Equivalent Generator Research Articles

Small‐signal stability analysis and particle swarm optimisation self‐tuning frequency control for an islanding system with DFIG wind farm

Linearised model for frequency control of an islanding system comprising an equivalent synchronous generator and an equivalent doubly fed induction generator (DFIG) is derived. Small signal stability analysis is performed to determine the stable regions for DFIG supplementary droop controller under various wind velocities. In order to achieve better dynamic frequency response under different system parameters, the DFIG droop gain is adapted in real-time using a self-tuning controller designed based on particle swarm optimisation technique. In order to validate the results from small signal analysis and to demonstrate the effectiveness of the proposed self-tuning frequency controller, digital simulations using MATLAB/SIMULINK are performed on a local power system in central Taiwan. It is concluded from the simulation results that the proposed self-tuning frequency controller offer better dynamic frequency response than the fixed-gain droop controller.

Thunderstorm generators operating as voltage sources in global electric circuit models

The description of global electric circuit (GEC) generators in continuous numerical models is analysed and discussed. It is shown that voltage-source generators, sometimes employed in simple lumped-element GEC models, have a consistent generalisation in continuous GEC models: just as current-source generators generalise to source current density distributions, voltage-source generators generalise to distributions of the relative potential on cloud boundaries. The difference between non-ideal and ideal current or voltage sources is investigated for both lumped-element and continuous GEC models. As in modern three-dimensional GEC models the formal generalisation of voltage-source thunderstorms turns out to be difficult to implement, two alternative approaches involving the replacement of voltage-source generators with equivalent current-source generators are developed. One approach is based upon a rough estimation of the source current producing the same contribution to the GEC as the original voltage source; the other approach uses the fact that each voltage-source generator can be shown to be a limiting case of a certain current-source generator with increased conductivity. For the first time voltage-source generators are implemented in a numerical GEC model (using both the direct generalisation and the suggested alternative approaches).

Интервальные критерии распознавания места короткого замыкания в энергосистеме

The problem of locating (place recognition) of a short-circuit (SC) fault in an electric system is considered. It is shown that each fault location is associated with two versions of a complex SC parameter reflected by a ray in its plane. The ray position is determined by the inner impedance angle of the electric network as the equivalent generator with respect to the SC place. The angle variation interval for a fixed SC place is determined by the variation of normal passive parameters of the electric system simulation model. The algorithmic model of the observed power transmission line is the fault locator’s structural element. The model behaves as a tool that converts the observed quantities into a complex measurement as a function of the supposed SC place. The measurement is reflected as a locus in the same plane as the SC parameter specified by the segment of beams. The interval of SC place coordinate values is determined by intersection of the locus with the segment extreme rays. The segment can be adapted to the impedance of purely emergency operating conditions, which is determined by the ratio of emergency components of voltage and current at the supposed fault places.

Robust load frequency control of nonlinear power networks

ABSTRACTThis paper proposes a decentralised second-order sliding mode (SOSM) control strategy for load frequency control (LFC) in power networks, regulating the frequency and maintaining the net inter-area power flows at their scheduled values. The considered power network is partitioned into control areas, where each area is modelled by an equivalent generator including second-order turbine-governor dynamics, and where the areas are nonlinearly coupled through the power flows. Asymptotic convergence to the desired state is established by constraining the state of the power network on a suitably designed sliding manifold. This manifold is designed relying on stability considerations made on the basis of an incremental energy (storage) function. Simulation results confirm the effectiveness of the proposed control approach.

Equivalent model considering frequency characteristics and renewable uncertainties for probabilistic power flow

The data is not always shared among sub-networks due to concerns about information privacy or difficulties in synchronous information exchange. It is difficult or even impossible to obtain the probabilistic power flow (PPF) by the centralised analysis. In this paper, an equivalent model considering static power-frequency characteristics (SPFCs) and renewable uncertainties is proposed. In this model, SPFCs of equivalent loads and generators are derived to retain SPFCs of original external loads and generators, respectively. In addition, probabilistic characteristics and correlations of equivalent loads are formulated based on Cholesky decomposition to preserve original external renewable uncertainties. The proposed model is further applied to PPF and then PPF can be solved via Monte Carlo simulation method, which makes that the PPF results can be obtained when the detailed data of the original external network cannot be shared. Owing to efficiently preserving the external SPFCs and renewable uncertainties in the proposed equivalent model, the accuracy of PPF results can be guaranteed. Simulation results of IEEE 14-bus and IEEE-118 bus systems demonstrate the effectiveness and superiority of the proposed equivalent model and its applications to PPF, compared with existing well known equivalent models and their applications to PPF.

