward coefficient to 1 at the initial stage, assuming that the grid harmonic voltage can be fully feedforwarded into the control system. Based on this assumption, we derive the impedance characteristics of the GFM inverter on both the grid side and the converter side under the proposed control strategy. The equivalent circuit of the inverter is shown in Figure 5. Through the harmonic signal extraction, the harmonic component of the inverter output voltage U_h(s) can be obtained as follows:

$$U_h\left(s\right)=U_g\left(s\right)-U_g\left(s\right)D\left(s\right)=G\left(s\right)U_g\left(s\right)$$

(10)

where G(s) is the transfer function of the harmonic signal extraction link, D(s) is the closed-loop transfer function of the SOGI, and its expression is given in (15).

$$G\left(s\right)={\displaystyle \frac{s^2+{\omega }_h^2}{s^2+k{\omega }_{h}s+{\omega }_h^2}}$$

(11)

As can be seen from Figure 5, the instruction voltage at the bridge arm of the grid-forming inverter changes, and the grid-connected current at this time is

$$I\left(s\right)={\displaystyle \frac{U_{ref}\left(s\right)}{Z_{inv2}\left(s\right)}}-{\displaystyle \frac{U_g\left(s\right)}{Z_{grid2}\left(s\right)}}$$

(12)

where Z_inv2(s) and Z_grid2(s) are the impedances of the inverter side and the grid side after the harmonic voltage feedforward compensation control is adopted:

$$Z_{inv2}\left(s\right)={\displaystyle \frac{Z\left(s\right)+Z_g\left(s\right)}{G_u\left(s\right)}}$$

(13)

$$Z_{grid2}\left(s\right)={\displaystyle \frac{Z\left(s\right)+Z_g\left(s\right)}{1-G\left(s\right)G_u\left(s\right)}}$$

(14)

By comparing Equations (8) and (9), the inverter side impedance of the GFM inverter is not affected by the harmonic voltage feedforward, while the grid side impedance changes. Figure 6 presents the Bode plot of the grid-side impedance before and after the introduction of harmonic voltage feedforward.

From Figure 6, it can be observed that after introducing the harmonic voltage feedforward, the grid-side impedance of the grid-connected inverter remained unchanged at the fundamental frequency, allowing for normal power transmission. At low harmonic frequencies, the grid-side impedance increases significantly. This verifies that the feedforward control reshapes the grid-side impedance characteristics, alleviates potential resonance issues, and effectively mitigates the impact of distorted grid harmonic voltages on the grid-connected current of the inverter, thereby improving the current quality.

3.2. Harmonic Extraction Method Based on Fundamental Component Subtraction

The composition of harmonic voltage at the inverter’s output port is complex, making it difficult to directly extract harmonic components. The traditional method requires designing independent Second-Order Generalized Integrator (SOGI) filters for each specific harmonic frequency [17], such as the 5th, 7th, etc. However, this paper proposes a harmonic extraction method based on fundamental component subtraction, which effectively avoids this cumbersome process. This method only requires designing one SOGI filter to extract the fundamental component, thus greatly simplifying the system structure and effectively avoiding cross-interference between different frequency components. The specific extraction process is as follows: first, collect the output voltage of the inverter; then, use the SOGI filter to extract the fundamental component from this voltage; finally, subtract the extracted fundamental component from the inverter’s output voltage to effectively extract the harmonic voltage.

In this paper, a SOGI is used for harmonic voltage extraction. It consists of two cascaded integrators forming a resonator, as shown in Figure 7.

In Figure 7, u_i represents the input signal, ω_h is the angular frequency corresponding to the fundamental component or harmonic component that needs to be extracted, k is the damping adjustment coefficient, and u_o1 and u_o2 are mutually orthogonal output signals. From the block diagram, the closed-loop transfer function of the SOGI can be derived as follows:

$$D\left(s\right)={\displaystyle \frac{u_{o1}\left(s\right)}{u_i\left(s\right)}}={\displaystyle \frac{k{\omega }_{h}s}{s^2+k{\omega }_{h}s+{\omega }_h^2}}$$

(15)

$$Q\left(s\right)={\displaystyle \frac{u_{o2}\left(s\right)}{u_i\left(s\right)}}={\displaystyle \frac{k{\omega }_h^2}{s^2+k{\omega }_{h}s+{\omega }_h^2}}$$

(16)

According to Equation (15), it can be seen that D(s) exhibits the characteristics of a band-pass filter, where k determines the bandwidth and ω_h determines the center angular frequency. When extracting the fundamental component of the voltage at the inverter’s output port, we set ω_h = 100 π (rad/s). To determine an optimal value for the bandwidth k, we take k values of 0.1, 0.5, 1, 1.5, and 2 respectively, and obtain the Bode plot of D(s) as shown in Figure 8.

