Delta-star Transformer Research Articles

Efficient dissipation-based nonlinear solver for multiphase flow in discrete fractured media

Solving nonlinear equation systems resulting from the Fully Implicit Method (FIM) remains a challenge for numerical simulation of multiphase flow in subsurface fractured media. The Courant numbers can vary orders of magnitude across discrete fracture-matrix (DFM) models because of the high contrasts in the permeability and length-scale between matrix and fracture. The standard Newton solver is usually unable to converge for big timestep sizes.Limited research has been conducted on nonlinear solver techniques for multiphase flow and transport in fractured media. We make an extension of a new dissipation-based continuation (DBC) method to DFM models. Our goal is to prevent timestep cuts and maintain efficient time-stepping for FIM. The DBC algorithm builds a homotopy of the discretized conservation equations through the addition of numerical dissipation terms. We introduce a continuation parameter for controlling the dissipation and ensuring that accuracy of the computed solution will not be reduced. Under the nonlinear framework of DBC, general dissipation operators and adaptive strategies are developed to provide the optimal dissipation matrix for the multiphase hyperbolic system.We assess the new nonlinear solver using multiple numerical examples. Results reveal that the damped-Newton solver suffers from serious restrictions on timestep sizes and wasted iterations. In contrast, the DBC solver provides excellent computational performance. The dissipation operators are able to successfully resolve main convergence difficulties. We also investigate the impact of star-delta transformation which removes the small cells at fracture intersections. Moreover, we demonstrate that an aggressive time-stepping does not affect the solution accuracy.

A Fault-Tolerant 24-Sided Voltage Space Vector Structure for Open-End Winding Induction Motor Drive

This article proposes a method of generating 24-sided polygonal voltage space vector structure composed of 24 real active vectors and a zero vector. Each active vector is a real vector in contrast to switched average vectors in literature. Generation of real 24-sided vectors minimizes switching losses and improves quality of phase voltage compared to switched averaged vectors technique. An important feature of the presented scheme is elimination of lower order harmonics up to 19th order from motor phase voltage throughout the modulation range that gives reduction in torque pulsation and near sinusoidal phase current. The proposed scheme extends the linear modulation range till 99.42 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> . Open-end winding induction motor is fed with primary and secondary inverters from either ends. Primary and secondary inverters are implemented by cascading two-level inverters. DC sources for both the inverters are realized using a simple star-delta transformer combination. The proposed concepts are verified with laboratory prototype and the respective results during the steady-state, transient, and fault scenario are presented. The supporting loss analysis and harmonic performance of the proposed drive is performed with existing topologies.

Optimized Controller Gains Using Grey Wolf Algorithm for Grid Tied Solar Power Generation with Improved Dynamics and Power Quality

This study proposes a control algorithm based on synchronous reference frame theory with unit templates instead of a phase locked loop for grid-connected photovoltaic (PV) solar system, comprising solar PV panels, DC-DC converter, controller for maximum power point tracking, resistance capacitance ripple filter, insulated-gate bipolar transistor based controller, interfacing inductor, linear and nonlinear loads. The dynamic performance of the grid connected solar system depends on the effect operation of the control algorithm, comprising two proportional-integral controllers. These controllers estimate the reference solar-grid currents, which in turn generate pulses for the three-leg voltage source converter. The grey wolf optimization algorithm is used to optimize the controller gains of the proportional-integral controllers, resulting in excellent performance compared to that of existing optimization algorithms. The compensation for neutral current is provided by a star-delta transformer (non-isolated), and the proposed solar PV grid system provides zero voltage regulation and eliminates harmonics, in addition to load balancing. Maximum power extraction from the solar panel is achieved using the incremental conductance algorithm for the DC-DC converter supplying solar power to the DC bus capacitor, which in turn supplies this power to the grid with improved dynamics and quality. The solar system along with the control algorithm and controller is modeled using Simulink in Matlab 2019.

Block-Based Development of a Mobile Application in Basic Electrical Concept for Diploma in Electrical Engineering Student

Electrical Technology is one of the main courses for Diploma in Electrical Engineering students in Politeknik Malaysia. The subject has been delivered conventionally; however, due to the Covid-19 pandemic, relatively it has changed the landscape in delivery method. Regarding this problem, an innovation by using an online learning application such as mobile applications is a must. There are many mobile applications provided in the Google Playstore; however, the function is either limited to one function for each mobile application or too complicated for diploma students. This paper presents the block-based programming language used in App Inventor to make the creation of mobile apps for basic electrical concepts for electrical engineering students in Politeknik namely My ReSist. This app is used to convert the resistance color codes to resistance values and calculate the total resistance in the circuit as well as to do Star-Delta transformations. Results showed that this mobile application is useful for students to solve basic electrical concept including total resistance in series and parallel circuit. It is proved that this app is user-friendly and attractive.