Steady-State Model of Grid-Connected Photovoltaic Generation for Power Flow Analysis

A new model of a grid-connected photovoltaic (PV) plant suitable for power flow analysis is proposed in this paper. Unlike existing models, the proposal departs from the equivalent generator representation of the PV plant and is based instead on the operation and control modes of PV panels and voltage source converters. The resulting set of nonlinear equations is assembled together with the network's equations to formulate a generalized power flow problem in a unified frame of reference, which is efficiently solved by using the Newton–Raphson algorithm. The complementarity condition approach is adopted for directly including all operation and control mode constraints of the PV plant in the power flow formulation, which permits the simultaneous and automatic handling of limits of all state variables associated with these constraints during the iterative solution process. The effectiveness of the proposed method is fully demonstrated by numerical examples.

Frequency regulation strategy based on variable‐parameter frequency limit control during black start

High-voltage direct current (HVDC) can speed up the recovery of a power system. However, both rectifier and inverter sides of HVDC are weak systems during a black start. To coordinate frequency characteristics of both sides within the frequency deviation constraint, a frequency regulation strategy based on variable-parameter frequency limit control (FLC) during a black start is proposed. First, the mathematical models of asynchronous interconnected AC–DC system are established, and the optimal FLC parameters leading to minimum frequency deviation of both sides are obtained. Subsequently, based on the characteristics of the optimal FLC parameters with the parameters of the equivalent generator and the capacity of the AC system, a frequency regulation strategy is proposed to adapt to the continuously changing parameters and configurations of the AC power system during a black start. Finally, the simulation model is established using PSCAD/EMTDC software to verify the control strategy and the correctness of the optimal FLC parameters.

Stability Analysis of a Microgrid System With a Hybrid Offshore Wind and Ocean Energy Farm Fed to a Power Grid Through an HVDC Link

This paper presents the stability analyzed results of a microgrid system containing an offshore wind farm (OWF), an offshore tidal farm (OTF), and a seashore wave farm (SWF) fed to an onshore power grid through a high-voltage dc (HVDC) link based on a voltage-source converter (VSC). The characteristics of the studied OWF, OTF, and SWF are simulated by an equivalent aggregated wind doubly-fed induction generator (DFIG), an equivalent aggregated tidal DFIG, and an equivalent aggregated wave permanent-magnet synchronous generator. A damping controller located at the converter station of the HVDC link is designed by using the pole-assignment approach to offer adequate damping to the studied microgrid system. A frequency-domain approach based on a linearized system model using eigenvalue analysis and a time-domain scheme based on a nonlinear system model subject to a disturbance condition are systematically achieved. It can be concluded from the simulation results that the proposed VSC-based HVDC link joined with the designed damping controller can effectively stabilize the studied microgrid system with hybrid OWF, OTF, and SWF under various disturbance conditions. The inherent fluctuations of the generated power of the microgrid system injected into the power grid can also be effectively mitigated by the proposed control scheme.

Geometrical constraint of sources in noninvasive localization of premature ventricular contractions

The inverse problem of electrocardiography for localization of a premature ventricular contraction (PVC) origin was solved and compared for three types of the equivalent cardiac electrical generator: transmembrane voltages, epicardial potentials, and dipoles. Instead of regularization methods usually used for the ill-posed inverse problems an assumption of a single point source representative of the heart generator was applied to the solution as a geometrical constraint.Body surface potential maps were simulated from eight modeled origins of the PVC in the heart model. Then the maps were corrupted by additional Gaussian noise with the signal-to-noise ratio (SNR) from 20 to 10dB and used as the input of the inverse solution. The inverse solution was computed from the first 30ms of the ventricular depolarization. It was assumed that during this period only a small part of the heart volume is activated thus it can be represented by a single point electrical source.Generally, the localization error was more dependent on the PVC origin position than on the type of the used heart generator. The most stable localization error between the inversely found results and the true PVC origin was not larger than 20mm for PVC origins located in the left ventricular wall and on the right ventricular anterior side. For such cases, the localization was robust to the noise up to SNR of 10dB for all studied types of the cardiac generator. For SNR 10dB the results became unstable mainly for the PVC origins in the septum and posterior right ventricle for the dipolar heart generator and for epicardial potentials defined on the pericardium when the range of the localization error increased up to 50mm. When the results for different electrical heart generators were considered altogether, the mean radius of the cloud of results did not exceed 20mm and the localization error of the cloud center was smaller than that obtained for a particular type of the cardiac generator.Combination of results from different models of a single point cardiac electrical generator can provide better information for the preliminary noninvasive localization of PVC than the use of one type of the generator.

Data for: Two-tier static equivalent method of active distribution networks considering sensitivity, power loss and static load characteristics

Abstract This paper presents a two-tier static equivalent method that can accurately simplify active distribution networks. This method proposes a new physical equivalent network composed of equivalent generator, branch and load. Based on the physical equivalent network, the two-tier static equivalent model is further constructed. In the upper tier equivalent model, the consistency of sensitivity and power loss are considered. In the lower tier equivalent model, static load characteristics are retained to further enhance the accuracy of the equivalent model. The test systems, containing both transmission and active distribution networks, are used to demonstrate the effectiveness of the proposed two-tier static equivalent method.