In practical engineering applications, the frequency of the grid voltage can deviate due to changes in load and other factors. When the grid frequency drops, GFM inverters provide active power support to the grid. However, at this point, the grid frequency has significantly deviated from the fundamental frequency. To maintain good compensation performance in such situations, the damping adjustment coefficient k should not be set too low. According to national power system standards, for systems with a rated capacity below 3000 MW, the allowable frequency deviation is 50 (± 0.5) Hz. When the fundamental frequency of the grid voltage varies between 49.5 and 50.5 Hz, it is required that the attenuation of the extracted fundamental voltage signal does not exceed 5%, ensuring subsequent control effectiveness. This means that the gain magnitude of u_o1 should not be less than −0.446 dB, necessitating a k value greater than 0.1 to maintain the bandwidth. Additionally, when the SOGI extracts the fundamental signal, it retains harmonic components of certain amplitudes near the fundamental frequency, causing slight attenuation in the final extracted harmonic signal. Therefore, it is necessary to minimize harmonic signal attenuation during the extraction process. To ensure proper harmonic extraction, the damping adjustment coefficient k should be less than 1.5. Furthermore, the value of k also affects the response speed of the SOGI. If k is too small, the response speed will be slower. Taking all factors into consideration, this paper selects a k value of 1.4142.

3.3. Design of Feedforward Coefficient

In fact, the full feedforward of grid harmonic voltage is not necessarily the best choice. When implementing feedforward, it is essential to consider both the steady state and dynamic performance of the entire system. In the actual process of extracting grid harmonic voltage, a certain time lag occurs. To compensate for this, it is considered to introduce a differential element into the feedforward factor [18]. Let the expression for the feedforward factor F(s) be

$$F\left(s\right)=K_{ph}+K_{dh}s$$

(17)

In the formula, K_ph represents the proportional coefficient in the feedforward factor, and K_dh represents the differential coefficient in the feedforward factor. Figure 9 shows the control block diagram of a grid-forming inverter based on grid harmonic voltage feedforward.

Based on Figure 9, the transfer function of the inverter output current I(s) with U(s) as the input can be obtained as follows:

$$\begin{array}{l}I\left(s\right)={\displaystyle \frac{L_f{C}_f{s}^4+\left(R_f+K_{ip}{K}_{pwm}\right)C_f{s}^3+\left(1+C_f{K}_{ii}{K}_{pwm}+K_{ip}{K}_{vp}{K}_{pwm}\right)s^2+\left(K_{ip}{K}_{vi}+K_{ii}{K}_{vp}\right)K_{pwm}s+K_{ii}{K}_{vi}{K}_{pwm}}{L_f{s}^3+\left(R_f+K_{ip}{K}_{pwm}\right)s^2+K_{ii}{K}_{pwm}s}}U\left(s\right)\\ \hspace{1em}\hspace{1em}-{\displaystyle \frac{\frac{\left(s^2+{\omega }_h^2\right)\left(K_{ph}+K_{dh}s\right)K_{pwm}{s}^2}{s^2+k{\omega }_{h}s+{\omega }_h^2}}{L_f{s}^3+\left(R_f+K_{ip}{K}_{pwm}\right)s^2+K_{ii}{K}_{pwm}s}}U\left(s\right)\end{array}$$

(18)

Compared to traditional inverter control algorithms, under the influence of grid harmonic voltage feedforward, the new output current contains parameters related to the feedforward factor. Obviously, the value of the feedforward factor will affect the quality of the GFM inverter’s output current. Changes in the K_ph and K_dh parameters affect the stability and responsiveness of the system. An increase in the K_ph parameter leads to an increase in the system’s phase margin, thereby enhancing its stability. However, an excessively large K_ph value can affect the rapidity of the system’s response. Conversely, an increase in the K_dh parameter reduces the system’s phase margin. In fact, to avoid introducing noise signals through the derivative component, the K_dh parameter should not be set too high. Meanwhile, if the system is connected to a weak grid, the high impedance of the grid may lead to a decrease in the system’s resonant frequency. It is necessary to reduce K_dh to avoid the amplification of high-frequency noise while appropriately increasing K_ph to maintain the harmonic suppression effect. After comprehensively considering the dynamic response of the entire system, we chose K_ph = 0.7 and K_dh = 0.0001.

3.4. Stability Analysis

To analyze the system stability, a mathematical model incorporating dual closed loops for voltage and current, harmonic feedforward, and an LC filter was established, as shown in Figure 10. Assuming that the inverter is equivalent to a first-order inertial link and considering PWM delay, the control object of the inner current loop is the transfer function from the inverter output voltage to the inductor current, which is

$$H_I\left(s\right)={\displaystyle \frac{1}{L_{f}s+R_f}}\cdot {\displaystyle \frac{1}{1+T_{s}s}},T_s={\displaystyle \frac{1}{2f_s}}$$

(19)

where f_s is the switching frequency.