A New Method Based on Boundary Element Method to Appraise CO2 Geological Storage Potential in Depleted Shale Gas Reservoirs

In recent years, greenhouse gases have increased in the atmosphere, and climate change concerns have triggered global efforts to find solutions for CO2 capture, separation, transport, and storage. Geological sequestration in the depleted unconventional reservoir is an effective measure to reduce the atmosphere’s CO2 content. The exact evaluation of the CO2 storage capacity can verify the feasibility of storing carbon dioxide and parameter optimization. A reasonable boundary element method to estimating the CO2 storage capacity of depleted shale gas reservoirs considering arbitrarily shaped boundaries is introduced. Firstly, the physical model with fracture networks is built based on the microseismic data. Then, the flow equation including the matrix and fracture can be obtained considering adsorption, and the star-delta transformation is used to deal with interconnected fracture segments. The point source function with an infinite boundary can be obtained after the Laplace transform method. Finally, the semianalytical flow solution is obtained by using the boundary element method in the Laplace region. Moreover, the results have a high agreement with commercial software for the regular boundary. The sensitivity of relevant parameters is analyzed by this method, and the importance of considering the boundary shape is emphasized. This method can evaluate the CO2 storage capacity of formation with the irregular boundary and is regarded as the guide of parameter optimization in CO2 storage.

Application of D-STATCOM for Harmonic Reduction using Power Balance Theory

In modern power systems due to prolific use of non-linear devices harmonics are present in the distribution system. To reduce the harmonics and source neutral current D-FACT along with a star-delta transformer and Power Filter is proposed in shunt. In this article, the three phase load has been taken from NTS Industries, which deals with FMCG products. This system includes 3 phase 3 wire system having industrial load such as mixer grinder, pulverizer, packaging machine, etc. A star-delta transformer along with three leg voltage source inverter and a capacitor used to filter out harmonics present in supply current. Power balance theory is used to control the D-FACT. A MATLAB Simulink model was created and the results were discussed.

Ant lion algorithm for optimized controller gains for power quality enrichment of off-grid wind power harnessing units

The proposed system uses an algorithm that works on the admittance of the system, for estimating the reference values of generated currents for an off-grid wind power harnessing unit (WPHU). The controller controls the voltage and maintains the frequency within the limits while working with both linear and nonlinear loads for varying wind speeds. The admittance algorithm is simple and easy to implement and works very efficiently to generate the triggering signals for the controller of the WPHU. The wind power harnessing unit comprising of a squirrel cage induction generator, a star-delta transformer, a battery storage system and the control unit are modeled using Matlab/Simulink R2019. An isolated transformer with a star-delta configuration connects the load and the generator circuit with the controller to reduce the dc bus voltage and mitigate current in the neutral line. The response of the system during the dynamic loading depends on the best possible compensator proportional-integral (PI) gains. The antlion optimization algorithm is compared with particle swarm optimization and grey wolf optimization and is found to have the advantages of good convergence, high efficiency and fast calculating speed. It is therefore used to extract the optimal values of frequency and voltage PI gains. The simulation results of the control algorithm for the WPHU are validated in a real-time environment in a dSpace1104 laboratory set up. This algorithm is proven to have a quick response, maintain the required frequency, suppress the current harmonics, regulate voltage, help in balancing the load and compensating for the neutral current.

Flux Error Function Based Controlled Switching Method for Minimizing Inrush Current in 3-Phase Transformer

Energization of the transformer leads to large magnetizing current called inrush current. It results in reduction in transformer life, reduction in circuit breaker life, and power quality issues in the system. For low and medium voltage level systems in generation and distribution, usually, gang operated circuit breakers are employed, which do not allow independent pole operation. This makes controlled switching more challenging in such systems. This paper proposes a controlled switching technique to minimize the inrush currents for a 3-phase transformer using gang operated circuit breaker. Optimum points for controlled closing and opening are obtained from a flux error function calculated from residual and prospective fluxes of the transformer. Practical challenges due to error in voltage measurements, variation in mechanical closing time, transients in flux, etc. and their solutions are also discussed in this paper. The proposed technique is validated by Controller Hardware-In-Loop (CHIL) test and a scaled-down laboratory test on 5 kVA, 210/400 V, Delta-Star transformer. In both cases, the inrush current is limited to 1pu, demonstrating the effectiveness of the proposed scheme. Furthermore, a field test is carried out on a 500 kVA, 6.6 kV/433 V, Delta-Star distribution transformer to confirm the viability of the developed switching technique.