Two-tier static equivalent method of active distribution networks considering sensitivity, power loss and static load characteristics

This paper presents a two-tier static equivalent method that can accurately simplify active distribution networks. This method proposes a new physical equivalent network composed of equivalent generator, branch and load. Based on the physical equivalent network, the two-tier static equivalent model is further constructed. In the upper tier equivalent model, the consistency of sensitivity and power loss are considered. In the lower tier equivalent model, static load characteristics are retained to further enhance the accuracy of the equivalent model. The test systems, containing both transmission and active distribution networks, are used to demonstrate the effectiveness of the proposed two-tier static equivalent method.

Stability Improvement of a Multimachine Power System Connected With a Large-Scale Hybrid Wind-Photovoltaic Farm Using a Supercapacitor

This paper presents the stability improvement of a multimachine power system connected with a large-scale hybrid wind-photovoltaic (PV) farm using an energy-storage unit based on supercapacitor (SC). The operating characteristics of the hybrid wind-PV farm are simulated by an equivalent aggregated 300-MW wind-turbine generator (WTG) based on permanent-magnet synchronous generator and an equivalent aggregated 75-MW PV array. The WTG and the PV array are connected to a common dc link through a voltage-source converter and a dc/dc boost converter, respectively. The power of the common dc link is transferred to the multimachine power system through a voltage-source inverter, step-up transformers, and a connection line. The SC-based energy-storage unit, which is integrated into the common dc link through a bidirectional dc/dc converter, is employed for smoothing out the power fluctuations due to variations of wind speed and/or solar irradiance. A proportional-integral-derivative (PID)-supplementary damping controller (PID-SDC) is designed for the bidirectional dc/dc converter of the SC to enhance the damping characteristics of the low-frequency oscillations associated with the studied multimachine power system. The root loci of the studied system are examined under wide ranges of wind speed and solar irradiance. The effectiveness of the proposed SC joined with the PID-SDC on improving the performance of the studied system under different disturbance conditions is also demonstrated using time-domain simulations.

Методы обработки и регистрации биосигналов для задач медицинской диагностики

In radio engineering signal processing methods are widely used including spectral, correlation, wavelet analyses, etc. These methods are effectively used in processing the biosignals of a human organism for medical diagnostic purposes. Methods for analyzing and producing electromagnetic and acoustic fields in various media and systems are also commonly used. These methods are promising and useful also in studying a human organism. The article presents the main results from the research work carried out by the staff of the MPEI National Research University’s Chair of Radio Engineering Fundamentals aimed at development and use of radio engineering methods in the field of processing and recording biosignals for medical diagnostic purposes. The article outlines the works on studying the heart electric field in electrocardiology devoted to reconstructing an equivalent electric heart generator from the signals recorded by multichannel electrocardiographic leads and coordinates of electrodes placed on the human trunk surface. The results from studying the human trunk inhomogeneous model in terms of the effect the chest internal inhomogeneities have on the distribution of surface potentials are presented. Matters concerned with separation of biorhythm signals are considered under the conditions when the organism vital activity signals are simultaneously generated by several quasi-periodic processes, with the signal of interest weakly manifesting itself. A methodology for assessing the level of emotional stress by conducting a cross-correlation analysis of heart and respiration rhythms is described. Matters concerned with constructing and analyzing the characteristics of temperature sensors implanted in the body with the use of surface acoustic waves are discussed.

A NEW SYMMETRY OF ELECTROWEAK LAGRANGIAN

Problems of the Standard Model, associated with the introduction of an electromagnetic field as a linear combination of fields on which various gauge groups representations are implemented, are analyzed. In this paper, we pay attention to the fact that in any model with gauge fields, the generators which are included in the covariant derivatives can be given only up to the transition to the equivalent representation. It is proposed that dynamic models with equivalent representations of generators should be physically equivalent. It means the requirement of the Lagrangian symmetry with respect to the transition from one equivalent generators representations to another. In particular, in the Lagrangian of the Standard Model, we have raising and lowering SU (2) group generators. The group multiplication law determines only the matrix elements modules of these generators while the arguments remain uncertain. In the paper, such uncertainty is considered as a local one. At different points of space-time, generators can be expressed in various equivalent representations. The compensation of the uncertain matrix elements arguments of the SU (2) group generators can be carried out with a local U (1) - transformation with the introduction of the corresponding gauge field, which can be considered as the electromagnetic field. The advantages of such electromagnetic field introduction in comparison with the method used in the Standard Model are analyzed.

