Phase-shifting Transformer Research Articles

Novel models of power system components for implicit solution of the adjusted power flow problem

AbstractThe solution of the adjusted power flow problem involves handling power system components whose control characteristics possess operational limits. Examples include generator reactive power limits, tap-changing and phase-shifting transformers, and FACTS devices. While the conventional method involves checking for limit violations in an outer loop drawn around the unadjusted power flow problem being solved by the Newton-Raphson (NR) method, for iterative processes, it is desirable to have smooth, continuously differentiable models implicitly handled within a single loop. A novel formulation for a subset of devices is presented for implicit handling within power flow. The steady state characteristics of tap-changing and phase-shifting transformers, and FACTS devices SVC and STATCOM, can be described using the “cut function”, a piecewise linear function traditionally employed in neural networks. A new approximation of the cut function is used for formulating novel equations describing the steady state characteristics. An augmented set of equations is formed and solved by the NR method, eliminating the need of an outer loop. The efficacy of the proposed method is demonstrated by employing it for plotting bus voltage profiles and determining maximum loadability of test systems. Comparisons with the conventional method show that significant savings in computation can be achieved.

Study of Partial-Phase Steady-State Operation Modes of Phase-Shift Transformer with Hexagonal Circuit and Regulating Autotransformer

The scope of the work was the study of the phase failure operating for the new FACT’s type phase-shifting device, intended for the flexible connection of AC power systems. The mathamatical model has been developed for conducting this study. The device contains the main phase-shifting transformer based on hexagon circuit with additional regulating autotransformer, this creates the possibility of circular regulation of phase shift angle between connected systems. The model includes two 6-winding three-legs transformers, for which two sets of parameters can be independently set based on the data for the short circuit and no-load modes. The data for the direct sequence parameters is usually provided by the transformer manufacturers, and the data for the zero sequence parameters could be obtained upon additional request. As a result of modeling, the vectors of the voltages and currents were obtained in all windings in the investigated modes with supply source phase failure. This makes it possible to analyze the admissibility of such modes and estimate the need for taking special measures of protection against them. It is shown that the voltages on the windings of the main transformer insignificantly depend on the connection mode of the regulating autotransformer, while the pattern of currents distribution in the windings of the main and regulating transformers to a large extent is determined by said connection mode of the autotransformer. The presence of perceptible zero-sequence current flowing through the grounded neutrals of the power supply source and load is noticed. This fact is connected with the release of insignificant magnetic flux from the magnetic circuit in the surrounding space

The Comparative Analysis of Phase Shifting Transformers

Phase shifting transformers (PSTs) are currently widely used in power systems to control power flow. In this manuscript, the results of the asymmetrical PST (APST) with the in-phase PST (called asymmetrical controllable PST-ACPST) were compared, allowing to control both longitudinal and quadrature voltage. The MATLAB simulation model of the ACPST was built to obtain influence of PST in selected models for selected parameters. Then the 30A laboratory PST device was built in the laboratory. The parameters of the MATLAB model were then adjusted to parameters of the real life PST model. This allowed verifying the results of the real life and computer simulations. Based on the ACPST simulation model, the APST model was built; for the given work conditions, the influence of both PSTs were compared. APST construction always resulted in higher output voltage than the input one. ACPST achieved the same power transfer for the lower output PST voltage, which is its main advantage. This dependency is a result of the greater ACPST angle compared to the classical APST. The ACPST also allowed adjusting longitudinal and quadrature voltages; therefore, this PST type can be installed in places where high flexibility is required, especially in systems with high renewable energy sources penetration.

Modified distance protection for transmission line with hexagonal phase-shifting transformer

Phase-shifting transformers (PSTs) provide an economical solution to control the power flow in the electric grids. However, the PSTs vitiate the conventional protection system applied. This paper studies the impact of the delta-hexagonal phase-shifting transformer on the performance of the distance protection relays for the transmission lines. Modified distance protection formulas are derived for both phase and ground faults. The proposed method uses the local measurements at the relay point and does not require voltage or current measurements from a remote substation. Alternatively, the tap position of the phase-shifting transformer is the data needs to be shared between substations which can be accomplished using a simple communication method. The proposed method is evaluated on a simulated transmission line using MATLAB/Simulink packages. The results show the ability of the proposed method to compensate for the PST effect on the distance protection relays.

