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A carrier-based PWM method for three-phase four-leg VSC
Abstract
In this paper a voltage modulation method based on a triangular carrier wave for the three-phase four-leg voltage source converter is described. The four-leg converter can produce three output voltages independently with one additional leg. The proposed modulation method for the four-leg converter can be implemented with a single carrier by a simple but useful "offset voltage" concept. The method is equivalent to the so called three-dimensional space vector PWM method, but its implementation is much easier. The maximum magnitude of the balanced three-phase voltage and the maximum magnitude of zero sequence voltage, which can be synthesized simultaneously, are derived. The feasibility of the proposed modulation technique is verified by computer simulation and experimental results. These results show that a proposed carrier-based pulsewidth modulation (PWM) technique can be easily implemented without conventional computational burden.
... The modulation scheme is an important impact factor for the performance of four-leg inverters. Lots of research has focused on modulation schemes of 4L-VSI, and the two commonly used modulation schemes are carrier-based pulsewidth modulation (CB-PWM) [6] and three-dimensional space vector modulation (3D-SVM) [7], [8]. Compared with voltage source inverter (VSI), current source inverter (CSI) has the advantages of inherent voltage boost ability, output shortcircuit protection, motor-friendly output voltages, and a longer lifetime. ...
... From (6), in order to control the output voltages as threephase balanced sinusoidal waves, three identical quasiproportional-resonance (QPR) controllers are used to generate three-phase current references: ...
... The outputs of these QPR controllers are the output currents references: ia * , ib * , and ic * . According to (6), then dj can be calculated as: ...
p>Four-leg current source inverter (4L-CSI) has abilities of zero-sequence current handling, voltage boosting, and output short-circuit protection, but it also has the drawbacks of bulkiness and low efficiency. To address these drawbacks, a three-level buck 4L-CSI (3L-Buck-4L-CSI) topology and a simple and high-efficiency modulation scheme are proposed. Due to the multilevel characteristics of 3L-Buck-4L-CSI, the volume of its DC inductor can be reduced greatly and the DC-link current could respond quickly. The proposed modulation scheme is an algebraic modulation scheme, in which the duty cycles are obtained by solving algebraic equations simply and directly. In addition, it reduces the DC-link current and the switching times compared with the conventional modulation schemes, which greatly improves the efficiency of the converter. The experimental results validate the effectiveness of the proposed topology and modulation scheme. </p
... A reference voltage signal for each of the four legs of the converter has to be calculated. Typically, a min/max algorithm is used to calculate the fourth-leg reference voltage, which is added to each of the other three phases, namely zero-sequence injection [50]. However, it is difficult to implement different switching patterns for shaping harmonic spectrum and use redundant switching states, especially important in multilevel converters [51]. ...
... From these equations, four voltages respect to the middle point of the converter are obtained, namely v az , v bz , v cz and v nz . Therefore, if both components of any of the pairs (v az , v nz ), (v bz , v nz ) and (v cz , v nz ) change in the same magnitude, it would not be noticed in the output voltages v an , v bn or v cn , but it allows to modulate output phase-voltages with a higher fundamental component and common-mode control [50]. Let us consider a set of reference phase-voltages v * an , v * bn and v * cn , given by an external controller. ...
... Once obtained v * nz , the references v * az , v * bz and v * cz are obtained from (28) to (30). Afterwards, this constant values are compared with one period of a triangular carrier during the next sampling time T s , generating, for example, the trigger signals for the eight devices of the two-level four-leg VSI [50], [172]. This process is repeated at each sampling time. ...
In three-phase unbalanced systems, where the circulation of zero sequence current is necessary, four-leg converters provide a neutral connection for single-phase or other unbalanced loads typically utilized in three-phase distribution systems. In addition, control of the magnitude and phase of the zero-sequence voltage and/or current are also achieved using four-leg power converters. However, even when four-leg converters have become very important in several fields as for instance, four-leg microgrids and aerospace applications, a comprehensive review of the converter topologies, control methods, modulation methods and output filters have not been hitherto published. In this paper, a comprehensive overview of the state-of-the-art of four-leg converters is presented, based on the selection of over 400 papers published in journals and conferences, identifying mature and incipient topologies, modulation strategies, control schemes and applications. Each topic presented in this work is thoroughly discussed and reviewed, analyzing characteristics, implementation issues, and reported advantages and disadvantages to provide a comprehensive overview of the current research and future challenges in four-leg converters. The most important applications of four-leg converters are also discussed in this work, including stand-alone power supply, uninterruptible power supplies, grid-connected 4-leg inverters, ground power units for aerospace applications, active filtering for power quality enhancement, cooperative control of 4-leg converters for micro-grid applications, among others. Finally, future work and conclusions are highlighted in this paper.
... Furthermore, the growing deployment of electric vehicles (EVs) has allowed the adoption of three-phase four-wire inverters as a front-end stage in on-board/off-board EV chargers, offering vehicle-to-grid (V2G), vehicle-for-grid (V4G), vehicle-to-home (V2H), vehicle-tovehicle (V2V), and vehicle-to-load (V2L) services in both three-phase and single-phase modes [7,8]. Different neutral forming topologies have been proposed and discussed, such as three H-bridges [4,9], split capacitors [1][2][3][4][5]9,10], four-leg [3,4,9,11], and independently controlled neutral module [2,7,12]. ...
... By replacing Equation (9) in Equation (11) and simplifying, it becomes: ...
... Electronics 2021, 10, x FOR PEER REVIEW 7 of 20 upper/lower envelopes correspond to half of the peak-to-peak values given in Equations (11) and (12). As expected, the simulation results show a very good match with the derived equations. ...
The current switching ripple in a three-phase four-wire split-capacitor converter is analyzed in this paper for all the four ac output wires in relation to both balanced and unbalanced working conditions. Specifically, analytical formulations of the peak-to-peak and root mean square (RMS) current ripples are originally evaluated as a function of the modulation index, separately for the three phases and the neutral wire. Initially, the single-carrier sinusoidal pulse width modulation (PWM) technique is outlined, as it generally concerns a straightforward and effective modulation. With the aim of mitigating the current ripple in the neutral wire, the interleaved multiple-carrier PWM strategy is adopted, also avoiding any repercussion on the phase one. Numerical simulations and experimental tests were carried out to verify all the analytical developments.
