Stationary Reference Frame Research Articles

Induction Motor DTC Performance Improvement by Inserting Fuzzy Logic Controllers and Twelve-Sector Neural Network Switching Table

Human civilization has changed forever since induction motors were invented. Induction motors are widely used and have become the most prevalent electrical componentsdue to their beneficial characteristics. Many control strategies have been developed for their performance improvement, starting from scalar to vector to direct torque control. The latter, which is a class of vector control, was proposed as an alternative to ensure separate flux and torque control while remaining completely in a stationary reference frame. This technique allows direct inverter switching and reasonable simplicity compared to other vector control techniques, and it is less sensitive to parameter variation. Yet, the use of hysteresis controllers in conventional DTC involves undesired ripples in the stator current, flux, and torque, which lead to bad performances. This paper aims to minimize the ripple level and ensure the system’s performance in terms of robustness and stability. To generate the appropriate reference control voltages, the proposed method is an improved version of DTC, which combines the power of fuzzy logic, neural networks, and an increased number of sectors. Satisfactory results were obtained by numerical simulation in MATLAB/Simulink. The proposed method was proven to be a fast dynamic decoupled control that robustly responds to external disturbance and system uncertainties.

Current Measurement Offset Error Compensation in Vector-Controlled SPMSM Drive Systems

Current measurement offset errors occur in current sensors and related circuits, because of various factors, such as thermal drift, aging, and nonlinearity. The current offset error results in undesired torque ripples, which deteriorate the speed and torque control performances of vector-controlled drive systems. This study proposes an online current measurement offset error compensator for vector-controlled surface permanent magnet synchronous motor (SPMSM) drive systems. The proposed compensator requires only phase current sensors and no additional hardware. This method is applicable for all systems using two and three phase current sensors. The current offset error is estimated using the motor parameters, stator current, and command voltage in the stationary reference frame. This scheme can continuously adjust the current offset during motor operation. In addition, this study analyzes the effect of parameter errors and confirms that the proposed method is robust to variations in the machine parameters. Simulation and experimental results are provided to verify the performance of the proposed current measurement offset error compensation method.

Self-Synchronizing Stationary Frame Inverter-Current-Feedback Control for LCL Grid-Connected Inverters

Current regulation of inductive–capacitive–inductive (LCL) grid-connected inverters usually requires multiple current sensors to actively damp the filter resonance. Inverter-side current regulation avoids this issue because of its inherent LCL filter damping properties but does not accurately control the grid-side current, particularly with distorted grids. Furthermore, both strategies typically require high-quality voltage sensors to maintain precise grid synchronization. This article proposes a novel current control strategy for LCL grid-connected inverters that only requires inverter-side current sensors. The strategy uses the resonator output states of a stationary reference frame (SRF) proportional resonant (PR) current regulator to estimate the grid voltage phase and filter capacitor current and, thus, achieve self-synchronized indirect regulation of the grid-side current. The effectiveness of the approach has been verified using simulation and matching experimental investigations.

Extended Digital Programmable Low-Pass Filter for Direct Noise Filtering of Three-Phase Variables in Low-Cost AC Drives

This paper proposes an extended structure of a programmable low-pass filter (PLPF) for direct filtering of three-phase variables in automotive AC drives. The PLPF adjusts its cut-off frequency according to the synchronous frequency of the AC motors. Moreover, it compensates gain attenuation and phase delay of the fundamental component signal. The conventional PLPF can only be applied to variables in the stationary reference frame. In order to obtain filtered three-phase variables, an inverse reference frame transformation is required. However, the extended structure, which includes reference frame transformations, can be directly applied to three-phase variables and remove the noise in the earlier stage before transformation. The extended PLPF is more useful for making signal flows clear and intuitive when organizing an algorithm that directly requires three-phase variables. The extended PLPF requires a moderate computational load corresponding with that of the conventional PLPF because its formula is simplified by use of Kirchhoff’s law. The reduction in the execution time is critical for implementing the filter based on low-cost microcontrollers. Using case studies, dead-time compensations and open-phase fault detection for AC drives show the effectiveness of the extended PLPF.