Use of a phase-shifting transformer for increasing the power transmission capacity, taking into account the mode of the adjacent network

In this research, we develop measures aimed at improving the efficiency of power systems by increasing their transmission capacity. To this end, a FACTS system based on the phase-shifting transformer with a thyristor switch developed at the Power Engineering Institute named after G.M. Krzhizhanovsky was used. The efficiency of the phaseshifting transformer under study for increasing the transmission capacity of power systems was determined by the maximum permissible cross-section flows of the Barnaul-Biysk node-2. The calculations were performed for normal and various post-accident schemes using the RastrWin3 software package. Such factors as the regulation of the taps of the phase-shifting transformer and various places of its installation were considered. For the section under consideration, the phase-shifting transformer increased the maximum permissible flow by 4–12%. The determining factor limiting the maximum permissible flow in the Barnaul-Biysk node-2 was found to be the current overload of the 110 kV lines of the adjacent network. The greatest effect of increasing the maximum permissible overflow was noted when the phase-shifting transformer was installed on the 220 kV line adjacent to the section, parallel to the 110 kV lines (which were overloaded when the mode became heavier), rather than on the 220 kV line included in the section. Similar calculations were performed for normal and post-accident schemes of an alternative option, which involved replacing wires and installing automatic equipment for limiting equipment overload on overloaded 110 kV lines. The obtained results show that the effect of increasing the transmission capacity for this option comprised 4%.

Finding the Best Programmable PWM Pattern for Three-Level Active Front-Ends at 18-Pulse Connection

The existing publications on the analysis of power quality indicators in modern electric power supply systems are void of a comprehensive approach to improving these indicators in power systems by implementing multipulse connections. To the authors’ knowledge, this paper is the first to analyze current harmonic distortions in an 18-pulse connection of three-level active front-ends (AFE) featuring a programmed PWM. Raw data were obtained from, and current quality was analyzed for the power circuit of the main electric drive actuating the rolls in the rolling stand of a plate mill. The key feature of such circuitry is that the synchronous motor of each work roll is connected to the grid with an 18-pulse connection that uses three phase-shift transformers, where the phase shifts are 0° (delta/delta), 20° (delta/polygon) and −20° (delta/polygon). The circuitry connects three frequency converters (FC) with the AFEs in parallel. Phase-shift transformers were found to periodically overheat in the process. When overheating occurred, a programmed PWM voltage waveform was applied where harmonics 17 and 19 were eliminated. The goal and objectives were to analyze why the transformer would overheat and to find out how the issue could be addressed. The authors developed a simulation model of the research object in order to assess power quality parameters. Simulation results obtained in Matlab/Simulink were used to estimate the total harmonic distortions (THD) and individual harmonic factors for up to the 50th secondary transformer winding and grid harmonic with four different programmed AFE PWM voltage waveforms. The results helped find the best such waveform to prevent phase-shift transformers from overheating; one with harmonics 5, 7, 17 and 19 eliminated. The experimental and mathematical modeling results in the paper were confirmed by positive effects after industrial implementation of the system. Research performed directly on the operating equipment has been classified by the company and is not publicly available. These results are highly versatile and could be used in similar research on other circuitries to ensure the electromagnetic compatibility of nonlinear power-consuming devices.

Application of particle swarm optimization for optimal setting of Phase Shifting Transformers to minimize unscheduled active power flows

Today’s interconnected power systems require increased flexibility in control to ensure the capability for maintaining power flows at acceptable limits. Recently, this issue has become increasingly important, mainly due to the significant unscheduled flows that can violate system security. In response to this challenge, the transmission system operators introduced various measures to control unscheduled flows. The most effective are Phase Shifting Transformers (PSTs). A higher number of PSTs operating in the transmission grid increases the total control capabilities. Since the achieved control effects can be both strengthened and weakened because of various actions of individual PSTs, coordinating the settings of the PSTs will achieve the best results. This paper addresses a new, intelligent approach by using a combination of two methods: the discrete particle swarm optimization method for the optimal setting of the individual PSTs and the power flow method for calculating the value of the optimization objective. The case studies consider the IEEE 118-bus test system as well as a model of the real network of Central Eastern Europe. In both cases, the minimization of unscheduled flows was adopted as the objective. As a result of PSTs settings optimization, a significant reduction of unscheduled flows was obtained.