The transfer function of the current PI controller is

$$G_i\left(s\right)=K_{ip}+{\displaystyle \frac{K_{ii}}{s}}$$

(20)

The control object of the outer voltage loop is the transfer function from the inductor current to the output voltage, which is

$$Z_C\left(s\right)={\displaystyle \frac{1}{C_{f}s}}$$

(21)

The transfer function of the voltage PI controller is

$$G_v\left(s\right)=K_{vp}+{\displaystyle \frac{K_{vi}}{s}}$$

(22)

The harmonic feedforward signal is generated through a feedforward coefficient block:

$$G_{feedforward}\left(s\right)=\left(K_{ph}+K_{dh}s\right)\cdot {\displaystyle \frac{1}{1+T_{s}s}}\cdot {\displaystyle \frac{1}{L_{f}s+R_f}}$$

(23)

The overall open-loop transfer function of the system is

$$G_{open}\left(s\right)=G_v\left(s\right)\cdot {\displaystyle \frac{G_i\left(s\right)H_I\left(s\right)}{1+G_i\left(s\right)H_I\left(s\right)}}\cdot Z_C+G_{feedforward}\left(s\right)$$

(24)

Based on the MATLAB/Simulink platform, a frequency domain analysis of the system was conducted. The system switching frequency fs was set to 20 kHz. The values K_ph = 0.7 and K_dh = 0.0001 were substituted into the overall open-loop transfer function, and the Bode plot of the system’s open-loop transfer function was plotted, as shown in the figure below.

As can be seen from the figure, the system gain margin Gm is 44.1 dB, and the phase margin Pm is 76.8°, indicating that the system has good stability.

4. Simulation Results and Discussion

This paper establishes a GFM inverter simulation model using the harmonic voltage feedforward method based on the MATLAB/Simulink simulation platform in order to demonstrate the effectiveness of the proposed control algorithm in suppressing harmonic currents under distorted grid conditions. The specific parameters used in the simulation are listed in

Table 2. Simulation parameters.

Parameter	Numerical Value
Internal Resistance of Grid-Side Line Rg/Ω	2
Equivalent Inductance of Grid-Side Line Lg/mH	5
Internal Resistance of Filtering Inductor Rf/Ω	0.01
Filtering Inductance Lf/mH	1.5
Filtering Capacitor Cf/µF	20
Grid Voltage Ug/V	220
DC Voltage Udc/V	800
Switching Frequency fs/kHz	20

.

4.1. Harmonic Suppression Under Mixed Harmonic Scenarios

After the GFM inverter is connected to the grid, it is set to operate with an active power output of 10 kW and a reactive power of 0 kvar, at which point the grid voltage quality is good. Between 1 and 4 s, a 10% 5th harmonic and a 5% 7th harmonic are injected into the grid voltage to simulate grid voltage distortion. Within 1~2 s, the GFM inverter employs the traditional control method, and after 2 s, it adopts the proposed harmonic voltage feedforward control method.

Figure 11 shows the active power output of the GFM inverter during the simulation process. Figure 12 presents a comparison of the three-phase currents before and after adopting the harmonic voltage feedforward method. Figure 13 displays the results of the fast Fourier transform (FFT) analysis.

As shown in Figure 11, Figure 12 and Figure 13, when the GFM inverter is operating under normal grid conditions, its output power can accurately track the set value, and the current quality is good. However, when the grid voltage is distorted, the output current of the GFM inverter will also be severely distorted. According to the FFT analysis comparison results in Figure 13, the total harmonic distortion (THD) of the current at this time reaches 9.69%, far exceeding the grid connection standards, which will result in serious harmonic pollution. Moreover, the distorted AC voltage and grid current will cause severe periodic fluctuations in the active power, which will degrade the quality of the output power of the GFM inverter. After adopting the proposed grid harmonic voltage feedforward method, the harmonic current output by the GFM inverter is effectively suppressed, with the current THD reduced to below 5%, meeting the grid connection standards. The fluctuation in the output active power is also relatively reduced.

4.2. Harmonic Suppression Under Unbalanced Grid Voltage Conditions

To verify the effectiveness of the proposed harmonic voltage feedforward control method in suppressing current harmonics for GFM inverters operating in an unbalanced grid, a 5% negative-sequence component was injected into the grid voltage to simulate an unbalanced condition. Between 1 and 4 s, a 10% 5th harmonic and a 5% 7th harmonic are injected into the grid voltage to simulate grid voltage distortion. The proposed control strategy was switched on at 2 s.

