Three-phase Four-leg Inverter Research Articles

Three-Dimensional Space Vector Modulation for Four-Leg Current-Source Inverters

Unbalanced loads are general in uninterruptible power supply (UPS), standalone power generation applications and the failure mode of three-phase inverters. Three-phase four-leg inverters are a well-known solution to handle neutral currents caused by unbalanced loads. In four-leg inverters, three-dimensional space vector modulation (3DSVM) is widely used. However, the 3DSVM of four-leg current source inverter (CSI) has not been systematically studied so far. To fill this gap, this paper proposes a 3DSVM for CSI. The definition of the current vector, the identification of the position of reference vector and the sequence of switches are introduced. Under unbalance loads, the symmetrical load voltage can be realized, which complies with IEEE Std. 1159-2019. The output current can comply with IEEE Std. 519-2014. The proposed 3DSVM has the potential to extend the advanced modulation strategies that have been implemented/ proposed on three-leg CSI.

Closed-Form Harmonic Compensation Using Resonant Controllers Applied to Four-Leg VSI

Harmonic compensation employing resonant controllers applied to voltage source inverters generally requires complex techniques or a trial-and-error process to design the controller parameters. This paper proposes a closed-form solution for designing digital Proportional-Resonant controllers applied to three-phase four-leg inverters. The proposal presents a sequential procedure that uses closed-form expressions to establish the harmonic frequencies at which resonant stages must be added to comply with individual voltage harmonic distortion standards. The method eliminates the need for a trial-and-error process and ensures compliance with THD and individual harmonic distortion limits. The frequencies that require compensation and the gains of the resonant controllers are determined by evaluating the difference that presents the output harmonic impedance of the inverter concerning normalized three-phase harmonic impedance limits defined in this work. Furthermore, this paper adopts the harmonic distortion restrictions imposed by the Standard IEC 61000-2-2, allowing the harmonic impedance limits to be defined for the reference non-linear load indicated in IEC 62040-3. Experimental results are presented to validate the proposed design using a 5 kVA four-leg inverter, feeding balanced, unbalanced, linear, and non-linear loads.

An individual sequencing control strategy for three-phase four-leg inverter under unbalanced loads

Under the influence of the unbalanced load, the negative and zero sequence components in the output voltage of the three-phase four-leg voltage source inverter(TPFL-VSI) will cause asymmetry voltage. This paper designs an individual sequencing control for the three-phase four-leg inverter to address this problem. The second-order generalized integrator is adopted to extract the current’s positive and negative sequence components. The virtual oscillator control(VOC) controls the positive sequence component, and the negative sequence component is suppressed by designing the virtual impedance and the multiple proportional resonance controller. The proportional resonance control is used to control the zero-sequence voltage of the fourth bridge arm. Considering that voltage deviation is caused by the access of negative sequence virtual impedance and load step, the secondary voltage compensation strategy is further added in the individual sequencing control to improve the droop relationship in the VOC and effectively solve the problem of system voltage instability. Ultimately, a TPFL-VSI model is built in Matlab/Simulink, and simulation results verify the feasibility and effectiveness of the proposed control strategy under different conditions.

An Active Power Decoupling Topology for Three-phase Four-leg Inverters with Unbalanced Load

Traditional three-phase four-leg inverters are widely used in microgrid systems because of their ability to carry unbalanced loads, but unbalanced load currents will cause instantaneous power to contain double-frequency fluctuations, which will affect the normal operation of the microgrid system. In order to solve the above problems, this paper proposes an improved three-phase four-leg topology and its control strategy, so that the secondary pulsating power on the load side can be provided by the decoupling capacitor. Then the working principle of the proposed topology and its control strategy is analyzed, and the relationship between the current stress of the power device and various influencing factors is deduced. Finally, An experimental prototype was built to verify the effectiveness of the proposed solution.