The Problem With the Relativity of Simultaneity

Relativity claims that the simultaneity between two (or more) observers, each traveling in different Inertial Reference Frames (IRFs) is such that for two spaceships moving through space at a high-speed relative to one another “inside the frame of reference of Ship A, everything is moving normally, but everything over on Ship B appears to be moving slower (and vice versa)”. However, as I will explain, this interpretation leads to an inconsistency which cannot be true. I point out the error being made in the interpretation of Minkowski diagrams that leads to this inconsistency, and how the diagram should be interpreted to correct this error. This paper demonstrates that a moving object’s rate of time is determined based on its speed relative to a stationary reference frame and that the light signals propagating between objects (from which observers can determine the other object’s rate of time) move at the speed of light c with respect to this stationary frame. If two objects are moving at the same speed through the stationary frame (but in different directions to each other) then they will have the same degree of time dilation and will thus have the same rate of time, despite the relative motion that exists between them.

A new non-inheriting homogeneous solution of the Einstein-Maxwell equations with cosmological term

We find a new homogeneous solution to the Einstein-Maxwell equations with a cosmological term. The spacetime manifold is $R \times S^3$. The spacetime metric admits a simply transitive isometry group $G = R \times SU(2)$ of isometries and is of Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non-null and non-inheriting: it is only invariant with respect to the $SU(2)$ subgroup and is time-dependent in a stationary reference frame.

LMI-Based Model Predictive Current Control for an LCL-Filtered Grid-Connected Inverter under Unexpected Grid and System Uncertainties

To guarantee a system stability and reliable operation of an inductor-capacitor-inductor (LCL)-filtered grid-connected inverter (GCI) under unexpected grid and system uncertainties, a linear matrix inequality (LMI)-based model predictive control (MPC) is presented in this paper. Even though the conventional MPC scheme is constructed by a simple concept, it is difficult to determine an optimized weighting matrix of the MPC cost function against parameter discrepancies. To overcome this problem, the MPC scheme is combined with LMI-based optimization. The system states are estimated by the LMI-based current-type observer in the stationary reference frame to implement the proposed scheme. Additionally, the MPC scheme is combined with the disturbance observer to eliminate offset error, which improves the reference tracking performance. In comparison with the other studies, the proposed control method ensures high robust control performance under grid voltage imbalance, parameter uncertainty, and frequency variation. In addition, the proposed approach achieves a robust active damping even for the grid impedance variation without the need of considering further damping method. The control design step is systematic and straightforward. Furthermore, unlike the conventional schemes, the proposed controller does not require an integral term and the 2nd harmonic compensation term to obtain a good reference tracking performance under grid imbalanced condition, which contributes to the reduction of the controller complexity by decreasing the order of the controller model. To verify the effectiveness of the proposed LMI-based MPC control scheme, the simulation and experiments are carried out by using prototype three-phase GCI. The comprehensive simulation and experimental results clearly demonstrate the robustness of the proposed current controller under various adverse test conditions with unexpected grid and system uncertainties.

A Novel Framework for Simulating Particle Deposition With Moving Bedforms

AbstractPrevious modeling studies of hyporheic exchange induced by moving bedforms have used a moving reference frame, typically corresponding to an individual moving bedform. However, this approach is not suitable for simulating the exchange and accumulation of immobile fine particles beneath moving bedforms, which commonly occurs in sand‐bed streams, as both moving and stationary features must be considered. Here we present a novel simulation framework that may represent arbitrarily shaped, generally aperiodic mobile bedforms within a stationary reference frame. We combine this approach with particle tracking to successfully reproduce observations of clay deposition in sand beds, and the resulting development of a low‐conductivity layer near the scour zone. We find that increased bedform celerity and filtration both lead to a shallower depth of clay deposition and a more compact deposition layer. While increased filtration causes more clay to deposit, increased celerity reduces deposition by flattening hyporheic exchange flowpaths.

Effects of induction machine parameters on its performance as a standalone self excited induction generator

A squirrel cage induction machine (SCIM) when aggregated with relevant capacitances and a prime mover, acts as self-excited induction generator (SEIG). As it hosts energy conversion the parameters of SCIM have considerable impact on the power extraction capability of SEIG. An aspect which is missing from the available research on SEIGs is evaluation of the affects of its rotor’s moment of inertia (J) and per-phase stator winding resistance (Rs) on performance indices. This work investigates the impacts of these factors on a SCIM’s performance as series compensated, short shunt SEIG. The study considers two distinctly designed SCIMs, in terms of J and Rs, operated as SEIG. In order to simulate their performance a stationary reference frame dq model including non-linear saturation and cross coupling effects is developed and verified experimentally. Several key investigations based on series capacitance selection, losses and efficiency, on-load performance with different power factor loads, transient performance with load perturbation and variable speed operation are carried out. The study reveals that SEIG with high J and lower Rs gives considerably better performance than its counterpart. The conclusions reported in the study are important especially for standalone/off grid application of SEIGs.