Figure 14 presents a comparison of the three-phase currents before and after adopting the harmonic voltage feedforward method under unbalanced grid voltage conditions. Figure 15 displays the results of the FFT analysis.

As shown in Figure 14 and Figure 15, when the GFM inverter operates under unbalanced grid conditions and harmonic components appear in the grid voltage, the THD of the output current of the GFM inverter without feedforward control is 9.02%. However, after adopting the proposed control strategy, the 5th harmonic content is reduced by 6.91%, the 7th harmonic content is reduced by 0.36%, and the THD is also reduced by 5.77%. Meanwhile, as can be seen from Figure 14, the waveform of the output current has been significantly improved. This indicates that the proposed control strategy remains effective under unbalanced grid conditions.

4.3. Harmonic Suppression Under Dynamic Load Changes and Harmonic Transients Conditions

To validate the effectiveness of the proposed control strategy under the conditions of sudden load variations and grid harmonic voltage fluctuations, after implementing the proposed harmonic voltage feedforward control strategy into the system, the active power reference value was stepped from 10 kW to 20 kW at 3 s, and then the 5th harmonic voltage content of the grid was increased to 15% at 4 s. The dynamic response of the system’s actual output active power and the changes in the output current were shown in Figure 16.

The simulation results presented in Figure 16 demonstrate the superior dynamic performance of the proposed control strategy: (1) when a step change in power reference is applied at t = 3 s, the GFM inverter achieves smooth power reference tracking within a regulation time of 0.2 s and rapidly establishes a new stable operating point; (2) upon the introduction of a sudden change in grid harmonic components at t = 4 s, both the output active power and d-axis current component of the inverter reach steady-state conditions within 0.18 s. The simulation results reveal that the system exhibits excellent dynamic characteristics during the regulation process, including fast response (response time < 0.2 s), minimal overshoot (<5%), and remarkable transient stability (oscillation amplitude attenuation rate > 90%). The implemented harmonic voltage feedforward control strategy effectively mitigates grid voltage harmonic disturbances on the output current, thereby ensuring stable system operation during dynamic power regulation. These simulation results validate the effectiveness of the proposed control strategy under dynamic operating conditions.

4.4. Comparative Analysis with the Conventional Feedforward Control Method

Conventional feedforward control is a control method that suppresses interference by directly compensating for the disturbance signal. This method uses low-pass filters or band-pass filters with fixed frequencies to extract harmonics, and calculates a fixed feedforward gain based on the system model [19]. To compare and analyze conventional feedforward control with the proposed control method, we injected 10% of the 5th harmonic and 5% of the 7th harmonic into the power grid to simulate the distortion of the grid voltage. At the same time, an additional 5% of the 5th harmonic component was introduced at 4 s to simulate a sudden change in harmonic conditions. Figure 17, Figure 18 and Figure 19 present the comparative analysis results of conventional feedforward control and the proposed control method.

Figure 17 and Figure 18 present a comparison of the output currents of the inverter between the conventional feedforward control method and the proposed control method when the grid voltage is distorted. It can be seen that when using the conventional feedforward control, the THD of the output current is 3.74%, whereas when using the proposed feedforward control, the THD of the output current is reduced to 3.23%. In addition, for higher-order harmonics other than the 5th and 7th harmonics, the suppression effect of the conventional feedforward control method is not as good as that of the proposed feedforward control method. This indicates that, compared to the conventional feedforward control method, the feedforward control strategy designed in this paper performs better in suppressing higher-order harmonics and can improve the quality of the output current more effectively.

From Figure 19, it can be seen that when there is a sudden change in the grid harmonic voltage, the dynamic response speed of the proposed feedforward control method is faster than that of the conventional feedforward control method, and the overshoot is significantly smaller than that of the conventional method. This indicates that the proposed feedforward control method has a certain improvement in enhancing the system’s dynamic performance compared to the conventional feedforward control method.

5. Conclusions and Future Work

The paper begins by analyzing the impact of grid voltage distortion on GFM inverters utilizing droop control. Subsequently, a harmonic voltage feedforward compensation control strategy is proposed, and the selection of the feedforward coefficient not only improves the quality of the output current of the GFM inverter, but also ensures the stability of its control. The simulation results validate the efficacy of the proposed control approach, after adopting the proposed method, the GFM inverter’s ability to suppress harmonic currents is enhanced. The THD of the grid current can be reduced from 9.69% to 3.23%. In comparison to existing methods, the proposed control strategy exhibits a straightforward structure, eliminates the need for PCC voltage detection, and is readily implementable. In the future works, the experimental validation results can be supplemented, and the availability under islanding operation conditions remains to be further investigated.