Complex Space Vector Research Articles

Generic Carrier-Based PWM Solution for Series-End Winding PMSM Traction System With Adaptative Overmodulation Scheme

The series-end winding permanent magnet synchronous machine (SW-PMSM) drive system is a new drive topology where the phase windings are connected in series. The generic carrier-based pulsewidth modulation (CBPWM) solution of SW-PMSMs will further promote their applications and avoid the computationally complex space vector PWM in multiphase SW-PMSMs. However, the existing CBPWM solution is complex and designed for symmetrical machines. Moreover, the current approach’s lack of the overmodulation method limits its application in the traction system. This article proposes an improved generic CBPWM solution for SW-PMSMs, which utilizes the vector space decomposition concept to extend the application in both symmetrical and asymmetrical machines. First, we will introduce the concept of the virtual duty axis and divide the modulation process into two steps, where the leg voltage sequence is initialized with reference phase voltages. Then, the virtual duty cycle is utilized to ensure the feasibility of the leg voltage sequence. Furthermore, we will provide an adaptative overmodulation scheme to ensure the stable fundamental currents in the whole speed range and improve the bus voltage utilization. Finally, the experimental results in three machines verify that the proposed solution can obtain better performance with lower switching frequency and have overmodulation capability.

Improved Multi-Stage Decoupling Space Vector Modulation for Asymmetrical Multi-Phase PMSM With Series Winding Connection

This article is devoted to developing a unique series-winding drive (SWD) topology, analyzing and implementing its control schemes for asymmetrical multiphase permanent magnet synchronous motor (PMSM). Proposed SWDs have higher voltage utilization than ordinary wye or delta connection, but vary with the number of inverter legs and connection sequence. Also, they have a simpler topology, fewer inverter legs, and power modules than the open-end winding drives. The article selects the typical asymmetrical six-phase (ASP) PMSM as the target. The complex space vector mapping is screened and simplified by unified hexadecimal coding for both eight-leg and seven-leg drives. Given the multiple suspaces in ASP-PMSM, a multistage decoupling space vector modulation scheme is proposed and improved for SWDs. It incorporates the processes of vector synthetization, cost function minimization, and zero-sequence compensation. Prototype fabrication and control experiments are carried out. Results show that the proposed MSD SVM is applicable to all connection sequences. It can suppress the harmonic current to a quite low level, in both steady-state and dynamic states. Also, this article discusses the current burden of the inverter and provides suggestions.

An Accurate Impedance Model of Line Commutated Converter With Variable Commutation Overlap

This paper proposes an accurate impedance model for line commutated converter (LCC) in the stationary frame. The commutation overlap process caused by the transformer leakage inductance complicates the modeling for LCC. Traditional impedance models are derived in positive sequence and negative sequence frame based on the simplified commutation overlap process, which degrades the modeling accuracy and limits the description of frequency coupling. This paper systematically analyzes the effects of the commutation overlap process on the impedance model, and the impedance model with the accurate commutation overlap process is established in the <i>dq</i>-frame. For clearly revealing the frequency coupling phenomenon of the LCC, the complex space vector is employed to extend the impedance model in the <i>dq</i>-frame to the complex <i>&#x03B1;&#x03B2;-</i>frame. A closed-loop model on PSCAD&#x002F;EMTDC is used to verify the proposed impedance model in the time-domain and the frequency-domain. The consistency between the simulation results and theoretical analysis effectively verifies the accuracy of the proposed model.