... The simplified strategies of 3-D SVM are mainly divided into abc-based space vector strategies [15], [16], [17], [18] and carrier-based pulse width modulation strategies (CBPWM) [19], [20]. In [19], 3-D SVM is equivalent to CBPWM, which reduces the complexity of the modulation algorithm. ...
... The simplified strategies of 3-D SVM are mainly divided into abc-based space vector strategies [15], [16], [17], [18] and carrier-based pulse width modulation strategies (CBPWM) [19], [20]. In [19], 3-D SVM is equivalent to CBPWM, which reduces the complexity of the modulation algorithm. However, it greatly reduces the flexibility of the modulation. ...
Three-dimensional space vector modulations (3-D SVMs), while inheriting the advantages of two-dimensional space vector modulations (2-D SVMs), have the capability to generate asymmetrical currents, making them widely applied in four-leg inverters. However, the computational burden due to the expansion of space and vectors adds potential limitations to the application of 3-D SVM. To overcome this limitation, this article proposes a simplified 3-D SVM based on the abc coordinate system, which is designed for four-leg current source inverters. The recognition of tetrahedra and the calculation of duration time is simplified through thoughtful design. This algorithm avoids irrational operations and table lookups, eliminates pointer function calculations, and alleviates the computational burden on the processor. Experimental results validate the effectiveness of the proposed 3-D SVM.
... Numerous Pulse Width Modulation (PWM) strategies for the 4L-VSI have been put forth in the literature. For instance, Carrier-based PWM (CPWM) [31] requires the creation of an unbalanced voltage by introducing an offset voltage (Vfn) into the three-phase voltage reference, which is then used as the voltage reference for the fourth leg [32]. ...
... When comparing them to carrier-based PWM, the 3DSVM provides many improvements, such as high dc-link exploitation and low output distortion [38]. On the other hand, it has some inherent limitations due to the necessity of complex modeling and longer computational time [32]. ...
This study introduces a new three-dimensional space vector modulation technique for a four-leg quasi Z-source inverter (4L-qZSI) integrating a qZSN and a two-level four-leg inverter. The proposed method encompasses three variants, namely 3DZSVM2, 3DZSVM4, and 3DZSVM8, designed to enhance steady-state operations and harmonic distortions for 4L-qZSI. One of the main contributions of this research is the establishment of a new modulation technique for the 4L-qZSI. The proposed method amalgamates the benefits of SVMs in both abc and αβγ coordinates. The design processes of the 3DZSVM algorithm are carried out in the newly proposed ρστ coordinates, while the space vector diagram (SVD) of the 4L-qZSI is utilized in the αβγ location. The proposed algorithm is applied in a single sector, optimizing time interval calculations and pulse creation without requiring trigonometric functions. Extensive simulation studies were conducted to validate the performance of the introduced modulation scheme for the 4L-qZSI. The simulation results show excellent steady-state performance and benefit over the conventional space vector modulation with zero sequences (CZPWM), including a power loss reduction of 50% and a 50% decrease in the THD of the output voltage. In addition, applying this technique results in enhanced output current quality, reduced power loss by 40%, and decreased inductive current ripple by 50% under unbalanced load conditions. Furthermore, the proposed 3DZSVM control strategy for 4L-qZSI is experimentally verified using the TMS320F28379D kit based on the Hardware-in-the-Loop (HIL) simulator. This demonstrates the practicality and effective performance of the suggested control strategy under unbalanced load conditions.
... Because the FESS motor is driven by a four-bridge arm inverter under both norm and fault conditions, attention should be paid to the operation of the four-bridge arm verter. There are two modulation methods for a four-bridge arm inverter: the 3D-SVPW method [21,22] and the carrier-based PWM method [23]. The 3D-SVPWM method is m complex than the carrier-based PWM algorithm, but the former has evolved from the tw dimensional SVPWM, and their core control ideas are similar to each other; therefore, 3D-SVPWM method is used as the modulation method of the inverter. ...
... Because the FESS motor is driven by a four-bridge arm inverter under both normal and fault conditions, attention should be paid to the operation of the four-bridge arm inverter. There are two modulation methods for a four-bridge arm inverter: the 3D-SVPWM method [21,22] and the carrier-based PWM method [23]. The 3D-SVPWM method is more complex than the carrier-based PWM algorithm, but the former has evolved from the two-dimensional SVPWM, and their core control ideas are similar to each other; therefore, the 3D-SVPWM method is used as the modulation method of the inverter. ...
This study presents a bridge arm attached to the FESS motor’s neutral point and reconstructs the mathematical model after a phase-loss fault to assure the safe and dependable functioning of the FESS motor after such fault. To increase the fault tolerance in FESS motors with phase-loss faults, 3D-SVPWM technology was utilized to operate the motor. The parameters of the zero-axis current compensation control were modified based on the dual-closed-loop control strategy for the speed and current. The simulation experiments conducted in this study demonstrate that the fault-tolerant control strategy adopted can significantly reduce excessive torque pulsation after the phase failure of the FESS motor, stabilize the motor output torque, and improve the fault-tolerance performance of the FESS motor’s control system for the FESS motor.
... In order to overcome the unbalanced load problem, the configuration and the control block diagram of a 4-leg CVCF inverter to adapt a linear/nonlinear or a balanced/unbalanced load is illustrated, as shown in Figure 2. The idea of a 4-leg CVCF inverter is to add one leg to the bridge of a conventional 3-phase 3-wire CVCF inverter to compensate for the deviation of the line-to-line voltage depending on the unbalanced load. The 4-leg CVCF inverter adopts an offset SVPWM algorithm to directly control the reference voltage of the N-phase as offset voltage, as shown in Figure 3 [15][16][17][18][19][20]. the αβ-dq0 transformers. ...