Assessment of the human exposure to transient and time-harmonic fields using the enhanced transmission line theory approach

ABSTRACTThe paper deals with the assessment of human exposure to the transient electromagnetic fields and high-frequency (HF) radiation. The formulation of the problem is based on a simplified cylindrical representation of the human body. The analysis is based on the enhanced transmission line (TL) theory. For this purpose, in order to quantify the induced current inside the human body, we solve linear system equations, where the electromagnetic field excitation is represented by two equivalent current and voltage generators. Once the axial current is determined, it is possible to calculate the specific absorption rate (SAR). Some illustrative computational examples are presented in the paper.

Third Order Sliding Mode Observer-Based Approach for Distributed Optimal Load Frequency Control

In this letter, we propose a third order sliding mode observer-based approach for optimal load frequency control in power networks which are partitioned into control areas. We model each area by an equivalent generator including second-order turbine-governor dynamics. Assuming to measure only few state variables, we design two third order sliding mode observers for each control area to locally estimate the unmeasured states. We introduce also a distributed second order sliding mode control strategy, which makes use of the estimates coming from the observers and achieves both frequency regulation and minimization of generation costs. The simulation results confirm the validity of the proposed approach.

Modeling and performance analysis of duck-shaped triboelectric and electromagnetic generators for water wave energy harvesting

Summary Triboelectric nanogenerator (TENG) is a newly proposed technology for effectively converting mechanical energy into electricity. Triboelectric nanogenerator has shown a great potential for harvesting the clean and abundant energy of ocean waves. Recently, a duck-shaped TENG device has been proposed as a lightweight, cost-effective, highly stable, and efficient system for scavenging the existing energy in water waves. In this paper, a detailed investigation on the performance of the duck-shaped TENG is presented. Then, a comparative analysis between the TENG device and an equivalent electromagnetic generator (EMG) for wave energy harvesting is performed. The electric output characteristics of both techniques under various mechanical and electrical conditions are obtained. The analysis demonstrates that at a low operating frequency of 2.5 Hz, the TENG and EMG achieve the peak power density of 213.1 and 144.4 W/m3, respectively. The present paper provides guidance for design and optimization of hybrid TENG and EMG technology toward scavenging the blue energy.

An energy function based design of second order sliding modes for Automatic Generation Control

This paper proposes a decentralized Second Order Sliding Mode (SOSM) control strategy for Automatic Generation Control (AGC) in power networks, where frequency regulation is achieved, and power flows are controlled towards their desired values. This work considers a power network partitioned into control areas, where each area is modelled by an equivalent generator including second order turbine-governor dynamics, and where the areas are nonlinearly coupled through the power flows. Asymptotic convergence to the desired state is established by constraining the state of the power network on a suitable sliding manifold. This is designed relying on stability considerations made on the basis of an incremental energy (storage) function. Simulation results confirm the effectiveness of the proposed control approach.

Dynamic equivalent of wind farm model for power system stability studies

ABSTRACTA new dynamic equivalencing method for stability assessment of a grid-integrated wind farm is proposed in this article. The accuracy of the method is validated for a 34-bus system with 28-unit wind farm connected to Indian utility system. This wind farm consists of several wind turbines of two different ratings. The electrical parameters of the equivalent generator are derived from the mathematical model of the squirrel-cage induction generator. The parameters of the equivalent wind-turbine generator are optimized to yield minimum deviation from the detailed system response using genetic algorithm. The small-signal and transient stability responses of the study system with detail wind farm and equivalent model are simulated using MATLAB. Equivalent model eigenvalues are compared to the centre of inertia based detailed system eigenvalue. In addition, the computed eigenvalues and time-domain responses of the proposed equivalent model, detailed wind farm are compared against weighted model proposed earlier. In most of the investigated cases, the average error of dynamic responses between the proposed equivalent and detailed models are less when compared to weighted model. Thus, the large-signal responses of the proposed equivalent model show superior agreement with detailed system response.

Method of calculating the maximum transmission capability with unified power flow controller

This study proposed an algorithm for calculating the maximum transmission capacity considering unified power flow controller (UPFC). At the beginning, the equivalent virtual generator, located on ends of UPFC's branch, is obtained based on the source model of UPFC. Then, for the purpose of obtaining the range of transmission power, the maximum (minimum) active/reactive power is treated as an optimising object. Meanwhile, the series voltage and shunt current of the UPFC, as well as other generators’ reactive power, are selected as control variables. As a result, the optimisation model could be formed in UPFC, SSSC and STATCOM modes, respectively, in which buses voltage and transmission limits are also supplied. Based on the characteristics of the above model, the interior point method is used to achieve the optimal solution. In the end, Nanjing western power grid and Suzhou southern power grid are tested to prove the effective and correctness of the introduced algorithm.