With the advancement of the “dual-carbon” goals, distributed renewable energy and electrified loads are rapidly integrated into low-voltage distribution networks, leading to prominent issues such as three-phase imbalance and voltage violations (Xu et al., 2022; Mocci et al., 2025; Tang et al., 2023). The flexible interconnection system for distribution areas employs power electronic conversion devices to establish flexible DC channels between and within distribution areas (Shi et al., 2023; Liu et al., 2023; Sheng et al., 2024). This system enables power quality management in AC distribution areas, dynamic capacity expansion of distribution areas, and efficient/reliable accommodation of large-scale high-penetration distributed generation and high-proportion electrified terminal loads (Xiao et al., 2024; Si et al., 2024; Cai et al., 2023; Zheng et al., 2024; Wang et al., 2008).

Compared with conventional three-leg four-wire flexible interconnection converters, three-phase four-leg (3P4L) converters offer advantages including higher DC voltage utilization, reduced requirements for DC-side input capacitance, and effective control of zero-sequence components. These merits have gradually made them a research hotspot for flexible interconnection converters in distribution areas. Shao and Ma (2008), Lu et al. (2020) implemented individual phase voltage control based on established mathematical models of three-phase four-leg inverters, but their control loops lack complete decoupling, resulting in suboptimal performance. Sun et al. (2020), Zhang et al. (2017), Tan et al. (2019) proposed sequence decomposition strategies combined with feedforward methods to address asymmetric output voltage issues through sequence-decoupled control, though grid harmonics were not considered. Yan et al. (2018), Nguyen and Choi (2018) utilized repetitive controllers to suppress harmonic components and improve grid current quality in three-phase four-leg grid-connected inverters, but their control structures and parameter tuning remain relatively complex.

However, the previous studies effectively address unbalanced loads and harmonic suppression on the AC side but fail to consider that double-frequency instantaneous power fluctuations caused by negative-sequence and zero-sequence components under three-phase AC imbalance conditions propagate to the DC side, inducing double-frequency disturbances. Current solutions for double-frequency power decoupling mainly include passive and active power decoupling methods. Passive power decoupling employs large parallel capacitors (Zeng et al., 2018) or LC resonant circuits (Wang et al., 2024) to absorb double frequency power but suffers from high implementation costs and limited effectiveness. Active power decoupling utilizes switching devices to exchange power with decoupling capacitors for pulsating power compensation (Tao et al., 2023; Huang et al., 2023; Zhang et al., 2023; Luo et al., 2023; Fan et al., 2023; Xu et al., 2020). While enhanced switching configurations improve secondary ripple suppression, they simultaneously escalate system power losses. Tan et al. (2025) proposes a control strategy for three-phase four-leg PWM rectifier under unbalanced grid voltage conditions, which aims at achieving not only no second harmonic in dc output voltage, but also unity power factor operation for each phase. Zhou and Lu (2025), Bhowmick et al. (2025) used an active power decoupling (APD) or boost converter circuit to suppression the double-frequency disturbances in DC bus, while the additional APD circuit will increase the system cost.

To address these limitations, this paper proposes a coordinated AC-DC distribution area power quality optimization strategy based on split-phase power decoupling and resonant control, comprehensively considering three-phase imbalance, voltage violations in AC distribution areas, and double-frequency ripple issues in DC distribution areas. The strategy is implemented within the three-phase four-leg flexible interconnected converter (3P4L-FIC) based distribution area architecture shown in Figure 1. Specifically, a power decoupling control strategy based on positive-negative-zero sequence separation is introduced at the inverter side (VSC2) to address the three-phase load unbalance issues. Simultaneously, a resonant-based double-frequency current suppression strategy is implemented at the flexible interconnection rectifier (VSC1) side to mitigate double-frequency voltage ripples in DC distribution areas. The proposed strategy can address three-phase unbalance issues in AC area and double frequency ripple issue in DC area simultaneously without extra components.

The rest of this study is structured thus. Section 2 presents the mathematical model of 3P4L Converters. Section 3 presents a mechanism of double-frequency DC voltage ripples under unbalanced operating conditions. Section 4 proposes a coordinated power quality improvement strategy for AC-DC distribution areas. Section 5 gives simulation validation and analysis, and Section 6 summarizes the key conclusions drawn from our study.

Conventional three-phase three-leg converters exhibit interphase coupling in output power, thereby lacking the capability for independent three-phase power regulation. In contrast, the 3P4L-FIC introduces a zero-sequence leg to the traditional three-leg topology (as illustrated in Figure 2), enabling each port to generate independent voltages, which structural enhancement facilitates decoupled control of unbalanced three-phase power.