A twelve-switch power conditioner for voltage and current compensation in three-phase four-wire grids

An interesting solution for problems associated with system voltage, such as sags and swells, as well as those associated with current such as low power factor and harmonic distortion is the unified power quality conditioner. However, one of its drawbacks is the high number of semiconductor devices since its conventional topology presents two full-bridge converters connected in a back-to-back configuration. Therefore, this paper proposes a twelve-switch converter topology as a power conditioner for voltage and current compensation in three-phase four-wire grids. The developed topology ally low voltage characteristic of dc bus of a hybrid power filter with a reduced number of semiconductor switches and the capability of homopolar voltage and current compensation through the converter fourth leg for the neutral wire connection. In the twelve-switch converter, there are two sets of three-phase four-wire outputs, each set behaving as an independent converter unit. One of these units is connected in parallel to the load by means of a series LC filter, working as a hybrid power filter and being responsible for the compensation of current harmonics and imbalance. The second converter unit is responsible for compensating harmonics, sags or swells in the grid voltage, in such way that the load receives a sinusoidal voltage waveform. Both converters are controlled in stationary reference frame through proportional-resonant controllers. Experimental results demonstrate the validity and the effectiveness of the proposed topology.

Induction Motor DTC Performance Improvement by Reducing Flux and Torque Ripples in Low Speed

Since induction motors were invented, human civilization has changed forever. Due to their beneficial characteristics, induction motors are widely used and have become the most prevalent electrical counterparts. Many control strategies for induction motors have been developed, varying from scalar to vector control. In the class of vector control, the Direct Torque Control (DTC) was proposed as an alternative that ensures separated flux and torque control while remaining completely in a stationary reference frame. It offers direct inverter switching, reasonable simplicity than other vector control techniques, and less sensitivity to parameter variation. However, the use of hysteresis controllers in conventional DTC involves non-desired ripples in the system's flux and torque, which leads to bad system performances, primarily in low-speed operations. This paper aims to minimize the chattering and ensure the augmented system's performance in terms of robustness and stability. The proposed method is an improved version of DTC, which combines the addition of the Space Vector Machine (SVM) algorithm to the DTC and the increased number of DTC sectors that generate reference control voltages. Satisfactory results have been obtained by numerical simulation in MATLAB/Simulink. Eventually, the proposed method is proven to be a fast dynamic decoupled control that robustly responds to external disturbance and system uncertainties, especially in the low-speed range.

Repetitive Predictive Control for Current Control of Grid-Connected Inverter Under Distorted Voltage Conditions

A repetitive predictive control for grid-connected inverter current control scheme is presented in this paper under voltage harmonic distortion in the stationary reference frame. Predictive control is an approach that uses a receding horizon to achieve the optimal track for the reference. In this approach, the repetitive controller behavior is added to the predictive control to increase its performance under distorted voltage conditions. In addition, to apply the controller in the generation system, controller is designed from the perspectives of the power system. The controller is designed considering the state-space model in the stationary reference frame. The controller performance was verified using a laboratory experimental setup under distorted grid voltage condition. Experimental results confirm that the proposed controller can effectively suppress harmonics under both normal operation and distorted grid voltage conditions, and also satisfy the requirements stipulated in IEEE Std. 1547.2-2008.

Inrush Current Management During Medium Voltage Microgrid Black Start With Battery Energy Storage System

This paper addresses the black start of medium voltage distribution networks (MV-DNs) by a battery energy storage system (BESS). The BESS consists of a two-level voltage source inverter interfacing MV-DN which has limited overcurrent capability. On the other hand, MV-DN normally includes several step-up and step-down transformers that are drawing sympathetic inrush current in energizing stage. Therefore, the major difficulty to perform black start by BESS during MV-DN island operation lies in the fact that the inverter has to simultaneous control the network voltage and its output current. This paper presents two control approaches for a BESS in order to control the inrush current during MV-DN black start. The proposed control schemes consist of droop, voltage and current loops in the stationary reference frame. The droop loop is used to generate the voltage reference. An intermediate voltage and inner current loops are designed for output voltage regulation, current reference generation as well as current tracking, respectively. New reference modifiers are included into droop and voltage loops to limit inrush current. The proposed control schemes are experimentally tested for energizing Ingå MV-DN in Finland by 1 MVA BESS, and their performance is compared in terms of inrush current value and voltage quality. The obtained results prove that both methods are able to feed the load with a fixed voltage in the steady-state as well as to limit the transformer inrush current considering the inverter overcurrent limit.