An Equivalent Calculation Method for Pole-to-Ground Fault Transient Characteristics of Symmetrical Monopolar MMC Based DC Grid

The pole-to-ground fault is one of the most typical faults in modular multilevel converters (MMCs) based DC grid. Analyzing the transient characteristics of fault voltages and currents is of great significance for fault identification, configuration of protection, and optimization of system parameters. This paper proposes an equivalent transient characteristics calculation method for pole-to-ground faults for symmetrical monopolar MMC based DC grid. Firstly, according to the mechanism of the pole-to-ground faults, the fault network and the steady-state network are formed. Then, the star-delta transformation is performed on modelling the MMCs in the fault network, which overcomes the problem that the number of the inserted sub-modules (SMs) in each arm is time-variant. Based on the discrete adjoint model, the pre-fault and faulted matrices describing the voltages and currents are established, and a general method for solving the transient voltages and currents is proposed. Finally, the proposed method is validated in a four-terminal symmetrical monopolar MMC based DC grid. The results show that the proposed method is of high accuracy, and is much more time efficient than time-domain simulation.

VCO‐less PLL control‐based voltage‐source converter for power quality improvement in distributed generation system

This paper presents the voltage-controlled oscillator (VCO) less phase-locked loop (PLL)-based control of voltage source converter. It is used in the distributed power generation system for improved power quality. This control extracts the fundamental component from the sensed load current using three phases to alpha–beta transformation without using VCO, unlike synchronous reference frame–PLL, where fundamental component extraction needs two transformations with the use of VCO. Owing to the absence of VCO in the proposed method, the computational burden of trigonometric operations is very less that results in a faster dynamic response under variable conditions. This characteristic makes it suitable for the distributed power generation system, where fast changes occur frequently. In this study, wind-based distributed generation system has been taken for study, which comprises of self-excited induction generator feeding non-linear load with varying electrical conditions. Using the proposed control, the reactive power compensation, harmonics reduction and load balancing are carried out in the system. In addition to it, neutral current compensation is also accomplished with the help of star–delta transformer connected at the load end. The system performances are investigated under steady state as well as in transient state and results are found satisfactory.

Power Quality Improvement in Stand-Alone SEIG-Based Distributed Generation System Using Lorentzian Norm Adaptive Filter

In this paper, Lorentzian norm based adaptive filter (LAF) is implemented to control voltage source converter (VSC) for improvement in power quality of three phase four wire wind based distributed generation system. This control algorithm operates VSC to control the terminal voltage and frequency in allowable range. In addition to above, neutral current compensation, load balancing, reactive power, and harmonic compensation are also carried out. Therefore, in the system, the generator always supplies the active fundamental component of load current. The LAF is derived from a sliding window type objective function with Lorentzian norm of past errors to overcome bad effect of impulsive environment on system. Hence, it is most suitable filter in wind-based distributed generation system application in order to neutralize the effect of wind impulses on the voltage and frequency of the generator. The entire system comprises induction generator, VSC, and star-delta transformer and nonlinear load is developed in MATLAB Simulink followed by a prototype in the laboratory. The control performance of the said filter is evaluated and validated by simulation and experimental analysis. After performance observation, results are found satisfactory.

Modeling vertical well in field-scale discrete fracture-matrix model using a practical pseudo inner-boundary model

The discrete fracture-matrix model (DFM) technique has contributed to the rapid development of fracture modeling. In terms of vertical well modeling, however, the current well models fail to handle the field-scale DFM utilization. In this study, a pseudo inner-boundary model is presented tailored to this problem. Specifically, the modeling methodology consists of mesh generation and transmissibility evaluation. Regarding the mesh generation, the model handles the 2-D triangular-gridded matrix and 1-D edge-gridded fracture. The strict geometric analogy to generate triangles for the wellbore is abandoned, instead, the wellbore is approximated by a source/sink point and returns to a circular geometry when evaluating the transmissibility. The treatment sheds the limitation of triangle size and proves to boost the generation efficiency. Regarding the transmissibility evaluation, the derived formulations apply the radial/linear approximation for flow in matrix/fracture well-gridblock, and various conditions are considered, including gridblock geometry (triangle and rectangle), flow state (steady-state, unsteady-state and pseudosteady-state) and well completion (fully penetrating well and partially penetrating well). In addition, the compatibility with the star-delta transformation is discussed. By refining the well-gridblock into several sub-triangles, the formulations could be rapidly implemented to non-triangle-based DFM (e.g. PEBI, Cartesian). The model performance is demonstrated in eight validation cases. The model is shown to provide results in close agreement with those of reference in cases where the direct comparisons are performed.