... In order to overcome the unbalanced load problem, the configuration and the control block diagram of a 4-leg CVCF inverter to adapt a linear/nonlinear or a balanced/unbalanced load is illustrated, as shown in Figure 2. The idea of a 4-leg CVCF inverter is to add one leg to the bridge of a conventional 3-phase 3-wire CVCF inverter to compensate for the deviation of the line-to-line voltage depending on the unbalanced load. The 4-leg CVCF inverter adopts an offset SVPWM algorithm to directly control the reference voltage of the N-phase as offset voltage, as shown in Figure 3 [15][16][17][18][19][20]. ...
In general, severe load imbalances in small AC micro-grid systems can degrade their operational performance and their maintenance. This is because the unbalanced load in the micro-grid affects the energy flow and the voltage regulation functions of each phase. In order to solve the voltage imbalance problem, several algorithms for the 3-phase 4-leg CVCF inverter have been proposed, but the control algorithms are not enough to operate the 4-leg CVCF inverter in a stable manner. Therefore, this paper proposes a single-phase voltage and power control algorithm for the 3-phase 4-leg CVCF inverter based on a dq control in order to improve the voltage imbalance problem caused by a severely unbalanced load, where the single phase voltage control algorithm is composed of an αβ-dq and a dq-αβ transformer, a voltage and a current controller, and an off-set controller and a PWM, and the single-phase power control algorithm is also composed of an αβ-dq and a dq-αβ transformer, an active/reactive power and a current controller, and an off-set controller and a PWM. Additionally, this paper performs modeling of the single-phase voltage and the power controller for a 4-leg CVCF inverter using the Matlab/Simulink S/W. From the simulation results, it is confirmed that the transient stability of the proposed single voltage control algorithm can be improved compared to the conventional control algorithm, and voltage control can also be maintained in a stable manner under extremely unbalanced conditions. Further, it is confirmed that 3-phase currents of the proposed single-phase power control algorithm are controlled in a stable manner under extremely unbalanced conditions.
... Various types of switching methods are also proposed to control the switches of all four legs [14], [15]. Three-dimensional space vector modulation (3-D SVM) is one of the most common methods used for this approach [10]. ...
... In the next step, the abc signals are imported to the PWM block to create the switching signals and produced the three-phase reference voltages of the inverter. The carrier-based PWM method has been used in this research for the generation of the inverter output voltages [14]. This method has been applied because of its strong performance and simple implementation. ...
span lang="EN-US">Stand-alone low voltage (LV) microgrids supplying small local loads far from the utility grid are becoming an increasingly popular alternative to a total reliance on the centralized utility grid. In most of LV microgrids, three-phase four-wire distribution systems are used to supply both single- and three-phase loads. Unequal distribution of loads can result in voltage unbalance problems. The use of the four-leg inverter is one of the best solutions for providing a neutral current path and compensating unbalanced load conditions in stand-alone LV microgrids. This paper proposes a fast control technique to compensate unbalanced voltage conditions for a four-leg inverter operating in a stand-alone LV microgrid. The suggested technique provides the current controller’s orthogonal component without introducing any additional dynamics or distortions. The major benefits of the recommended per-phase control technique over conventional orthogonal signal generation (OSG) methods are enhanced steady-state and dynamic performances as well as independency to the system parameters. Several simulation results are provided to confirm the superior performance of the suggested methods.</span
... It can be linearly controlled until MI becomes 1, but it shows non-linear output when MI is over 1. The space vector modulation was a typical scheme to improve the sinusoidal modulation with offset voltage control [27][28][29][30]. Figure 6 shows an equivalent circuit for the MMC operated in NLC. The most traditional scheme is to generate the pole voltage same as the phase voltage command, which is called the sinusoidal modulation. ...
... It can be linearly controlled until MI becomes 1, but it shows non-linear output when MI is over 1. The space vector modulation was a typical scheme to improve the sinusoidal modulation with offset voltage control [27][28][29][30]. ...
This paper proposes an offset voltage control scheme for the modular multilevel converter (MMC) operated in nearest level control (NLC) to improve the total harmonic distortion (THD) of AC phase voltages. The offset (neutral-to-zero-point) voltage is adjusted so that the magnitude of each AC pole voltage maintains constant value with N + 1 level in the range of whole modulation index (MI). The validity of the proposed scheme was confirmed by computer simulations for the MMC with 22.9 kV/25 MVA and experimental works for the scaled MMC with 380 V/10 kVA. It was confirmed that the proposed control scheme can generate linearly variable AC phase voltages with improved THD in the over-modulation region as well as the normal-modulation region.
... A fault-tolerant inverter topology was discussed in (Liu et al. 1993) based on the connection of the stator winding's neutral point to the midpoint of split capacitors. Another topology is known as 4L-NAL, which consists of connecting the motor's neutral point to a fourth inverter leg (Kim and Sul 2004). The latter topologies are suitable only for star-connected drives. ...
This paper proposes a new fault-diagnosis method and fault-tolerance control (FTC) strategy applied to the field-oriented control (FOC) of induction motor drives. The proposed diagnosis method for open-switch faults (OSFs) relies solely on measured current behavior. The diagnostic variables are extracted from the average absolute values of the normalized phase currents. The simulation results show that the diagnosis method can detect the OSFs in less than 36% of the fundamental phase current period without additional sensors. A total of nine types of OSFs can be diagnosed accurately and quickly. In addition, the obtained results demonstrate the method’s robustness against load-transient conditions. Compared with existing diagnosis methods, this technique relies on two diagnostic variables and an adaptive detection threshold. To improve the drive’s reliability against OSF effects, a fault-tolerant control scheme is developed based on reconfiguring the voltage source inverter (VSI) topology. In this case, the faulty VSI phase is connected to the DC-link midpoint through bidirectional power switches. Most FTC systems reported in the literature require a change in the drive’s control algorithm. Hence, this paper presents a low-cost FTC scheme without changing the FOC algorithm. Simulation results are carried out in MATLAB-Simulink to validate the effectiveness of the proposed fault diagnosis method and the FTC strategy.
... These converters are called four-leg four-wire converters (4L4Ws). Many works focus on 4L4W converters because of their higher capacity to compensate for homopolar currents and greater design flexibility [6,[12][13][14][15][16]. Despite its potential for higher efficiency, concerns regarding system complexity and cost implications persist, since this configuration requires more semiconductors and components than 3L4W converters. ...