A New Interpretation of the Steady-State Two-Reaction Theory of a Salient-Pole Synchronous Machine

This work contributes two improvements to the well-established two-reaction theory of a salient-pole synchronous machine. Namely, a single circuit is proposed that explicitly accounts for the saliency in the machine. By defining new machine reactances and using a current-controlled voltage source, the proposed single circuit proposed provides an alternative to coupled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis circuit models. The new reactances are also used in a revised phasor diagram to make apparent the internally developed power of a salient-pole synchronous machine that is similar to a round-rotor synchronous machine. The revised two-reaction theory is illustrated using the mathematical model of a three-phase salient-pole synchronous machine whose equations are derived using complex space vectors instead of traditional matrix transformations. A detailed derivation is presented and the resulting equations can directly be used to solve for the steady-state operating EMF and power angle from the terminal voltages and currents in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">abc</i> coordinate system. The ease of their application is demonstrated using a numerical example of the steady-state circuit equations and the revised phasor diagrams.

Multi-carrier switching strategy for high-bandwidth potential balancing control of multilevel inverters

&lt;span lang="EN-US"&gt;This paper confers on investigation of a direct torque control (DTC) of induction motor drive by 3 level neutral point clamp (NPC) multilevel inverter. The imbalance problem may deteriorate the electric drive performances which might cause a short circuit condition. Various balancing control strategies were proposed, however, most of them employed complex space vector modulation (SVM) and hysteresis-based controller that generates variable switching frequencies. The proposed method will offer a reliable balancing control strategy with a constant switching frequency, and moreover, it will provide excellent electric drive performances. This research proposed a new multi carrier switching modulation strategy that establish a high-band-width control for neutral point potential in the NPC inverter. Potency of the proposed high-bandwidth potential balancing strategy is validated through the MATLAB/SIMULINK environment.&lt;/span&gt;

Guest Editorial: Special Section on Complex Vector Theory and Its Application in Power Electronic Systems

Complex space vectors have for decades proven their usefulness for modeling, analysis, and control design in electric power engineering. One fundamental benefit is that they allow two variables—the d and q components of the vector—to be expressed in a single-input–single-output (SISO) notation. Symmetric three-phase systems and dynamic elements can be modeled using complex-coefficient transfer functions. Various extensions, primarily the corresponding two-row real space vectors and two-by-two transfer function matrices—giving a multi-input–multi-output (MIMO) model—allow asymmetric systems and elements to be modeled as well.

Enabling Grid-Feeding Converters With a Dissonant-Resonant Controller for Negative-Sequence Voltage Elimination

The mitigation of the adverse effects of voltage unbalance in equipment and power quality can be performed by the power electronic converters that interface distributed generators to the grid. Inspired in a resonant controller, this article presents a dissonant-resonant controller for negative-sequence voltage elimination for a grid-feeding converter connected to the grid. The controller eliminates the negative-sequence voltage at the converter output with a regulable precision, it does not require knowing the grid impedance for successful operation, and it can be a good candidate for parallel operation because it operates not like an integrator, but like an “untuned” integrator. Using the stationary $\alpha \beta$ frame, a closed-loop model is developed in a complex space vector built from the complexification of the stationary components. This allows extracting stability conditions for safe closed-loop operation as well as deriving design guidelines for the controller parameters. Numerical and experimental results show the ability of the proposed controller to meet its design goals, thus, corroborating the theoretical approach.

Impedance and Stability Analysis of Voltage-Source Converter Interconnection Based on a Universal Admittance Model

A universal admittance model of voltage-source converter applicable to various DQ-frame-based control architectures is developed from the sequence-domain complex space vector analysis. The lumped sequence admittances of converter interconnection considering multicoupling effects are derived based on the converter admittance model, in which two coefficients are defined to quantify the cross-coupling effect between the ac and dc networks. From the universal model, the converter admittances with three typical control architectures and the lumped admittances of converter interconnection are calculated, compared, and verified with time-domain point-by-point simulations. Experiments are also conducted for further verification. Stabilities of the converter interconnection with the three typical control architectures are analyzed and compared. The obtained results indicate that introducing the outer dc voltage control can not only reinforce the coupling between ac and dc circuits but also degrade the stability performance of ac and dc circuits both.