A semi-analytical model to evaluate productivity of shale gas wells with complex fracture networks

With the increasing of clean energy demands and the maturing of shale gas extraction technology, multiple fractured horizontal well (MFHW) has become the most key technology for shale gas development. After hydraulic fracturing, fracture networks, which consist of natural fractures, hydraulic fractures and secondary fractures, are formed around the wellbore. Compared to conventional gas reservoirs, shale gas reservoirs are characterized by the complex fracture networks and gas adsorptions in shale matrix. Therefore, it is essential to propose a new productivity evaluation method for shale gas wells to handle these characteristics.In this paper, to account for special characteristics of MFHW, a complex fracture model for shale gas reservoirs is established. With the new method, shale reservoirs are depicted by De Swaan dual porosity model, where the secondary fractures and hydraulic fractures are characterized by discrete units. Therefore, together with micro-seismic data, fracture networks can be exactly described using this new model. With a well-depicted facture network, Green function and superposition method are then adopted to model the flow in the reservoir, and finite difference method is used to solve the equations of one-dimensional flow in fracture system. Besides, to deal with the complex flow in the fracture intersection, star-delta transformation is applied Finally, the equations of reservoir and fracture system, the solution in Laplace domain is obtained, which can then be transferred to real domain using the Stehfest algorithm.Comparisons were made between the results of the proposed model and that of a numerical model accomplished by commercial simulator Eclipse for a specific case to verify the accuracy of the model. Results show that the semi-analytical method is more efficient than numerical method by reducing the computing time without losing accuracy. Moreover, the semi-analytical productivity evaluation method can describe fracture networks more exactly. Then, a field case from Sichuan Basin of China is applied in the analysis. The results shows that desorption gas takes up 10%-30% of the total production in this case. Besides, the effects of storage capacity ratio and inter-porosity flow coefficient on type curves were analyzed based on the production decline curves. In addition, pressure profiles of different production times are obtained by the superposition of pressure potential.

A Systematic Method for Finding the Input Impedance of Two-Terminal Networks

ABSTRACTWhen a network is a simple ladder network, its input impedance can be obtained simply using series–parallel reduction techniques. If there are bridging elements, such as bridged-T network or Wheatstone bridge, the network cannot be solved just by these techniques. Then one has to take the help of star–delta transformation. A systematic method is given for obtaining the input impedance of any complicated network. We shall deal with resistive networks first, and then all-L and all-C networks. Finally, more complex RLC networks in jw-domain are covered.

Transient behavior of complex fracture networks

Abstract Interacting with the pre-existing natural fractures, multi-stage hydraulic fracturing along horizontal wells creates complex fracture networks in the reservoirs. The flow behavior of these created networks is significantly different from that of traditional single or multiple planar fractures due to complex interplay of flow caused by the interconnected fractures. Therefore, modelling the flow behavior of such fracture networks is essential if one intends to evaluate well performance or characterize fracture properties. In this paper, we present a semi-analytical model for the transient behavior of complex fracture networks in which hydraulic and natural fractures can interconnect with arbitrary angles. To model the flow behavior more rigorously, the fractures within the network are represented explicitly rather than idealized as dual-porosity media with the matrix around them. This approach allows us to concentrate on the details of network properties, especially for the complex geometry and varying conductivity within the fracture. In the model, the transient responses are obtained from coupling a reservoir flow model and a fracture network flow model dynamically. Source functions in Laplace domain and superposition principle are adopted to model the flow behavior in reservoir analytically and the transient flow equation in the network is solved by finite difference method numerically. Furthermore, Star-Delta transformation commonly used in discrete fracture network simulation (DFN) is adopted to solve the interplay of flow between the interconnected fractures. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator for orthogonal network. The parameter analysis indicates that the planar penetration coefficient of natural fractures and the varying fracture conductivity have a great effect on the transient responses and drainage pattern for orthogonal networks. Finally, a field example from the Barnett Shale shows the capacity and practical use of the semi-analytical model to evaluate well performance and stimulation effectiveness of complex fracture networks in unconventional reservoirs.