This article presents a new modulation technique called three-dimensional sigma–delta (3D-ΣΔ) modulation for high-frequency three-leg four-wire voltage source converters (VSCs) that use wide-bandgap (WBG) semiconductors. These WBG devices allow for the use of high switching frequencies with a greater efficiency than silicon devices. The proposed 3D-ΣΔ technique enables operation at a variable switching frequency, resulting in a significant reduction in switching losses compared to classical pulse-width modulation (PWM) techniques. Moreover, the 3D-ΣΔ technique uses a fast-processing 3D quantiser that simplifies implementation and considerably reduces computational costs. The behaviour of the 3D-ΣΔ modulation is analysed using MATLAB/Simulink and PLECS. The experimental results performed on an active power filter that uses silicon carbide (SiC) MOSFETs demonstrate an improvement in converter efficiency compared to the conventional SPWM technique. Additionally, the experimental results show how 3D-ΣΔ allows for the compensation of harmonics and homopolar currents, thereby balancing the electrical grid currents. The experiments also show that the proposed 3D-ΣΔ modulation outperforms an SPWM technique in terms of power quality, since the former achieves a larger reduction in the harmonic content of the power grid. In conclusion, the proposed modulation technique is an attractive option for improving the performance of four-wire converters in active power filter applications.
... However, incorporating a fourth leg in the two-level converter to provide the neutral wire requires a new modulation control technique. A carrier-based PWM using an offset voltage or zero-sequence injection method is one of the most straightforward and strong performances to implement [20] for PWM. Therefore, it is applied in this study to generate and control the converter output voltage. ...
Most current grid-connected strategies are grid-following converters (GFL), where the converter is designed to follow grid
voltage and inject current into the grid. This method might not be the most satisfactory control strategy in recent years,
particularly in low inertia and weak grids, due to possible interaction triggered by a phase-locked loop (PLL) during dynamics
conditions. Therefore, a grid-forming converter (GFM) control mode was developed to allow the converter to emulate the
characteristic of the synchronous machine as an ideal voltage source to support the grid’s voltage, frequency, and grid stability
during normal and fault conditions. This paper investigates the GFM converter’s based Virtual Synchronous Machine (VSM)
on Fault Ride Through (FRT) capability when symmetric and asymmetric faults are present on the grid. The proposed FRT
approach for limiting the converter current uses indirect voltage control across the output of the filter inductor.
... The reference voltage vector (Vref) is determined when three voltage vectors are connected closest to the coordinate center. Defining reference voltage vector (Vref) needs some basic principles of geometry in accordance with the formulation developed by [20]- [22]. ...
This research analyzes the asymmetric control strategies in multilevel inverters, including asymmetric techniques in space vector modulation of power converters. Modulation parameters such as reference voltage vector (Vref), switching time, and duty cycle are derived in the three-dimensional spatial vector geometry formulation. Asymmetric space vector pulse width modulation (SVPWM) is unique in specifying modulation parameters, has unequal tetrahedron patterns, accompanied by application examples for the upper and lower sector pairs of a tetrahedron. The combination of the switch in the form of an inclined cylinder produces twelve pairs of asymmetric tetrahedrons where the voltage vector positions are in the other twenty-four tetrahedrons. The calculation shows processing dead-time in switching, which is used for current compensation in three-phase power converters.
... The phase voltage references with respect to the point N are denoted as u * an , u * bn , u * cn and u * fn . Fig. 5 shows the calculation procedure, as proposed in [7]. On the other hand, modulations of an MMC can be classified as either direct or indirect modulations. ...
... It can be calculated based on the voltage levels of the MMC, which reduces the THD of the output voltages at the PCC. The calculation method proposed in [7] is implemented in this work, as shown in Fig. 5. ...
... [14,16] . 表2 [17] . ...
... D. Sharon, et al. [48], suggested in this switched link PWM current source converters are presented. J. Kim, and S. Sul, et al. [49], addressed a voltage modulation method based on a triangular carrier wave for the three-phase four-leg voltage source converter is described. Y. ...
In this paper presents a literature survey on improvement of power factor and reduction of harmonics in three phase induction motor by Pulse Width Modulation (PWM) techniques. Also presents the current status of the improvement of power factor and reduction of harmonics in three phase induction motor by PWM techniques. Authors strongly believe that this survey article will be very much useful to the researchers for fi nding out the relevant references in the fi eld of improvement of power factor and reduction of harmonics in three phase induction motor by PWM-techniques.
... Although effective, the 3D-SVM itself is complex for implementation because of the computational demands for processing numerical voltage vectors [12]- [13]. By independently modulating the fourth phase-leg with an offset zero-sequence voltage, the carrier-based modulation successfully decouples the modulation of the fourth phase-leg from that of the remaining three phase-legs, significantly simplifying the implementation complexity [14]. Nonetheless, the offset zero-sequence voltage, which is specifically designed for benefitting the inverter with higher dc-link voltage utilization [15], reduced switching losses [16], or lower EMI noises, is online calculated in an open-loop manner [17], leading the CM part in the three load voltages to be open-loop regulated. ...
Three-phase four-leg four-wire (3P4L4W) three-level (3L) inverters have the ability to supply both balanced and unbalanced loads. This letter establishes common-mode (CM) and differential-mode (DM) circuit models for the 3P4L4W 3L inverter. The 3L phase-leg CM voltage is determined by the voltage balancing control (VBC) for the split dc-bus voltages, that the DM load voltages are subject to the DM voltage control for the 3L phase-leg, and that the CM load-voltage is subject to the control for the fourth phase-leg. On this basis, a decoupled modulation is proposed where the 3L phase-legs are modulated to attain VBC and closed-loop DM load-voltage control, whereas the fourth phase-leg is independently modulated to realize the closed-loop CM load-voltage control. The proposed work has been experimentally verified, showing that the 3P4L4W 3L inverter with this decoupled modulation scheme can provide well-balanced ac load voltages and low total harmonic distortion (THD) for any type of ac loads: balanced, unbalanced, linear, and nonlinear.