Impedance Modeling and Stability Analysis of Three-Phase Four-Wire Inverter with Grid-Connected Operation

With the continuous penetration and development of renewable energy power generation, distributed grids and microgrids are becoming increasingly important in power systems. In the distribution networks and microgrids, the grid impedance is comparatively large and cannot be ignored. Usually, the parallel compensation is used to improve the grid quality. In these three-phase four-wire power systems, analyzing the impedance characteristics of the grid-connected inverter is vital to carry out the small-signal stability analysis. Thus, it is vital to consider the influence of the zero-sequence component in addition to the positive-sequence component and the negative-sequence component when it comes to analyzing system stability. In this paper, the impedances of three-phase four-wire split capacitor inverter and three-phase four-leg inverter are established. Based on the achieved impedance, the similarities and differences between the impedances of three-phase four-wire split capacitor inverter and impedance of three-phase four-leg inverter are studied. The main difference is reflected in zero-sequence impedance. Additionally, the zero-sequence impedance characteristics and the dominating factors deciding the zero-sequence impedance are analyzed. Then, the stability of the system considering the grid impedance and impedance of three-phase four-wire inverter is investigated by separately considering the stability of the positive–negative-sequence component and the stability of the zero-sequence component. Several cases of small-signal instability caused by the positive–negative-sequence component or zero-sequence component are revealed. The experimental results validate the theoretical analysis.

Minimization of Capacitor Voltage Difference for Four-Leg Inverter Dual-Parallel IM System

In the situations where multiple motors operate at the same speed, this article designs a dual-parallel induction motor (IM) system supplied by three-phase four-leg inverter for cost reduction and fault tolerance of the normal system. The dc offset and ac fluctuation of capacitor voltages exist in this system due to the motor phases connected to bus capacitors&#x2019; midpoint. It seriously affects voltage utilization and stable operational range. A novel synchronous control scheme with the ability of ac voltage fluctuation minimization (AVFM) and dc voltage offset elimination (DVOE) is proposed. The unified model of dual IMs is used to design the speed regulator, and the model predictive flux control method is combined with space vector modulation to realize torque and flux control of dual IMs. AVFM is realized by controlling the electrical angle difference of dual IMs as <inline-formula><tex-math notation="LaTeX">$\pi$</tex-math></inline-formula>, which is first presented in this scheme. An angle regulator is proposed to control the electrical angle by adjusting stator flux amplitude. DVOE is realized by injecting a compensatory voltage vector, which is simplified in this scheme to avoid the voltage filter or additional coordinate transformation in the conventional method. Experiment results verify the effectiveness of the proposed scheme.

A coordinated virtual impedance control scheme for three phase four leg inverters of electric vehicle to grid (V2G)

The three-phase four-leg (3p4L) inverter can be utilized to interface electric vehicles (EVs) with the distribution networks. Vehicle to grid (V2G) inverters are employed to charge EVs from the utility grid as well as compensating harmonics and unbalanced voltages & currents on demand. Motivated by this scenario, this paper proposes a coordinated virtual impedance control scheme for a vehicle to grid three phase four leg (V2G 3p4L) inverter. The proposed control scheme achieves simultaneously multifunctional objectives consisting of effective and good harmonic rejection capability, power sharing among V2G 3p4L inverter units with a smaller error, reactive power/voltage support during load power changes and balanced/unbalanced voltage sag conditions. An independently neutral current control approach is proposed for the fourth leg of the V2G 3p4L inverter to regulate the DC-link along with neutral current control capability. Besides, the proposed control scheme achieves grid connected mode (GCM) or standalone mode (SAM) operation capability as well as fulfilling smooth transition between operation modes without reconstructing control structure. Compared to well-known control schemes in the literature, synchronization during operation modes is also achieved without transients in voltage and current. Comprehensive tests under various scenarios validate the excellence of the proposed control scheme over existing methods.

Space Vector Pulse-Width Modulation Control Strategy for Four-Leg Inverters Under Single Line-to-Ground Faults in Islanded Microgrids

In this paper, we propose a novel switching modulation scheme for three-phase four-leg inverters that enables the separation of the fault points occurring in AC distribution networks. The proposed method is aimed at continuously supplying normal voltage to the remaining healthy phases while applying zero voltage to any faulty phase when a single line-to-ground (SLG) fault occurs in the distribution network. This modulation scheme allows isolation without physically blocking the point of failure. This can prevent unnecessary continuous outages in the AC distribution network. To this end, we propose a novel coordinate transformation method to extract accurate values for the magnitude of unbalanced three-phase voltages. A novel space vector pulse-width modulation (SVPWM) method for switching schemes that are used under fault conditions is also presented. The proposed coordinate transformation considers a plane lying in a three-dimensional (3-D) space that describes the rotation of a three-phase voltage vector. This transformation converts a physical quantity that rotates in 3-D space into a value that moves in two-dimensional (2-D) space. Subsequently, the use of synchronous reference frame (SRF) transformation enables the detection and control of the voltage magnitude in case of an SLG fault. Additionally, switching vectors are selected to apply zero voltage to the faulty phase by analyzing the switching vector diagram of a four-leg inverter. Mathematical analyses conducted for the entire process are detailed herein. Further, the experimental results of four-leg inverters designed for the 10 kW class verify the proposed strategies.