A Simplified Analysis of an Electrical Network with Resistive and/or Reactive Elements

Typically star-delta transformation is adopted in determining the equivalent impedance between two terminals of an electrical network [2]. Shown relevantly in [1] is a simplified approach, less time-consuming to determine the equivalent resistance between two terminals of an electrical circuit made of resistive elements (of equal values) and, hence the resultant currents in the ciurcuit are determined. This concept is extended and generalized in this study to a class of networks with unequal resistances and/or reactances to determine the equivalent impedance between two nodes. This generalized approach is more comprehensive and universal in analyzing electrical network with complex impedances (regardless of their values). It is applicable to both contexts of circuits with pure resistive elements (as in d.c. analysis) as well as with complex impedances encountered in a.c. analysis.

A NEW SIMPLIFIED APPROACH TO FIND THE EQUIVALENT RESISTANCE OF ANY COMPLEX EQUAL RESISTIVE NETWORK

As we are familiar with the star-delta transformation to determining the equivalent resistance [4] between any two terminals of a complex network and to find the overall current of a closed circuit, but sometimes circuit become too complex such that it consumes a lots of time while solving the network to find the equivalent resistance between two known terminals. So, here we have developed a new simplified approach for the solution to find the equivalent resistance between the desired terminals for equal resistance network and to find the overall current in a closed circuit.

Photovoltaic based distribution static compensator for power quality improvement

This paper deals with a model of photovoltaic (PV) array or battery operated DC/DC boost converter fed three-leg VSC (Voltage Source converter) with star delta transformer for power quality improvement. A synchronous reference frame theory is proposed for three-phase four-wire DSTATCOM (Distribution Static Compensator) which includes voltage source converter and a dc link capacitor. The proposed DSTATCOM provides reactive power compensation, source harmonic reduction and neutral current compensation at the point of common coupling (PCC). The PV array or battery operated boost converter is used to step up the voltage to match the DC link requirement of the three-leg VSC. The main advantage of this proposed approach is that, it will provide continuous compensation for the whole day. The star/delta transformer provides isolation to the VSC and path to the zero sequence fundamental as well as harmonics neutral current. To derive the reference current in order to generate the firing pulse to the VSC, the overall system is designed, developed and validated by using MATLAB–SIMULINK environment.

Fault Location in Multitapped Transmission Lines Using Unsynchronized Data and Superposition Theorem

Lines with several taps are frequent and involve a large number of small towns and customers. With the need for costs reduction, this solution has been adopted in Brazilian utilities, with measurements only at the two terminal substations of the main line. The relevance of the problem is related to the long time for fault location when there are several secondary tap lines, depriving a large number of customers of energy during this period. Since there is not yet an adequate approach for this configuration, without additional hardware and measurements in tap lines, this paper presents a low-cost solution focusing on the synchronization of data measurements and the fault location in the main line or in the tap lines. The algorithm can handle the critical condition of zero-sequence infeed of star-delta transformers connected to tap lines, detecting the faulty section through the superposition theorem and finally obtaining the fault distance. Simple and accurate enough expressions were developed for fault location in order to help computer implementation of the algorithm. The algorithm also enables fault location in double-circuit main lines with several tap lines. The results, considering various line configurations and fault types, are presented, showing the accuracy and efficiency of the proposed method.

Parallel Operation of DFIGs in Three-Phase Four-Wire Autonomous Wind Energy Conversion System

This paper deals with a control algorithm for two parallel-operated doubly fed induction generators (DFIGs) driven by wind turbines in a three-phase four-wire autonomous system feeding local loads. The proposed autonomous wind energy conversion system (AWECS) is using back-to-back-connected pulsewidth-modulated insulated-gate-bipolar-transistor-based voltage source converters with a battery energy storage system at their dc link. The system utilizes separate rotor-side converters for each DFIG for maximum power tracking (MPT) through its rotor speed control. However, a common dc bus and a battery bank and stator-side converter are used for voltage and frequency control at the stator terminals of the DFIGs. A delta–star transformer is connected between the stator-side converter and the stator terminals of DFIGs for optimizing the voltage of dc bus, and the load-side neutral is connected to the neutral of the star side of the transformer. The proposed electromechanical system is modeled and simulated in MATLAB using Simulink and Sim Power Systems set toolboxes. The performance of the proposed AWECS is presented to demonstrate its capability of MPT, stator voltage and frequency control, harmonic elimination, load balancing, and load leveling.