... However, as the imbalance rate of the load increases, the current flowing to the neutral line increases, which occurs a voltage imbalance problem at the dc-link stage. As a result, it causes problems such as imbalance of output voltage and increased voltage distortions [1][2][3][4][5][6][7][8]. The 4-leg inverter can be applied with the space vector pulse width modulation (SVPWM) algorithm even if a leg is added, which makes switching control easy and the dc-link voltage utilization ratio high [9][10][11][12][13][14]. ...
In this paper, we analyzed the output voltage imbalance and the cause of the offset voltage in 3-phase 3-leg inverters by using Millman’s theory. Based on this result, we proposed a voltage imbalance compensation algorithm using the dc offset voltage that appeared at the neutral point voltage of the load. To apply the proposed imbalance compensation algorithm, it needs a circuit structure of 3-phase 4-wire such as split dc-link capacitor 3-leg inverter and 4-leg inverter. Therefore, the total harmonic distortion (THD) of the load phase current according to the imbalance rate of the load was analyzed for the two inverters. Then, PSIM simulation and experiments based on a 10 kW-prototype of split dc-link capacitor 3-leg inverter were implemented to verify the validity of the proposed imbalance compensation algorithm.
... phase-four-wire-(3P4W) 3L inverter. The only difference is the neutral wire which provides the path for the zero-sequence component in load currents and thus makes the 3P4W 3L inverter capable to supply both balanced and unbalanced ac loads [10]. Nonetheless, the neutral wire also provides the path for high-switching zero-sequence harmonic currents, leading to increased inductor current ripple. ...
Three-level (3L) converters have been widely used in industry for decades. Compared to the three-phase-three-wire (3P3W) 3L inverter, the three-phase-four-wire (3P4W) one is able to supply the unbalanced loads but has to afford much larger filter inductors because the neutral wire provides a path for high-switching zero-sequence currents. To save filter inductances, a neutral inductor is proposed to insert in the neutral wire. Meanwhile, a complete design methodology is put forward to design the filter inductors and the neutral inductor. With low-frequency zero-sequence currents flowing through the neutral wire, the three-phase load voltages might become unbalanced and/or distorted. To improve the voltage quality, a resonant controller, with the resonant frequency at fundamental output frequency (fo), is presented to add into the zero-sequence voltage loop for balancing load voltages; concurrently, the other resonant controller, with the resonant frequency at 3fo, is presented to insert in the zero-sequence voltage loop or neutral current loop for mitigating voltage distortion. Finally, all of the proposed works are verified on a 3P4W T-type inverter.
... Here three legs of the converter are connected to the three phases of the grid and a fourth leg provides zero sequence voltage to either a fourth conductor in four-wire power grids, a shunt-type active power filter or an earth fault compensator [147]. The necessary calculations to properly control the PWM for the approximation of the desired signal curves on all four legs of the converter requires a powerful software and hardware equipment of the digital signal processor of the controller [148,149]. This is even more difficult for four-legged converters, which are considered underdeterminate systems due to the fact that three reference voltages have to be transformed into four derived control commands [150]. ...
Both the operation of power electronic feeders as well as consumers in electrical grids and the transition to electricity generation based on renewable plants create challenges with regard to voltage quality in electrical grids. Therefore within this thesis a control concept of a storage supported device for the simultaneous provision of various system services is elaborated, analyzed and evaluated. Moreover, an approach for the energy and power management of the energy storage of this plant is presented. Essential topics of the examination are the determination of the present level of power quality, the derivation of suitable power quality indicators as well as the power distribution to the system services. In addition, the storage technologies redox-flow battery and flywheel storage, are implemented using models and combined into a hybrid storage system. For operation of the storage system with maximum efficiency an approach depending on the power values and state of charge values of the stores is investigated.
The organic horticultural farming system is a horticultural farming technique that relies on natural materials in its production and is a sustainable agriculture, in contrast to the conventional horticultural farming system which still relies on chemicals in its production process. The purpose of this research was to compare organic and conventional horticultural farming systems in Getasan district, Semarang. This study is a cross-sectional descriptive-analytical study that employed survey methodologies. This study was conducted from July to December 2019 using a sample of 314 respondents, 90 organic horticulture farmers and 224 conventional horticulture farmers as research subjects. Research results showed that the average total additional cost of restoring soil nutrients in 100 m2 / year for organic horticulture farming was IDR. 69,958.33 less than the cost for conventional farming systems, which was IDR. 79,550.00 per 100 m2 per year, with a p-value of 0.032*. The cost of purchasing fertilizer in year / 100m2 on a conventional horticultural farm was IDR. 90,575.78, greater than the cost of organic horticulture farming which was only IDR. 73,170.38 with a p-value< 0,001*. The average yield of organic horticulture farms was somewhat higher than that of conventional farms during each growing season. The average annual income from yields in 100 m2/year for organic horticulture production was IDR 2,449,246.32, while conventional IDR. 2,369,641.10 with p-value of 0.441 although not statistically significant. The average profit per 100 m2 / year for an organic horticultural farming system was IRD. 1,549,303.42, which is greater than the profit value for a conventional horticultural farming system, which was IDR. 1,450,109.82, 959,289.06, although statistically not significant, with p-value = 0.228. The total annual production cost for the organic horticulture farming system was less than the conventional system, which was IDR 901,346.78 for the organic horticulture farming system and IDR. 921,084.17 for conventional, for every 100 m2 / year with p-value = 0.383, even though not statistically significant. Statistically, there was no significant difference in labor costs between the two agricultural systems, p-value 0.702, but descriptive analysis shows that the average labor cost per 100 m2/year for organic horticulture farming was IDR. 588,859.57, which is less than IDR. 591,760.50 for conventional horticulture farming. Based on the parameters analyzed, the outcome of this study demonstrates that the organic horticulture farming system is superior to the conventional horticultural farming system. Key words: Environmental value Fertilization costs, Cultivation profits, Labor expenses, Production costs
This paper conducts an analysis of the Finite Set Model Predictive Control (FS-MPC) approach as it is applied to a three-phase four-leg converter in conjunction with a pho-tovoltaic system connected to a distributed system. Residential areas receive their power supply from a delta/wye-connected distribution transformer featuring a grounded neutral conductor, which establishes a three-phase four-wire distribution system. Typically, the loads in a low voltage distributed system are single-phase and unbalanced, potentially leading currents into the neutral that could overload the neutral conductor. The control strategy ensures sinusoidal currents with a high power factor while reducing the neutral current within the system. Simulations and experimental results are included to validate the efficacy of the proposed control strategy.