Sequence-Impedance Modeling of Voltage Source Converter Interconnection Under Asymmetrical Grid Fault Conditions

Nonlinear behaviors of voltage source converter (VSC) and the interconnection under grid fault conditions are discussed in the article. Based on the discussion, a sequence-impedance model is developed from the complex space vector analysis. Lumped sequence admittances of the converter interconnection and perturbation propagation considering the coupling between ac and dc circuits are presented in this article. The influence of the phase-locked loop design for improving low-voltage ride-through performance on the sequence-admittance model is also introduced. The sequence admittances are calculated, compared, and verified with point-by-point simulations and experiment. Obtained results indicate that the sequence-admittance model is effective for describing and predicting the behavior of VSC interconnection under asymmetrical grid fault conditions.

Effect of Reactive Power Characteristic of Offshore Wind Power Plant on Low-Frequency Stability

Oscillation phenomena of offshore wind power plant (OWPP) in a wide frequency range can be caused due to impedance interactions between grid-connected inverters (GCIs) and transmission cables. In this article, impedance model of GCI with outer power control loop, inner current control loop and phase-locked loop is first established in dq reference frame. The correctness is validated by frequency scanning method. Then, the effects of active and reactive power/current references on dq impedance characteristics of GCI with/without consideration of power control loop are investigated using complex space vectors and complex transfer functions. Furthermore, RLC circuit model of transmission cable considering frequency-dependent characteristics is also established for dq-domain IBSC. On the basis of them, it's found that low-frequency oscillation phenomena of OWPP under power control mode may occur if active power reference exceeds a certain threshold value, which can be mitigated by injecting a certain amount of negative reactive power. Impacts of PLL parameters, length of transmission cable and number of paralleled GCIs on required negative reactive power for low-frequency stabilization are further investigated. Both Matlab/Simulink-based simulation and OPAL-RT-based real-time verification are implemented in an OWPP with four permanent magnet synchronous generators to validate the correctness of the reactive power characteristic analysis results and the feasibility of mitigating low-frequency oscillation phenomena by negative reactive power injection.

Hexagon hysteresis current control-based STATCOM for grid connected wind turbine system

The use of renewable power sources, like wind power, has been increased recently due to climatic changes caused by fossil fuels and fast depletion of fossil fuels. This has lead to the tremendous increase in the interconnection of wind turbines to power system grid. This interconnection of wind turbines on a large number in grid causes problems such as power quality, maintaining system voltage, reactive power compensation, control of grid frequency and aspects of power system grid stability. In this paper, STATCOM utilises hexagon hysteresis current control (HHCC) to improve the power quality. The proposed control scheme supplies the required reactive power to the system and thus, relieves the source, leading to unity power factor (UPF) at the source and also, it injects currents to reduce THD to satisfy IEC standard. In the proposed HHCC, the current control has been achieved by transforming the three phase (a, b, c) system into stationary (α, β) reference frame and the complex space vector concept is employed. Further, the proposed system's dynamic response has been studied and the results have been presented.

Hexagon hysteresis current control-based STATCOM for grid connected wind turbine system

The use of renewable power sources, like wind power, has been increased recently due to climatic changes caused by fossil fuels and fast depletion of fossil fuels. This has lead to the tremendous increase in the interconnection of wind turbines to power system grid. This interconnection of wind turbines on a large number in grid causes problems such as power quality, maintaining system voltage, reactive power compensation, control of grid frequency and aspects of power system grid stability. In this paper, STATCOM utilises hexagon hysteresis current control (HHCC) to improve the power quality. The proposed control scheme supplies the required reactive power to the system and thus, relieves the source, leading to unity power factor (UPF) at the source and also, it injects currents to reduce THD to satisfy IEC standard. In the proposed HHCC, the current control has been achieved by transforming the three phase (a, b, c) system into stationary (α, β) reference frame and the complex space vector concept is employed. Further, the proposed system's dynamic response has been studied and the results have been presented.