Using the current through the filter inductor L _f of the three-phase four-leg inverter i f T s , the voltage across the capacitor u f T s , and the current i g T s through the load-side filter inductor L _g as state variables, and defining the input voltage u d c T s , input current i p T s , and output voltage u k n T s as output variables (k = a, b, c), the state-space equations can be formulated as follows d d t i a f T s i b f T s i c f T s + R L f i a f T s i b f T s i c f T s = 1 L f d a f V d c T s d b f V d c T s d c f V d c T s − 1 L f u a f T s u b f T s u c f T s + L n L f d i n T s d t (1) d d t u a f T s u b f T s u c f T s = 1 C f i a f T s i b f T s i c f T s − 1 C f i a g T s i b g T s i c g T s (2) d d t i a g T s i b g T s i c g T s = 1 L g u a f T s u b f T s u c f T s − 1 L g u a n T s u b n T s u c n T s (3) Where i k f and i k g represent the currents flowing through inductors L _f and L _g in phase k, respectively. u k f and u k n denote the voltage across capacitor C _f and the converter output voltage in phase k, respectively. d k f (k = a,b,c) is the phase duty cycle, derived by averaging the switching functions of the bridge-arm switches over a switching period and filtering out switching-frequency harmonic components. i n corresponds to the current flowing through inductor L _n .

From Equations 1–3, it is evident that if the neutral inductor and its equivalent resistance are neglected, the three-phase four-leg inverter system reduces to three independent single-phase full-bridge inverter systems. When the neutral inductor is considered, however, mutual coupling arises between the bridge legs, preventing the system from being treated as three decoupled inverter units. This observation underscores the inherent difficulty in achieving decoupled control of the three-phase four-leg inverter in the three-phase stationary coordinate frame.

Translating the fundamental sinusoidal components from the three-phase stationary coordinate frame into a two-phase stationary coordinate frame, followed by Laplace transformation, yields the system’s frequency-domain control model, expressed as s i α f T s i β f T s i 0 f T s + R L f i α f T s i β f T s i 0 f T s = 1 L f d α f V d c T s d β f V d c T s d 0 f V d c T s − 1 L f u α f T s u β f T s u 0 f T s + 3 L n s L f i 0 T s (4) s u α f T s u β f T s u 0 f T s = 1 C f i α f T s i β f T s i 0 f T s − 1 C f i a g T s i b g T s i c g T s (5) s i α g T s i β g T s i 0 g T s = 1 L g u α f T s u β f T s u 0 f T s − 1 L g u α n T s u β n T s u 0 n T s (6)

It can be seem from the Equations 4–6 that under small-signal perturbations around the quiescent operating point, since the DC voltage V d c is regulated under constant-voltage control by Distribution Area II (DA II), the perturbation in V d c is neglected during small-signal analysis of the inverter. Consequently, by separating the DC components and eliminating second-order differential terms at the quiescent operating point, the small-signal model in the rotating coordinate frame is derived as s + R L f i ∧ α f i ∧ β f i ∧ 0 f = 1 L f d α f V d c d β f V d c d 0 f V d c − 1 L f u ∧ α f u ∧ β f u ∧ 0 f + 3 L n s L f i ∧ 0 (7) s u ∧ α f u ∧ β f u ∧ 0 f = 1 C f i ∧ α f i ∧ β f i ∧ 0 f − 1 C f i ∧ α g i ∧ β g i ∧ 0 g (8) s i ∧ α f i ∧ β f i ∧ 0 f = 1 L g u ∧ α f u ∧ β f u ∧ 0 f − 1 L g u ∧ α n u ∧ β n u ∧ 0 n (9)

From Equations 7–9, it can be observed that the mathematical model of the three-phase four-leg converter is mutually decoupled in the α axis, β axis and 0-axis, which facilitates controller design and simplifies the implementation of three-phase decoupled control. Furthermore, the mathematical model of the α β -axis is identical to that of a conventional three-phase three-leg converter, while the 0-axis mathematical model incorporates coupling with three times the zero-sequence inductance L _n .