This paper presents a novel wide bandgap four-leg inverter with common mode (CM) voltage elimination implemented using a Typhoon HIL 402 as the system-level controller. The four-leg inverter is built using GaN devices to minimize the switching losses and is controlled through pulse density modulation. The CM elimination method satisfies the MIL-STD-1399 requirements including maintaining balanced voltages during unbalanced load conditions. The MIL-STD-461G conducted emission (CE) limits for current and voltage (CE101 and CE102 respectively) are also met without the use of a CM choke. Both simulation and experimental results are presented to demonstrate the efficacy of the novel control method. The control approach is detailed, and comprehensive experimental results are provided for motor drive applications at 230V under varying load conditions including the effects of deadtime on the proposed CM elimination approach and in meeting the standard requirements. Modulation strategies including sine-triangle pulse-width modulation (SPWM) and space vector pulse-width modulation (SVPWM) are also implemented in both simulation and experimentally to compare with the ΣΔM. In addition, switching power losses and dc-bus utilization comparisons with a Si inverter are included. Based on the dc-bus utilization results, an approach to increase the dc-bus utilization of the proposed CM elimination approach is presented.
This paper presents a comprehensive model predictive control (CMPC) method to control a three-phase four-legged inverter (TP4LI) for PV systems. The proposed TP4LI model aims to predictively model and control switching frequency and higher voltage/current switching to reduce losses. The CMPC model can be operated in four modes, namely standard MPC mode (Mode I), switching frequency reduction (SFR) mode (Mode II), high voltage/current switching loss reduction (SLR) mode (Mode III), and SFR plus SLR mode (Mode IV, a combination of Modes II and III). The proposed CMPC approach controls the TP4LI to (1) successfully track balanced and unbalanced reference currents with balanced or unbalanced loads; (2) reduce switching losses; and (3) keep the generated current total harmonic distortion (THD) within the industry’s recommended limits. The TP4LI model with the CMPC approach was verified and validated in the MATLAB/Simulink for a PV system. The simulation results show good tracking and performance of the TP4LI for balanced and unbalanced reference currents with balanced and unbalanced loads in all four modes of operation.
Five-phase permanent-magnet synchronous motor (PMSM) has the ability of fault-tolerant operation, which is beneficial for high reliability occasions. A fault-tolerant current vector control strategy based on five-phase six-leg inverter is proposed for open-circuit fault in this article. It deals with single-, double-, and triple-phase fault conditions. First, the overall control scheme is established based on the mathematical model of five-phase surface-mounted PMSM. To release more control degrees of freedom, the constraint for the sum of fault-tolerant phase currents is removed, and the control variates method is used to calculate the optimal fault-tolerant currents. Furthermore, to achieve the current tracking, the corresponding reduced-order current transformation matrices are derived, and the corresponding main power topology, the five-phase six-leg voltage source inverter (VSI), is established. The unbalanced operation of the topology is investigated, the equivalence to the full-bridge VSI is proved, and the voltage utilization and voltage unbalance of five phase half-bridge, full-bridge, and six-leg inverter are compared. Then, the corresponding carrier-based PWM control strategy based on zero-sequence injection has been proposed, which is equivalent with the three-dimensional space vector PWM algorithm and is computationally efficient. The experimental results confirm the effectiveness of the proposed fault-tolerant control strategy.
Unbalanced distribution of single-phase loads and the presence of nonlinear loads causes voltage unbalance in a low-voltage microgrid. Unbalanced voltages at distribution nodes severely affect the operation of many power system installations, hence requiring correction. This paper proposes a perturb and observe-based control strategy, suitable for four-leg inverters to reduce the voltage imbalances in the microgrid. The proposed method requires measurement of the voltage unbalance factor at the point of connection of the inverter to the microgrid, and injection of negative-sequence current. The negative-sequence current to be injected is generated by the superposition of two orthogonal components. These components are perturbed in four incremental neighborhoods, and the corresponding voltage unbalance factors observed. The system is shifted toward the minimum of the observed voltage unbalance points from where the system is perturbed, observed, and shifted again until the system reaches and stays at the minimum unbalance neighborhood. The shape of the 3D surface obtained by plotting voltage unbalance factor with respect to these negative-sequence current components current has been explored to develop the algorithm. Different case studies have been performed on a 25-bus, IEEE-13 bus, IEEE-34 bus, and 19-bus unbalanced radial distribution system configured as a microgrid to study the effectiveness of the proposed algorithm.
Three-phase four-leg voltage-source inverter has been extensively investigated in recent years for its compactness, small size, and high efficiency, and it has been proved to be the best solution for providing transformer-less neutral connection to three-phase asymmetric loads. The main purpose of this article is to apply 3-D unbalanced coordinate transformation to the four-leg inverter, which supplies stand-alone asymmetric loads, to maintain the balance of the output capacitor voltages, and obtain simpler control structure and better control performance. First, a double closed-loop PI control structure can be designed based on the Clarke and Park transformations. Second, the phases and amplitudes of the capacitor voltages are locked based on the 3-D unbalanced coordinate transformation. Furthermore, the Clarke transformation oriented on the inductor currents is replaced by a 3-D unbalanced coordinate transformation, and the corresponding unbalance indices are continuously adjusted according to the unbalance indices of the capacitor voltages, so as to recover the capacitor voltages to the balanced condition. The simulation and experimental results of the whole control system for the four-leg inverter are provided in the end, so as to verify the feasibility and effectiveness of the 3-D unbalanced coordinate transformation for application to the power electronic systems.