Enhanced Complex Space Vector Modeling and Control System Design of Multiphase Magnetically Levitated Rotary–Linear Machines

Rotary–linear electric machines can perform coupled rotary and linear motion. In addition, they can have magnetic bearings (MBs) integrated and magnetically coupled with the rotary, linear, or rotary–linear machine operation. Since rotary–linear machines with MBs have not been thoroughly analyzed in the literature, the models that provide understanding of their operation and give basis for the control system implementation are not entirely covered. Hence, in this article, an enhanced complex space vector-based model of the rotary–linear machine with MBs is derived and expressions for the torque, thrust force, and MB force are given. The rotary–linear machine complex space vector of the voltage, current, or flux linkage is defined using the proposed transformation with two complex frames: one related to the rotation and MBs and another to the linear motion. This results in complex space vectors with two complex units; however, the techniques used for a conventional complex space vector calculation can also be applied to the proposed complex space vector description. This is also experimentally validated on a hardware prototype of a magnetically levitated linear tubular actuator (MALTA), whose position control system is designed and implemented based on the enhanced space vector modeling approach, with the dynamic operation of the MALTA, including linear motor operation with an axial stroke of 10mm and a mechanical frequency of 17Hz.

Improvement of Induction Motor Torque Characteristics by Model Predictive Current Controller

This paper describes the Model Predictive control (MPC) strategy to control the Torque of the Induction Motor (IM) according to the reference torque provided. IM fed with an Three Level Neutral Point Clamped (NPC) Inverter. MPC paves the way to replace complex Space Vector Modulation (SVM) into a simple understandable algorithm. It uses the discretized model of the IM. Stator current is used as a control variable hence called Model Predictive Current Control (MPCC). MPCC is derived from Field Oriented Control (FOC) Technique. MPCC achieves improved nominal torque compared to FOC, But current harmonics are high rather it’s simplicity encourages it’s usage and further development in MPC strategies for Embedded Drives. By the end of the paper, both FOC and MPCC controls of IM drive were discussed using MATLAB/SIMULINK.

A Stationary-Frame Current Vector Control Strategy for Single-Phase PWM Rectifier

Traditional current control methods for a single-phase rectifier in an electric traction drive system suffer from either long response time or nonzero steady-state error. A novel current vector control strategy in stationary-frame is therefore proposed, in this paper, to improve the control performance of a rectifier. The mathematic model of the single-phase two-level pulse rectifier was first analyzed by complex space vector. Then, the principle of the proposed current control method was described. Based on this, the implementation and parameter tuning method of the current control algorithm based on a space complex vector in a two-phase stationary coordinate system are presented. Moreover, two kinds of general current control algorithms are analyzed and compared with the proposed algorithm to demonstrate the advantages of the proposed algorithm. The proposed control scheme absorbs advantages of the conventional control schemes, including fast response, zero steady-state error, and active and reactive power independent control, but overcomes their shortcomings. Finally, the theoretical analysis is verified by means of simulation as well as a hardware-in-loop experimental test on an experimental laboratory setup and some comparisons with conventional current control algorithms prove the advantages of the utilized method.

A Duty Cycle Space Vector Modulation Strategy for a Three-to-Five Phase Direct Matrix Converter

The duty cycle space vector (DCSV) modulation strategy is of universal significance, and the method can be utilized for different modulation approaches. In this paper, the vectors of input voltages and currents are equivalently represented by a complex two-dimensional space vector, and the vectors of output voltages and currents are equivalently represented by two two-dimensional space vectors. Then, input–output relationships in both the d1-q1 space and the d3-q3 space are obtained. Because the desired output voltages are only mapped onto a reference voltage space vector in the d1-q1 space, the reference in the d3-q3 space is regarded as zero, in order to reduce harmonics of output voltages to the greatest extent. Then, the duty cycle space vector modulation strategy of the three-to-five phase direct matrix converter (DMC) is deduced. Considering the influence of the zero vector on system performance, the duty cycles are decomposed and recomposed to obtain the space vector pulse width modulation (SVPWM) strategy based on the duty cycle space vector. Finally, the accuracy and feasibility of the theory are verified through experiments.