Universal System for Detection and Compensation of Current Sensor Faults in Three-Phase Power Electronic Systems

Abstract The article discusses the universal current sensor fault detection and compensation mechanism, which can be applied in three-phase power electronics (PE) symmetrical system. The mechanism is based on the assumption that a symmetrical system can be described using different components in the stationary reference frame. The solution given in article as a Cri-base detector was tested in electrical drives with induction motors (IMs) and permanent magnet synchronous motors (PMSMs). This study also proves that the same algorithm can work stable in active rectifier systems. Such an application of this detector has not been previously reported in the literature. The article describes the detection of various types of faults in different phases. The fault-tolerant voltage-oriented control (FTVOC) of an active rectifier is compared with previously described solutions for IMs and PMSMs. By analysing in various types of systems, the work proves the universality of the detector based on Cri markers.

Frequency Estimators for SOGI FLL: Modeling, Design, and Equivalence for FLL Advancements

Different frequency estimators have been reported for frequency-locked loop (FLL) implementations. One example is the widely employed gradient descent estimator in second-order generalized integrator (SOGI) FLL. Whether this estimator differs from those in some existing FLLs is unknown. Therefore, in this article, gradient descent and two other estimators with amplitude normalization in the stationary and synchronous reference frames are developed for SOGI FLL implementation. By obtaining linear model of SOGI FLL with the three estimators, equivalence of their FLL is established. Thus, it is shown that when the estimator parameters are designed based on the established equivalence, the FLL dynamics is dictated by the SOGI stage. Thus, research involving orthogonal signal generation is crucial to FLL’s rapid advancements. Furthermore, harmonic rejection in SOGI FLL with the estimators is considered where it is shown that SOGI FLL with amplitude normalization in the synchronous reference frame is ideal for applications involving harmonics.

Frequency-Domain Stability Criteria for Converter-Based Power Systems

Frequency-domain stability criteria are developed for converter-based power systems with any number of converters. The converters may be grid following or grid forming, and the grid can be an ac or hybrid ac-dc network. The converters and the network are all modeled in a common (stationary) reference frame based on small-signal sequence immittances. Coupling over frequency and ac-dc coupling are considered in the most general form. For each type of systems, a frequency-domain model is developed first by nodal analysis and then reformulated to fit the form of a feedback loop with open-loop stability guaranteed by practical conditions. System stability is then determined by a Nyquist-like criterion without the need to check open-loop right-half-plane poles. Further simplification of the system models is made possible by a) generalized <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-port equivalent circuits that include both types of coupling, b) equivalence of stability at internal and external nodes, and c) relationship between dynamics at the perturbation and the coupling frequency. Reduction of a system model into separate single-input-single-output models is presented for several special systems along with their practical applications. Quantitative and experimental results are presented to verify the developed theories.

Development and implementation of a voltage harmonic elimination method for the single-phase inverter operating with nonlinear load

Single-phase inverters are widely used in power conversion systems. When operating with linear loads, these inverters produce regulated quasi-sinusoidal output voltages. When feeding nonlinear loads, they absorb non-sinusoidal (distorted) currents and the inverter's output voltage deteriorates - it contains high levels of harmonics. This paper presents a method to reduce the harmonics in the output voltage. The control strategy is based on selective harmonic elimination - the method eliminates some of the low order harmonics of the output voltage. The method uses stationary reference frame voltage and current controllers. The voltage controller regulates the fundamental and eliminates certain harmonics using a modulation-demodulation technique. In the paper, the 3rd, 5th and 7th harmonics are eliminated. However, the scheme can be expanded to eliminate more higher-order harmonics. It is shown that the control proposed, significantly reduces the total harmonic distortion of the inverter's output voltage, from 5.8% to 1.64% (at full load).