Design of linear phase shift transformer and analytical calculation of no-load electromagnetic field

Linear phase-shift transformer is a new type of transformer, which can be used in multi-rectifier and multi-inverter system. Taking the design of a linear phase-shifting transformer for multiple superimposed inverters as an example, a layered magnetic field analysis model of the linear phase-shifting transformer is established. Firstly, the primary side slot is treated as a smooth structure, then the model is layered and the current density of primary side is calculated by the single Fourier method Taking into account the boundary conditions of the transformer, the distribution expressions of the vector magnetic potential and the magnetic flux density in the solution region are derived, the relative permeability function of the air gap is established and the influence of the slot effect on the air gap electromagnetic field is calculated. In this paper, the distribution of electromagnetic field without load is calculated. Finally, the feasibility of the method is verified by simulation, which provides basis for the following engineering calculation and optimization design of linear transformer.

Power Bidirectional Flow Converter Based on Linear Phase Shift Transformer

This article points out that the bidirectional power converter based on a linear phase-shifting transformer can be modularized, designed to improve equipment utilization. The analysis of the working status of the bidirectional power flow converter under inverter and rectifier conditions is introduced. The working conditions of the converter in the inverter and rectification state are simulated, and the output voltage and harmonics are analysed. The simulation results show that the system can meet the output index requirements under both inverter and rectification conditions, can be modularized, can reduce the number of components used in the device, and provide strong support for the optimization of subsequent prototypes.

Phase Shifting Transformer Electromagnetic Model Dedicated for Power System Protection Testing in a Transient Condition

Complex phase shifting transformer protection scheme and complexity of the object itself created a need to use simulation programs for their analysis. Often phase shifting transformer (PST) are modeled as a simplified series impedance and quadrature voltage source which cannot be used for power system protection analysis, especially in a transient condition. Therefore, the procedure of building realistic PST model was presented by using available transformer models with calculation of their parameters including interconnections between units. Paper consist calculations based on case study with symmetrical dual-core PST example. Additionally, theoretical background of PST principle, operation, and their impact of power system protection were introduced with numerus examples of PST model verification.

Расчет параметров режима электрической сети с учетом изменяющегося реактивного сопротивления фазосдвигающего трансформатора

The aim of the work is to study the effect the variation of the phase-shifting transformer (PST) reactance has on the accuracy of calculating its control angle and the electrical network operating parameters obtained as a result of this control. The operating parameters, in particular, active power flows in the electrical circuit branches, are controlled by changing the PST angle; however, in view of the PST design features, this control entails a change of its reactance. Depending on the design features of different PST models and the control angle value, the PST reactance may be constant or vary in a significant range. In connection with a growing use of PSTs in industrially developed countries and with the fact that the first samples of this equipment have emerged in the CIS countries, including Russia, an increased attention is paid to this topic in a number of domestic and foreign publications. In particular, matters concerned with the stability of electric operation modes are considered in view of the fact that the PST reactance depends on its control angle, and the effect this dependence has on the operating parameters is estimated. The necessity of taking into account the varying PST reactance in calculating its control angle for controlling active power flows is considered for different cases. Forced redistribution of active power flows in the closed loops of an electrical network by means of a PST can be used to reduce active power losses and to maintain the required loading of the power lines for various reasons, for example, for commercial purposes or in the case of transit power flows between different countries. In view of the complexity of calculations, constant values of the PST reactance are usually assumed, but this approach is valid not for all types of PST designs. In the majority of PSTs, their reactance varies with increasing the control angle. Therefore, calculations carried out without taking this feature into account may yield a fortiori incorrect correspondence between the control angle and the transformer reactance value. In turn, an error will be introduced in the accuracy of the PST control angle calculations, as well as in the calculations of the operating parameters that should be obtained from the control action.

Determining Optimal SVC Location for Voltage Stability Using Multi-Criteria Decision Making Based Solution: Analytic Hierarchy Process (AHP) Approach

Due to latest blackouts in the world, voltage instability and voltage collapse have become the main issues studied in electrical power systems. For this purpose, various Flexible AC Transmission Systems (FACTS) devices have been utilized for many years, increasing voltage stability while at the same time improving system performance, reliability, supply quality and providing environmental benefits. These devices location for enhancing voltage stability is a significant problem for actual power networks. When determining the best location of the controller, an optimal solution should be found to increase the loading margin and also reduce voltage deviation and power losses. In the literature, the weight coefficients of the criteria were chosen equally or approximate values were obtained by trial and error method and Multi-Criteria Decision Making (MCDM) techniques have never been used in finding the optimal location of FACTS devices. This article presents a novel technique for optimal location of Static Var Compensator (SVC) devices in power systems using MCDM. The simulation was conducted on Power System Analysis Toolbox (PSAT) in MATLAB. In the proposed approach, IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems were used and the optimal location was found out with Analytic Hierarchy Process (AHP), an MCDM technique. The consistency of the results has been checked and the reliability has been increased, and the results of the application are promising. In addition, the optimal location of the SVC for different contingencies was found, and the effects of the overloaded lines and Phase-Shifting Transformer (PST) on the network were analyzed.