Frequency-Adaptive Repetitive Control for Three-Phase Four-Leg V2G Inverters

Three-phase four-leg inverters with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter are employed as onboard vehicle to grid (V2G) inverters due to their advanced features—high utilization of the dc bus voltage, counteraction of unbalanced voltages, and so on. Repetitive control (RC) can exactly track periodic signals with known frequency, which offers a simple high-accuracy current tracking and harmonic suppression solution for three-phase four-leg inverters. However, the conventional RC (CRC) offers slow dynamic responses due to the embedded delay element, and grid frequency fluctuation would cause significant performance degradation of CRC controllers in V2G applications. Moreover, the three-order <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter often causes complexity in developing good performance feedback control schemes for the inverters, especially for complex three-phase four-leg ones. To address these problems, an easy-for-implementation hybrid control scheme that combines a frequency-adaptive RC (FARC) controller with a deadbeat (DB) controller is proposed to obtain fast and accurate control of feed-in grid current for the onboard three-phase four-leg V2G inverters with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter in the presence of grid frequency variation and load changes. The fast-response DB control scheme is based on a simplified first-order model of an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter. The FARC controller is immune to grid frequency fluctuation. Simulations and experiments have been done to prove that the DB plus FARC control strategy can provide an excellent current control solution for the three-phase four-leg V2G inverters.

Digital Control of a Three-Phase Four-Leg Inverter to Feeds Non-Linear Loads

This paper presents a new control strategy for three-phase four-leg inverters, to meet the requirements of total and individual harmonic content imposed by IEC 61000-2-2 when the inverter feeds a non-linear reference load defined by IEC 62040-3. The analysis and design of the controllers are based on a discrete-time model, developed in the 0 reference frame. The proposed control strategy consists of an inner current control loop and an outer loop to control the phase voltages, using Proportional-Resonant controllers. The concept of harmonic impedance, proposed initially for single-phase inverters, is used to tune the controllers. Simulation and experimental results are presented to validate the harmonic impedance obtained and the design of the proposed control strategy when the inverter feeds non-linear loads

Prediction of DC-Link Voltage Switching Ripple in Three-Phase Four-Leg PWM Inverters

This paper presents a thorough prediction of DC-link voltage switching ripples in the three-phase four-leg inverters operating in balanced and unbalanced working conditions. The unbalanced modes examined here employ the highest degree of AC current imbalance while still preserving three-phase operation. This behavior can be found in many grid-connected or standalone grid-forming three-phase converters that supply “heavy” single-phase loads, comprising a recent trend in smart-grid, smart electric vehicle (EV)-charging applications. In this sense, for instance, the smart EV chargers might be employed in conditions when different power is drawn/injected from/to the grid, providing power conditioning services to the latter. The analysis of three-phase four-leg inverters is then extended to single-phase operations typical of home-charging or vehicle-to-home (V2H) applications. Their performances in terms of DC-link voltage switching ripple are demonstrated. Two of the most common carrier-based PWM modulation techniques are employed to drive the three-phase inverter—namely, sinusoidal PWM and centered PWM (carrier-based analogy of the space vector modulation). The derived mathematical expressions of peak-to-peak and RMS values of DC-link voltage switching ripple for balanced and unbalanced conditions are handy for designing the associated DC-link capacitor and estimating the overall efficiency of the converter. Extensive numerical simulations and experimental tests have been performed to validate the presented analytical developments.

Disturbance observer-based composite voltage synchronisation control of three-phase four-leg inverter under load variation

The three-phase four-leg inverter is widely used in microgrid recently. The control strategy is critical for the performance of nonlinear four-leg inverter system owing to the problems of coupling, disturbances of nonlinear/unbalanced loads, variable operating condition, etc. In view of the above problems, a nonlinear composite controller is proposed for four-leg inverter system under reference frame by integrating a higher-order sliding mode observer (HOSMO) and finite-time feedback control technique. The HOSMO can observe the uncertainties and disturbances by means of the soft sensing manner for feedforward compensation, which economises some sensors for their states being inconvenient to measure. In addition, it is a novel way for the HOSMO to realise the decoupling of the inverter system under frame. The finite-time feedback controller works in coordination with the HOSMO which provides more rapid convergence rate and further improves anti-disturbance capacity of the system. Finally, the simulation results with PI comparison illustrate the feasibility of the proposed method for stabilizing system.