Rotor Asymmetries Faults Detection in Induction Machines Under the Impacts of Low-Frequency Load Torque Oscillation

Low-frequency torque oscillations (LTOs) characteristic components emerge in the stator current spectrum of induction machines (IMs) as additive frequencies near the rotor asymmetry fault (RAF) indices especially in gearbox-based electromechanical system. The interactions between these two components make the fault detection process complicated and lead to false alarm. In this paper, a new technique for detection and separation of RAF from LTOs in IMs based on single phase stator current data is proposed. The method benefits from a novel pre-processing stage based on several sign functions. Hence, a two-axis rotating reference frame with a single phase of stator current of IMs with no prior knowledge of the rotational speed is introduced. The proposed method maps the static reference frame obtained through single stator current and its associated Hilbert transform to the proposed rotating reference frame which can separate the effects of LTOs from RAF, effectively. The validity of the proposed technique is tested through theoretical analysis, and experiments in both steady-state and transient conditions. In this regard, Synchro-squeezing Wavelet Transforms (SWT) is used for time-frequency analysis of faulty stator current in transient conditions. The obtained results confirm the effectiveness of the proposed approach to separate the RAF characteristic frequency from LTOs even in line-fed IMs applications.

Optimal design of controllers and harmonic compensators for three-level cascaded control in stationary reference frame for grid-supporting inverters-based AC microgrid

In this paper, new optimal procedures are introduced to design the finest controllers and harmonic compensators (HCs) of three-level cascaded control for three-phase grid-supporting inverters based-AC microgrid. The three control levels, comprising primary, secondary and synchronization control levels, are developed in stationary αβ-frame and based on the proportional–integral (PI) controllers and the proportional-resonant controllers along with additional HCs. The new optimal design guidelines of microgrid’s controllers and HCs are aimed to fulfill the study requirements. The optimization objectives and constraints are employed to minimize both the total harmonic distortion (THD) and individual harmonics of microgrid’s voltage to enhance the quality of microgrid’s output power. The THD of microgrid’s voltage can be reduced to 0.19% under the nonlinear loads. Moreover, the microgrid’s voltage and frequency can be perfectly regulated with zero deviations. Furthermore, these new optimal procedures accelerate the speed of synchronization process between the external power grid and the microgrid to be accomplished in time less than 20 ms. Additionally, an accurate power-sharing among paralleled operated inverters can be achieved to avoid overstressing on any one. Also, seamless transitions can be guaranteed between grid-tied and isolated operation mode. The optimal controllers and HCs are designed by a new optimization algorithm called H-HHOPSO, which is created by hybridizing between Harris hawks optimization and particle swarm optimization algorithms. The effectiveness and robustness of the H-HHOPSO-based controllers and HCs are compared with other meta-heuristic optimization algorithms-based controllers and HCs. A microgrid, including two grid-supporting inverters based optimal controllers and optimal HCs, are modeled and carried out using MATLAB/SIMULINK to test the performance under linear and nonlinear loads, and also during the interruption of any one of two inverters. The performance is investigated according to IEC/IEEE harmonic standards, and compared with the conventional control strategy developed in synchronous dq-frame and based on only PI controllers.

Robust Control of GTIs under wide grid impedance ranges: An approach combining metaheuristics and LMIs

This paper provides a new design procedure for robust state feedback current controllers suitable for grid-tied inverters under wide grid impedance ranges. The proposed procedure is based on the combination of particle swarm optimization and linear matrix inequalities. The control gains, designed offline, are obtained through the minimization of a novel objective function that takes into account the grid current tracking error in the stationary reference frame, limits for the control signal, and robust stability. Linear matrix inequalities are used in the design stage to theoretically certify the closed-loop robust stability systematically and efficiently, based on a polytopic model of the grid-tied inverter, which avoids the need for exhaustive and time-consuming a posteriori tests. Real-time simulations and experimental results are presented, attesting that the closed-loop system with control gains provided by the proposed procedure is robustly stable for wide ranges in the grid inductances. Moreover, the grid currents exhibit an optimized transient performance and steady-state responses in compliance with harmonic distortion limits from IEEE 1547 Std., even encompassing operation from stiff to weak grid conditions and in the presence of distorted grid voltages. To provide a comparison, results based on other well-established state feedback design techniques are also presented, highlighting the superior performance obtained with the proposed procedure.