Analytical Calculation of Magnetic Field in Fractional-Slot Windings Linear Phase-Shifting Transformer Based on Exact Subdomain Model

Fractional-slot windings linear phase-shifting transformers (FW-LPSTs) are a new type of transformer that can be used as an important component of multi-rectifier and multi-inverter systems. The FW-LPSTs are proposed for the first time, and few scholars have studied their magnetic field. However, accurate calculation of magnetic field distribution of the FW-LPSTs is the premise of the optimal design of the ontology, and the establishment of an accurate analytical model which remains a challenging task is the key to solving the magnetic field distribution. In view of the limitation of traditional analytical theory in solving the magnetic field, the FW-LPST model based on the exact subdomain method is proposed to obtain the exact magnetic field distribution. Considering the influences of the permeability and the structural parameters of the slot subdomain and the interaction of all slots on the distribution of the magnetic field, the governing equations of the air gap and slot subdomains are established using magnetic vector potential as the variable. According to the boundary conditions of each subdomain, all equations of the boundary condition are listed based on the Fourier series method. Finally, the vector magnetic potential and open-circuit magnetic flux density distribution of each subdomain are solved. The model accurately analyzes the influence of the cogging effect on the magnetic field distribution. The inductances of the primary side and the induced potentials of the secondary side are solved using the magnetic flux linkage method. The accuracy of the proposed analytical model is verified by comparison of the results obtained with those obtained by the finite element method.

SMART GRID TECHNOLOGY, TRANSMISSION OF ELECTRICAL ENERGY IN POWER SUPPLY AND LIGHTING SYSTEMS OF CITIES

Modern power supply and lighting systems of cities are complex electrical systems of an automated type, in which the processes in individual power supply systems and city lighting systems are interconnected and interdependent. Therefore, the search for efficient technologies for the transmission of electrical energy in them is an extremely difficult task. The real state of the power supply and lighting systems in cities today is characterized by low operating efficiency, largely due to the low quality of electrical energy and insufficient compensation of reactive power in them. The mutual influence of power supply and lighting systems in cities, as well as the presence of significant voltage deviations and the overflow of additional reactive power in the networks, causes an increase in voltage and power losses in them, as well as a decrease in the efficiency of networks and connected consumers, in general. Unfortunately, the existing methods and technical means based on them cannot fully solve this problem. The research carried out made it possible to clarify the nature of the processes in the power supply systems and the sanitation of cities and to determine the methods and technical means based on the Smart Grid concept. They are based on the use of phase-shifting booster transformers with an electronic control system. Their use made it possible to provide the possibility of complex control of the voltage modes of active and reactive power with the possibility of installation at any point in the network and centralized control from a single centre. The calculations show that the use of the developed methods and technical means provides an opportunity to reduce power losses in networks by 10–15% and energy costs for consumers by 50–75%.

A reliable differential protection algorithm for delta hexagonal phase-shifting transformers

Phase-shifting transformers (PST) are exhibited to continuous variations in phase angle. This continuously-varied phase shift can cause miss operation for the current-based differential protection relay by generating false trip signal. This paper discusses the experimental validation of a proposed current differential protection technique. The currents of the exciting winding are calculated based on the relationship between the magnetic and electric characteristics of the transformer. Then, these currents are provided for calculating the restraint and operating currents of the protective relay. The first stage is to design and fabricate the delta hexagonal (Delta/Hex) phase-shifting transformer and, then, constructing a complete laboratory system. PST terminal currents and tapping value are sensed and, then, they are provided to the relay for calculating the excitation current. To check the relay security, different types of external faults are considered. Similarly, extra internal faults, both with and without impedance, are represented to test the relay dependability and sensitivity. Also, the protective relay is checked to discriminate between fault currents that occur during the transformer energization and healthy inrush currents.

Market power analysis in power systems using PSO based must run indices

The development of restructuring has encouraged and brought up competitive markets in power systems. However, the exercise of market power evokes monopoly into the power system and tends to decrease competitiveness. This article assesses the market power of a generating company in a power system using must run indices and proposes a method to mitigate market power. Modified must run generation, must run share (MRS) and nodal must run share indices are used to quantify the market power of generating companies. Phase shifting transformers (PST) are installed in selected lines for mitigating the market power. Particle swarm optimization is used in the determination of must run indices and optimizing the angle of Phase Shifting Transformers. IEEE 14 bus test system is used to illustrate the proposed technique. The analysis also includes the impact of contingencies. Sensitivity analysis is performed to analyze the impact of phase shifting angle variation on MRS. The results clearly quantifies the market power of a generating company and show that the market power incurred by the generating companies can be minimized by installing PST with optimum phase shift angle.