The three-phase four-leg inverter is directly connected to the low-voltage distribution network via an LCL filter. In the three-phase four-wire system, due to the inclusion of zero-sequence voltage and current components, the system’s instantaneous real power p , instantaneous imaginary power q , and instantaneous zero-sequence power p 0 are defined (Akagi et al., 2007) as follows (with coordinate transformation applied for constant-power transformation) p 0 p q = v 0 0 0 0 v α v β 0 v β − v α i 0 i α i β (10)

It can be seem from Equation 10 that the zero-sequence instantaneous power in the system is independent of the positive- and negative-sequence instantaneous powers. According to (Dong et al., 2020; Gao et al., 2016), the instantaneous complex power output from the converter’s AC side can be expressed as (excluding the zero-sequence component). p = P 0 + P c 2 ⁡ cos 2 ω t + P s 2 ⁡ sin 2 ω t q = Q 0 + Q c 2 ⁡ cos 2 ω t + Q s 2 ⁡ sin 2 ω t (11)

In Equation 11, P 0 and Q 0 represent the DC components of the instantaneous active and reactive power, respectively. P c 2 and P s 2 denote the amplitudes of the double-frequency AC components in the instantaneous active power, while Q c 2 and Q s 2 correspond to those in the instantaneous reactive power.

The zero-sequence voltage and current components are defined as u k 0 = U 0 ⁡ cos ω t i k 0 = I 0 ⁡ cos ω t + φ k = a , b , c (12)

In the Equation 12, U 0 and I 0 denote the magnitudes of the zero-sequence voltage and current vectors, respectively. φ represents the phase angle between the zero-sequence voltage and current vectors, and ω is the rotational angular velocity. Therefore, the instantaneous zero-sequence power can be expressed as p 0 = 3 U 0 I 0 ⁡ cos ⁡ φ − 3 U 0 I 0 ⁡ cos 2 ω t + φ q 0 = U 0 I 0 ⁡ sin 2 ω t + φ (13)

In the equations, p 0 denotes the zero-sequence instantaneous active power, and q 0 represents the zero-sequence instantaneous reactive power. From Equation 13, it is evident that the zero-sequence power itself cannot produce constant power. Therefore, there is no method to eliminate the oscillatory components while retaining only the DC component.

By integrating the above analysis, the total instantaneous power of the three-phase four-wire system is expressed as p = P 0 + P c 2 ⁡ cos 2 ω t + P s 2 ⁡ sin 2 ω t + p 0 q = Q 0 + Q c 2 ⁡ cos 2 ω t + Q s 2 ⁡ sin 2 ω t + q 0 (14)

From Equation 14, under unbalanced operating conditions, the instantaneous power fluctuations at the second harmonic frequency generated by the negative-sequence and zero-sequence components will penetrate into the DC side, causing second harmonic frequency disturbances in the DC network. This seriously affects the reliability and stability of the system.

Figure 3 shows the overall block diagram of the proposed coordinated power quality improved control strategy for 3P4L-FIC distribution areas, which consists of two part. One is the split phase power decoupling control strategy for three phase unbalance compensation of the AC distribution network, which is based on the positive, negative, and zero sequence separation control on the inverter side (VSC2) of the 3P4L-FIC. The other one is hybrid proportional-integral and resonant controller (PI-R) based double-frequency voltage ripple suppression strategy for DC-bus, which is implemented on the rectifier side (VSC1) of the 3P4L-FIC. The proposed coordinated strategy can address three-phase unbalance issues in AC area and double frequency ripple issue in DC area simultaneously without extra components.

A simulation model of the dual-terminal low-voltage flexible interconnected grid, as shown in Figure 1, was developed on the MATLAB platform. The converter system parameters and control parameters are summarized in Tables 1, 2. Based on measurement data from a demonstration construction project in a city in Guizhou Province, this study analyzes whether the distribution area experiences operational issues such as three-phase imbalance and voltage deviation under typical conditions, with the power factor set to 0.9. The operational data for Distribution Area I are as follows:

Scenario 1: Data from 12:00 noon are selected as a typical case of high photovoltaic (PV) penetration and low load proportion, three phase load and photovoltaic access data for substation area I are summarized in Table 3.

Scenario 2: Data from 18:00 (6:00 p.m.) are selected as a typical case of high load proportion and low PV penetration. The three phase load and photovoltaic access data for substation area I are summarized in Table 4.

This paper proposes a coordinated power quality improvement strategy for 3P4L-FCI based AC-DC distribution areas. To address issues such as three-phase imbalance and voltage limit violations in AC distribution areas, a split-phase power decoupling control strategy utilizing the three-phase four-leg converter is developed, effectively reducing the PCC voltage unbalance rate, source-side output current unbalance rate, and voltage deviations under two extreme operating conditions. Furthermore, by analyzing the double-line-frequency pulsation mechanism of the DC bus voltage under unbalanced AC distribution conditions, a double-frequency ripple suppression scheme based on a hybrid proportional-integral and resonant controller (PI-R) controller is proposed, which significantly mitigates the double-frequency components in the DC bus voltage. Finally, a MATLAB/Simulink-based simulation model of 3P4L-FCI based AC-DC distribution areas is established. The results validate the effectiveness of the proposed control strategies.