In the conventional sliding mode control, the four-leg distribution static compensator (DSTATCOM) currents are controlled based on a current error in each phase. However, the four currents in a four-wire system can not be independently controlled variables and hence one of the four controllers is redundant in conventional schemes. Further, the current dynamics of a DSTATCOM converter are coupled through converter pole voltages in the natural reference frame. This leads to cross-coupling in the sliding variable equations with respect to four manipulated input variables. Considering the above points, in this paper, the current due to Thevenins equivalent load neutral-point voltage is considered as a fourth independent controlled variable and the corresponding system dynamic equations are presented. To get a decoupled feature, a new sliding surface function is structured. The performance of a DSTATCOM with the proposed control scheme under various operating conditions is validated through a detailed simulation study and experimental results, obtained from a laboratory prototype of four-leg DSTATCOM.
This paper presents a carrier-based pulsewidth modulation (PWM) method that reduces the common-mode voltage (CMV) of a three-level four-leg converter. Based on an analysis of space vector PWM (SVPWM) and sinusoidal-PWM switching patterns, the fourth-leg pole voltage of a three-phase converter, known as the “f pole voltage,” is manipulated to reduce the CMV. To synthesize the f pole voltage for the suppression of the CMV, positive and negative pole voltage references of the f leg are calculated. In addition, the offset voltage to prevent distortion of the a, b, and c phase voltages regarding the neutral point is deduced. The proposed PWM strategy can be easily implemented in the software of a DSP-based converter control. The three-level four-leg converter with the proposed PWM algorithm results in a remarkable reduction in the peak-to-peak value of the CMV. From the simulation and the experimental results, the peak-to-peak value of the CMV when using the proposed PWM method is 33% compared to that when using the SVPWM method, while the number of CMV transitions during the switching period in the proposed PWM method is only 25% of that when using the SVPWM method.
Unbalanced loads cause the imbalance of the grid current and the resulting imbalance of the grid voltage when the imbalance rate of the grid current increases considerably. To cope with this problem flexibly at low cost, we modify the circuit structure from previously installed Δ-Y transformer 3-phase 3-leg inverter to split dc-link capacitor 3-leg inverter eliminating the transformer. And then we propose two kinds of compensation algorithms for balancing the grid current that can basically utilize a preinstalled control board. It is divided into reactive compensation, where dc-link of the inverter does not supply effective power to the grid but compensates for the imbalance of grid current, and effective compensation, where dc-link of the inverter supplies effective power to the grid for compensating the unbalanced grid current. We design an additional power calculator board to obtain power information, and apply it to a 10kW prototype, and then verify its validity through PSIM simulation and experiments.
Continuous and discontinuous pulse-width modulation (PWM) schemes and a novel space vector modulation methodology are proposed in this paper for four-leg DC-AC inverters. Using a space vector definition that includes the zero sequence voltage component and partitioning the feasible sixteen modes into two separate sets-one set having zero sequence voltages with positive magnitudes and the other set with the zero sequence voltages with negative magnitudes-the novel space vector implementation technique is determined as also the discontinuous carrier based PWM scheme. For the continuous carrier based PWM scheme, the indeterminate defining output voltage equations expressed in terms of the existence functions of the switching devices are solved using an optimization technique. The modulation schemes determined are shown by experimental results to synthesis any desirable balanced or unbalanced three-phase voltage sets when operating in the linear modulation region.
In the paper, two control methods of a four-leg three-phase
invertor for UPS and active filter applications are discussed. The
inverter output voltage is represented as a three-dimensional space
vector. Two PWM schemes are investigated: open loop sinusoidal PWM; and
feedback multilevel hysteresis PWM current control. Some simulated
figures and experimental oscillograms illustrating the properties of the
both presented PWM methods are given
The author evaluates the state of the art in pulsewidth modulation for AC drives fed from three-phase voltage source inverters. Feedforward and feedback pulsewidth modulation schemes with relevance for industrial application are described and their respective merits and shortcomings are explained. Secondary effects such as the influence of load-current dependent switching time delay and transients in synchronized pulsewidth modulation schemes are discussed, and adequate compensation methods are presented. Recorded oscillograms illustrate the performance of the respective pulsewidth modulation principles. The author provides a guideline and quick reference for the practicing engineer to decide which methods should be considered for an application of a given power level, switching frequency, and dynamic response.
In this paper, a novel voltage modulation scheme is described. With the effective voltage concept, the actual switching times for each inverter arm are deduced directly as a simple form. With the help of the presented zero sequence voltage allocation algorithm, the proposed PWM method has the high performance voltage generation capability exactly same as the conventional space vector PWM method with reduced effort. As well as giving a detailed explanation of the new PWM algorithm, the paper presents the comparison results with the conventional method such as space vector PWM and sinusoidal PWM method. In the proposed PWM method, the execution time can be reduced more than 25% as compared with the conventional space vector PWM method, and memory size will be minimized to 15% of the conventional PWM method.
In this paper, position-sensorless operation of the permanent magnet motor is introduced. To estimate the rotor position and speed, a new closed-loop flux observer is proposed for wide speed operation. To extend the operation range of the proposed algorithm, a direct voltage sensing circuit is proposed that enables correct disturbance voltage rejection and stable operation of the proposed flux observer at extremely low speed. Experimental results of position-sensorless torque control are shown in order to verify the feasibility of the new algorithm using the proposed voltage sensing circuit.
Three space vector modulation schemes are analyzed for a four-leg
voltage source inverter. The analysis is performed with respect to
switching losses and total harmonic distortion under both balanced and
unbalanced load conditions over the entire range of modulation index
values and over varying load power factor angle. The analysis has been
verified using simulation
Classical space vector PWM with equal duration of application of
zero state vectors V0 and V7 was modified. The time of application of
vector V7 (and V0) was made changeable from 0 to 100% over the time T
<sub>0</sub> for their combined application. The ratio of the duration
of application of vector V0 vs. V7 can be kept constant or changed on a
sample by sample basis with a significant impact on the characteristics
of the PWM. Correlation between modified space vector and triangle
comparison methods was established. It was proved in the paper that
modified space vector PWM (with a classical space vector PWM as a
special case) can be implemented as a triangle comparison method with
added zero sequence. A new algorithm suitable for implementation of
modified space vector method on digital or analog hardware for triangle
comparison PWM was proposed. Because the algorithm combines the theory
of space vector PWM with ease of implementation of a triangle comparison
PWM it was named “hybrid” PWM (HPWM)
A four-wire active filter has been implemented. It neutralizes
current harmonic effects, caused by any configuration of nonlinear loads
in three-phase, four-wire systems. The results of a laboratory
implementation are presented. These results are compared with those from
computer simulations. Key design issues are discussed
A novel active harmonic-neutralizing filter is proposed which
eliminates current harmonic effects, caused by any configuration of
nonlinear loads in a three-phase, four-wire systems. The authors present
proposed filter topologies and simulation results verifying the concept.