Stability Analysis Method for Three-Phase Multi-Functional Grid-Connected Inverters With Unbalanced Local Loads Considering the Active Imbalance Compensation

This paper proposes a small-signal stability analysis method for the three-phase multi-functional grid-connected inverter (MFGCI) system with an unbalanced local load based on impedance modeling. To attenuate the imbalance introduced by the local load, a modified power quality-compensation algorithm for the MFGCI based on the conservative power theory is proposed and incorporated into the stability analysis. The impedance model of the three-phase system is developed by adopting the complex space vector method to simplify the stability analysis process in this paper. In addition, based on the proposed impedance model and stability analysis, it is proven that the unbalanced local load can affect the stability of the system when the grid-impedance is not negligible. Furthermore, the adoption of the active imbalance compensation can reshape the impedance characteristics of the unbalanced system and improve the stability. The accuracy of the proposed impedance model, and the stability analysis results are verified by the simulation and experimental results.

Unified Impedance Model of Grid-Connected Voltage-Source Converters

This paper proposes a unified impedance model of grid-connected voltage-source converters for analyzing dynamic influences of the phase-locked loop (PLL) and current control. The mathematical relations between the impedance models in the different domains are first explicitly revealed by means of complex transfer functions and complex space vectors. A stationary ( αβ -) frame impedance model is then proposed, which not only predicts the stability impact of the PLL, but also reveals its frequency coupling effect. Furthermore, the impedance shaping effects of the PLL on the current control in the rotating ( dq -) frame and the stationary ( αβ -) frame are structurally comapred. The frequency-domain case studies on a three-phase grid-connected converter are next presented, and subsequently validated in time-domain simulations and experimental tests. The close correlations between the measured results and theoretical analysis confirm the effectiveness of the stationary-frame impedance model.

Fast Switching Direct Torque Control Using a Single DC-link Current Sensor

This paper presents a fast switching direct torque control (FS-DTC) using only a single DC-link current sensor. In FS-DTC, six new active voltage complex space vectors (CSVs) are synthesized by the conventional active voltage space vectors (SVs). The corresponding sectors are rotated in the anticlockwise direction by 30 degrees. A selection table is defined to select the CSVs. Based on the "Different Phase Mode", the output sequence of the selected CSV is optimized. Accordingly, a reconstruction method is proposed to acquire the phase currents. The core of the FS-DTC is that all of the three phase currents can be reliably reconstructed during every two sampling periods, which is the result of the fast switching between different phases. The errors between the reconstructed and actual currents are strictly limited in one sampling period. The FS-DTC has the advantages of the standard DTC scheme such as simple structure, quick torque response and robustness. As can be seen in the analysis, the FS-DTC can be thought of as an equivalent standard DTC scheme with 86.6% of the maximum speed, 173.2% of the torque ripple, and 115% of the response time of the torque. Based on a dSPACE DS1103 controller, the FS-DTC is implemented in an induction machine drive system. The results verify the effectiveness of the FS-DTC.

Comparative Analysis of Discontinuous and Continuous PWM Techniques in VSI-Fed Five-Phase Induction Motor

This paper reports on flux harmonic distortion factor and current ripple analysis for various discontinuous pulse-width-modulation (PWM) techniques, which are applicable in conjunction with five-phase two-level inverter-fed induction motors. The analysis is based on the application of the complex space vector approach. The results are compared throughout with the corresponding continuous PWM techniques. Different space vector PWM and carrier-based PWM methods are encompassed by the analysis. This paper is supported by extensive simulation results. Verification of theoretical findings is provided through experimental measurements on a five-phase induction motor.