Design of Phase-Shifting Transformer Based on Simulink Matlab Simulation

Using variable speed drive for controlling speed of three-phase induction motor in industrial sector gives an advantage of reducing consumption of electrical energy; on the other hand, it also causes a disadvantage of source current harmonic. To solve the problem of source current harmonic, a method of using phase-shifting transformer is applied. This method may be applied in a system with two VSDs or more connected to a three-phase power supply. The application of this phase-shifting transformer method could be as simple as using of two transformer with Y-y (wye-wye) and Y-d (wye-delta) three-phase winding connections to give a phase-shifting of 30 or more complex as it uses two transformer with Y-y and Y-z (wye-zigzag) three-phase winding connections to give a phase-shifting less than 30. This paper proposes design of five different phase-shifting transformer configurations to produce 30, 20, 15, 12 and 10 phase-shifting. Simulation on a computer-based software, Simulink Matlab, then confirmed that the proposed phase-shifting transformer design gives a very accurate result regarding to phase-shifting and magnitudes of input and output voltage of the phase-shifting transformers.

Open-Circuit Fault Diagnosis and Maintenance in Multi-Pulse Parallel and Series TRU Topologies

Transformer rectifier units (TRUs) are a reliable way for dc generation in several electric applications. These units are formed by multiple three-phase uncontrolled bridge rectifiers connected according to two main topologies (parallel and series), and fed by a phase-shifting transformer, which can have different configurations. Fault diagnosis of the uncontrolled bridge rectifier diodes is one of the most important concerns on the electronic devices, nonetheless, rectifier units are inherently not protected in front of open-circuit (O/C) faults, which cause malfunction and performance deterioration. In order to solve this drawback, the proposed fault diagnosis method is based on the O/C fault signature observed in the dc-link output voltage of TRUs rectifier. It allows detecting the O/C diodes of parallel and series TRUs with different phase-shifting transformer configurations and for the most usual fault scenarios. Moreover, it also helps the prediction of diodes that could be exposed to failure after the fault, which provides corrective maintenance for the TRU development. The proposed method is illustrated from MATLAB numerical simulations of a 12-pulse TRU, and is validated with experimental tests.

A New Five-Level Voltage Source Inverter: Modulation and Control

In this article, a new five-level voltage source inverter is proposed for high-power applications. The proposed inverter is competitive in performance, component count, and control complexity compared with the conventional multilevel inverters. Also, the proposed inverter has a simple structure as it does not have any dc-link neutral points, unlike hybrid converters. Furthermore, the proposed topology can be connected in a back-to-back due to the presence of a common dc-link. Also, there is no need of isolated dc source and a complex phase-shifting transformer. In addition, a simple voltage balancing approach based on a level-shifted carrier pulsewidth modulation scheme is proposed to control the flying capacitor voltages. The proposed approach will make use of the redundancy switching states to balance the flying capacitor voltages in the proposed inverter. The steady-state and transient performance of the proposed five-level voltage source inverter and voltage balancing approach is validated through MATLAB simulation studies at different power factors and modulation indices. The simulation studies are further evaluated experimentally by a scaled-down laboratory prototype. Furthermore, the feasibility of the proposed topology is analyzed under the performance indices of voltage and current harmonic distortion, flying capacitor voltage ripples, converter power losses, and converter efficiency.

Co-optimization of multi-stage transmission expansion planning and grid operation

The ongoing transformation of the power system characterized by an increased share of renewable energy sources requires additional transmission capacities. Nevertheless, the need for new transmission capacities can be reduced by optimizing grid operation. This contribution presents a novel approach to the co-optimization of multi-stage transmission expansion planning and grid operation within a mixed-integer linear programming formulation. The expansion via AC systems and phase shifting transformers (PSTs) is combined with the control of PSTs and the determination of congestion management interventions such as redispatch of power plants or curtailment of renewable energies. The number of potential expansion candidates is reduced by linear programming relaxations. Exemplary results based on a synthetic test system containing 120 buses evidence the impact of the proposed approach on overall system costs. The proposed co-optimization reduces the total costs by 16.5 % when applied instead of the sole expansion via AC technology.