Implementation of three-phase four-leg inverter using SiC MOSFET for UPS applications

This study implemented a 30 kW, 750 Vdc, silicon-carbide (SiC)-based uninterruptible power supply(UPS) applied it on a three-phase four-leg inverter. For component selection, LC filter and DC-link capacitor were designed based on the PSIM simulation. SiC MOSFET was used to achieve higher efficiency and better reliability than the conventional Si IGBT-based UPS applications. Furthermore, desaturation (DeSat) protection method was applied to protect the overcurrent during the short-circuit condition of SiC MOSFET. Thus, the DeSat protection method was applied to SiC MOSFET, thereby enabling a 1 μs protection by complementally switching and zener diode voltage optimization. Accordingly, the transient time of the DeSat protection can be disregarded, thereby enabling fast protection. Meanwhile, several topologies have been studied for unbalanced loads compensation. The current research used a three-phase four-leg inverter topology for compactness and neutral current control. In addition, voltage compensation became possible even in unbalanced load condition by introducing a dual-loop controller for the three-phase four-leg inverter. A dual-loop controller comprises PR and PI controllers to the stationary αβo and synchronous dqo reference frames, respectively. Thermal and efficiency tests were also performed in the rated power test. Under a 30 kW load condition, the surface epoxy molding compound temperature of SiC MOSFET was approximately 72 °C, and the highest efficiency was approximately 99.1% under 10 kW load condition. Finally, the effectiveness of the implementation was demonstrated through the experiment results.

Harmonic and unbalanced voltage compensation with VOC‐based three‐phase four‐leg inverters in islanded microgrids

This study proposes a novel method that combines sliding mode control (SMC) and virtual oscillator control (VOC) to eliminate voltage harmonics and unbalance caused by non-linear and unbalanced loads in a three-phase low-voltage microgrid. The conventional VOC is modified to fit the three-phase four-leg inverter systems and a novel SMC control is designed using the high-pass filter technique and linearised super twist algorithm. The proposed control method can keep the voltage harmonics and unbalance at the point of common coupling within the IEEE standard limits, under heavily non-linear and unbalanced load conditions. The validity of the proposed method is verified by both offline simulations in Matlab/Simulink and Control Hardware-in-the Loop simulations using an OPAL-RT platform.

Predictive Duty Cycle Control for Four-Leg Inverters With ${LC}$ Output Filter

Three-phase four-leg inverter is a well-known solution to handle unbalanced and nonlinear loading conditions in three-phase transformerless uninterruptible power supply applications. For such power converters, finite control set model predictive control (FCS-MPC) is considered as a promising control alternative due to its simplicity, fast dynamic response, and capability to include nonlinearities and constraints. However, the absence of modulator in FCS-MPC implementation leads to several shortcomings, such as higher load voltage total harmonic distortion (THD), large tracking error of control objectives, and variable switching frequency. Furthermore, the fourth leg operates with a higher average switching frequency than the other three main legs, which complicates the $LC$ filter design. To overcome the aforementioned shortcomings, a new predictive duty cycle control is proposed in this article. Extensive experimental results are shown to verify that the proposed method can achieve enhanced steady-state performance with significant reduced load voltage THD and tracking error under different operating conditions, such as nonlinear single-/three-phase unbalanced load and single-phase short-circuit fault, while preserving the fast dynamic performance of FCS-MPC. Steady-state and dynamic performances of the proposed method are compared to FCS-MPC and double-vector MPC approaches to validate the superiority of the proposed scheme.

Minimum Loss Discontinuous Pulse-Width Modulation Per Phase Method for Three-Phase Four-Leg Inverter

The three-phase four-leg inverter (TPFLI) provides unbalanced voltage to a load or injects unbalanced current to a grid to compensate unbalanced current. However, it has a high switching loss because of the fourth leg. This paper presents a discontinuous pulse-width modulation (DPWM) method that minimizes the per-phase switching loss of the TPFLI. The discontinuous three-dimensional space-vector pulse-width modulation (3D SVPWM) can be implemented in the TPFLI by injecting the same offset voltage as the conventional DPWM of three-phase three-leg inverter (TPTLI). However, the conventional DPWM is unsuitable for TPFLI because of its unbalanced current. We demonstrate that the discontinuous phase can be chosen according to the offset direction when a voltage reference vector is specified. Based on this result, a new per-phase minimum-loss discontinuous PWM strategy is developed and compared with the conventional DPWM. This method can also be applied to the TPTLI and implemented by injecting an offset voltage generated using the inverter phase voltage reference and phase current. Furthermore, the lifespan of a TPFLI can be extended by preventing deterioration of a specific leg. The validity of the proposed method is verified through simulation and experiments.