Theoretical analysis of the circuit is included to facilitate a detailed
converter design. The proposed topology is shown to have distinct
advantages over traditional approaches to the problem, particularly over
the three single-phase inverter approach
The paper presents a three-dimensional space-vector-modulation
scheme for three-phase four-wire active power filters. The focus is on
the implementation of a fixed frequency pulse width modulation (PWM)
scheme with a minimum number of switch commutations per period and
maximum DC bus voltage utilisation. For three-wire applications, space
vector modulation is known to provide better utilisation of the DC
voltage compared to a sinusoidal PWM approach. This concept is extended
to four-wire applications by employing a four-leg active power filter.
The largest symmetrical region in which the active filter's voltage
space vector may reside is identified. Restricting the voltage space
vector to this region avoids over-modulation and thereby prevents the
production of low order harmonics. A digital controller is employed to
provide deadbeat current control. The combination of the digital
controller and the modulation scheme gives the four-leg active power
filter the capability to independently track reference current waveforms
in the three phases within one switching period. The four-leg active
power filter may be used for harmonic compensation, reactive power
compensation, load balancing, and neutral current compensation.
Experimental results obtained from a 5 kVA laboratory active power
filter validate the proposed modulation scheme as well as the control
design
Four-leg voltage-source converters can effectively provide the
neutral connection in three-phase four-wire systems. They can be used in
inverter, rectifier, and active filter applications to handle the
neutral current caused by the unbalanced and/or nonlinear load or
unbalanced source. In this paper, three-dimensional (3-D) space vector
modulation (SVM) schemes are proposed for controlling the four-leg
voltage-source converters. Important issues for 3-D SVM, such as
definition of 3-D vectors, identification of adjacent switching vectors
in the 3-D space, and switching vector sequencing schemes and
comparisons are addressed. The proposed 3-D SVM is a superset of the
traditional two-dimensional (2-D) SVM, and thus it inherits all the
merits of the traditional 2-D SVM. A 100 kW 5 kHz four-leg inverter and
a 20 kHz four-leg rectifier prototypes are built and controlled by the
proposed 3-D SVM. Experimental results are presented to validate the
effectiveness of the 3-D SVM
Voltage unbalance in AC supply systems is typically corrected by
means of a shunt connected thyristor-controlled static VAr compensator.
This approach has the disadvantage of slow response, harmonic injection
into the AC system, and the requirement for large passive components.
The proposed system consists of a three-phase PWM voltage source
inverter, connected in series with the line through a three-phase
transformer. The unbalance compensation is achieved by canceling the
negative sequence component of the line-to-line voltages of the source.
It is also shown that by having the inverter operate with unbalanced
switching functions, it is possible to balance the load voltage and to
control the amplitude of the positive sequence component in order to
perform load voltage regulation. A complete mathematical description of
the method is presented, demonstrating that the compensation can be
achieved with low kVA inverters and low harmonic injection.
Implementation procedures, design equations, and a design example are
also included in order to illustrate the proposed method. Experimental
results of a 1.5 kVA laboratory prototype system confirm the feasibility
of the technique
In this paper, a new voltage modulation technique named
“unified pulsewidth modulation (PWM)” is described for
high-performance voltage generation in a three-phase voltage-fed
inverter. By considering the operation of the inverter, a simple but
useful concept named “effective time” can be established
and, by fully employing this concept, a new voltage modulation technique
is presented with a detailed explanation and actual test results. The
results show that various carrier-based PWM schemes can be implemented
with reduced computational burden and a seamless change from one
modulation scheme to another is possible
Pulsewidth modulation has been one of the most intensively
investigated areas of power electronics for many years, and the number
and combination of permutations seem to be endless. However, a general
hierarchical consensus appears to have emerged from this work which
ranks space vector modulation techniques, regular sampled modulation,
and sine-triangle modulation strategies in decreasing order of merit
based on harmonic performance. However, what has not been clearly
identified is why space vector modulation should lead to a reduced
harmonic current ripple compared to regular sampled modulation,
especially since it is straightforward to show that they produce
identical low-frequency fundamental components. This paper addresses
this issue by showing how it is the placement of the zero space vector
component within the carrier interval that determines the harmonic
performance of the modulation strategy, rather than any intrinsic
differences between the various methods of calculating the switching
instances
A space vector concept for deriving the switching times for
pulsewidth-modulated voltage source inverters is compared with the
conventional sinusoidal concept. The switching times are deducted from
assumptions for minimum current distortion, the resulting mean voltage
values are shown, and the differences between these and the established
sinusoidal PWM (pulse-width modulator) are elaborated. Based on an
analytical calculation the current distortions and torque ripples are
evaluated and compared with the values obtained with the conventional
method. The space vector representation results in lower current
harmonics and possibly a higher modulation index. A modulator based on
an 8086 microprocessor has been implemented, and its performance is
reported
a new series voltage compensator scheme for the unbalanced utility conditions
- lee
S.-J. Lee and S.-K. Sul, "A new series voltage compensator scheme for
the unbalanced utility conditions," in Proc. EPE'01, 2001.
Analysis and comparison of space vector modulation schemes for a four-leg inverter
- V H Prasad
- D Boroyevich
- R Zhang
V. H. Prasad, D. Boroyevich, and R. Zhang, "Analysis and comparison
of space vector modulation schemes for a four-leg inverter," in Proc.
IEEE-APEC'97 Conf., 1997, pp. 864-871.