Single‐stage high‐frequency‐isolated three‐phase four‐leg buck–boost inverter with unbalanced load

A three-phase four-leg inverter shows its preponderance on providing energy to unbalanced load and high DC-link utilisation. To increase the power density of the traditional three-phase four-leg inverter with power frequency isolation, this study proposes a single-stage isolated three-phase four-leg inverter. To ensure the symmetry of three-phase output voltages, the proposed converter provides the path for neutral current resulted by the unbalanced load. It achieves buck-boost DC/AC conversion by introducing the transformer whose turns ratio provides additional voltage gain. The working frequency of the transformer is in accord with the switching frequency, so high-frequency electrical isolation is realised with a single-stage structure as well. The specific mode analysis and the relationship between the switching states and the voltage vectors are presented. A modified three-dimensional space vector pulse width modulation algorithm with a simplified section partition method is proposed, which guarantees the voltage-second balance of the transformer within one switching cycle as well. In order to explore the feasibility of the topology and control strategy, the simulation is done by MATLAB/Simulink. Then a prototype was built in the lab and the experimental results verify that the inverter can produce balanced voltages under both balanced and unbalanced load.

Finite‐time composite control scheme for three‐phase four‐leg inverter under variable operating conditions

Three-phase four-leg inverters widely used in microgrid can effectively provide the power for the non-linear/unbalanced loads. Here, the non-linear composite controller is proposed for three-phase four-leg inverter system under d q 0 reference frame by integrating a higher order sliding mode observer and finite-time control technique. The observer adopts the soft sensing manner to feedforward compensate external disturbances caused by current variation of AC bus node, which relaxes some physical constraints. Meanwhile, the higher order sliding mode observer realises the decoupling of the inverter system, which paves the way for the construction of the non-smooth finite-time control law. Finally, the simulation results with PI comparison illustrate the feasibility of the proposed method for improving the robustness, stability, and rapid recovery capability of system.

Circulation suppression of synchronous/interleaving paralleled 400 Hz three‐phase four‐leg inverter based on third harmonics injection

In this study, the third harmonic injection method based on analogue circuit is applied in the interleaving parallel three-phase four-leg (3P4L) inverter, the adverse effects of injected signals on the circulating current are found, and the corresponding control strategy solution is proposed. At the beginning of this study, by using the large-signal model of leg, it is proved that four legs can be decoupled, on the basis of this conclusion, the current sharing control strategy based on dual-loop scheme and third harmonic injection can be applied in paralleled 3P4L inverter, however, peak value of circulating current is increased by zero-sequence component which is caused by injected signals. Therefore, output impedance analysis method is applied, and the control strategy including zero-sequence component feedforward loop is proposed, which can be implemented with analogue circuit, and is suitable for the 400 Hz synchronous/interleaving paralleled inverter systems. Finally, the effectiveness of the control strategy is verified by simulation and experiment.

A Simple High-Performance Current Control Strategy for V2G Three-Phase Four-Leg Inverter With LCL Filter

Electric vehicles (EVs) can behave as distributed energy storage devices for providing on-demand smart grid support service, that is, an emerging vehicle-to-grid (V2G) technology. A high-performance and easy-implementation current control strategy for V2G three-phase four-leg inverter with LCL filter is proposed. It consists of a deadbeat (DB) controller and a paralleled repetitive controller (RC). The DB controller is based on the weighted average inductor current (WAIC) scheme, which simplifies the third-order LCL filter to be an equivalent first-order $L$ filter. The stability of the DB-controlled inverter with the unmodeled system time delay is analyzed. The DB controller is of very fast response and easy implementation but is not immune to system time delay and various uncertainties. To overcome the disadvantages, a plug-in RC is added to reinforce the DB controller to remove harmonic distortion from the feed-in current in the presence of parameter uncertainties. A lab prototype of 10-kW grid-connected three-phase four-leg inverter has been built up to validate the proposed current control strategy. The simulations and experiments are provided to demonstrate the validity of the proposed control strategy.