Inertia Constant Research Articles

A comparative study on the grid integrated wind energy conversion systems (WECS) using different generator models

A huge number of wind generators are going to be connected with the existing network in the near future. Therefore, it is necessary to analyse various models of wind energy conversion systems (WECS) for the purpose of studying the impacts upon grid. This paper presents comparative study on grid connected WECS having two different wind turbine generator systems (WTGS): model 1 [WTGS having doubly fed induction generators (DFIGs)] and model 2 [WECS having permanent magnet synchronous generators (PMSG)]. Both models are connected to AC grid through an efficient power electronic interface. Transient simulations are carried out under the condition of sudden short circuit disturbance and effect of increased generator inertia constant, friction factor and base speed is analysed. The power quality is also analysed in terms of total harmonic distortion (THD) for both models and steps are taken to improve the power quality by reducing THD.

How to design a powerful family of particle swarm optimizers for inverse modelling

In this paper, we show how to design a powerful set of particle swarm optimizers to be applied in inverse modelling. The design is based on the interpretation of the swarm dynamics as a stochastic damped mass-spring system, the so-called particle swarm optimization (PSO) continuous model. Based on this idea we derived a family of PSO optimizers (GPSO, CC-PSO and CP-PSO) having different exploitation and exploration capabilities. Their convergence is related to the stability of their first (mean trajectories)- and second-order moments (variance and temporal covariance). Good parameter sets are located inside their first stability regions close to the upper border of their respective second stability regions where the attraction from the particles oscillation centre is very weak. In this region of weak attraction, both convergence to the global minimum and exploration of the search space are possible. Based on this idea, we have designed a particle–cloud algorithm where each particle in the swarm has different inertia (damping) and acceleration (rigidity) constants. We explored the performance of these algorithms for different PSO members using different benchmark functions, showing that the cloud algorithms have a very good balance between exploration and exploitation. Also, the cloud design helps to avoid two main drawbacks of the PSO algorithm: the tuning of the PSO parameters and the clamping of the particles velocities. We also present the lime and sand algorithm that changes the time step with iterations. This feature helps to avoid entrapment in local minima when the time step is increased, and enables exploration around the global best when the time step is decreased. All these designs are based on the theoretical analysis of the PSO dynamics. We explain how to use this knowledge to the solution and appraisal of inverse problems. Finally, we briefly introduce the combined use of PSO and model reduction techniques to allow posterior sampling in high dimensional spaces.

Non-linear flexural–torsional dynamic analysis of beams of arbitrary cross section by BEM

In this paper, a boundary element method is developed for the non-linear flexural–torsional dynamic analysis of beams of arbitrary, simply or multiply connected, constant cross section, undergoing moderately large deflections and twisting rotations under general boundary conditions, taking into account the effects of rotary and warping inertia. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading in both directions as well as to twisting and/or axial loading. Four boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to the angle of twist and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique leads to a system of non-linear coupled Differential–Algebraic Equations (DAE) of motion, which is solved iteratively using the Petzold–Gear Backward Differentiation Formula (BDF), a linear multistep method for differential equations coupled to algebraic equations. The geometric, inertia, torsion and warping constants are evaluated employing the Boundary Element Method. The proposed model takes into account, both the Wagner's coefficients and the shortening effect. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy, the range of applications of the developed method as well as the influence of the non-linear effects to the response of the beam.

Automatic generation control of a multi area hydrothermal system using reinforced learning neural network controller

This paper deals with automatic generation control (AGC) of a three unequal area hydrothermal system. Reheat turbines in thermal areas and electric governor in hydro area are considered. Appropriate generation rate constraints are considered in the areas. Bacterial foraging (BF) technique is used to simultaneously optimize the integral gains ( K Ii ) and speed regulation parameter ( R i ) keeping frequency bias fixed at frequency response characteristics. The integral controller in this case is termed as BFIC. The performance of a multilayer perception neural network (MLPNN) controller using reinforcement learning is evaluated for the system. In this reinforcement learning, the weights are dynamically adjusted online using backpropagation algorithm with error being the area control error (ACE). The performance of the MLPNN controller is compared with that of BFIC. Also, the performance of MLPNN controller over a wide range of system loading conditions and step load perturbations is compared with BFIC. Investigations clearly reveal the superior performance of MLPNN controller over BFIC. Sensitivity analysis subject to wide changes in system loading, inertia constant ( H) and size and location of step load perturbation is carried out to investigate the robustness of the controller with the optimum K Ii and R i obtained at nominal condition.

An Effective Distributed Model for Power System Transient Stability Analysis

The modern power systems consist of many interconnected synchronous generators having different inertia constants, connected with large transmission network and ever increasing demand ...

Practical Assessment of Synchronous Generator Dynamic Model Parameters

The paper presents analysis of evaluation methods of synchronous generator dynamic model parameters according to field test data. The list of parameters of the dynamic model for analysis of electromechanical transient processes and stability conditions in power systems is presented. The parameters of direct and quadrature axes can be evaluated according to frequency response test applied to the stopped generator. Regime tests of operating generator can be used for evaluation of direct axis parameters as well as for value of inertia constant. The open circuit characteristic is used for assessment of saturation characteristic. The methodic of parameters’ evaluation is created and equations for their evaluation according to field test data are presented.

Nonlinear Effects in Elastic Flexural-Torsional Vibrations of Beams of Arbitrary Cross Section

In this paper a boundary element method is developed for the nonlinear flexural-torsional dynamic analysis of beams of arbitrary, simply or multiply connected, constant cross section, undergoing moderate large deflections and rotations under general boundary conditions, taking into account the effects of rotary and torsional warping inertia. Four boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to the angle of twist and solved using the Analog Equation Method, a BEM based method. The geometric, inertia, torsion and warping constants are evaluated employing the Boundary Element Method. The proposed model takes into account, both the Wagner's coefficients and the shortening effect. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy, the range of applications of the developed method as well as the influence of the nonlinear effects to the response of the beam.

Performance comparison of several classical controllers in AGC for multi-area interconnected thermal system

This paper presents automatic generation control (AGC) of interconnected two equal area, three and five unequal-areas thermal systems provided with single reheat turbine and generation rate constraints of 3% per minute in each area. A maiden attempt is made to apply integral plus double derivative (IDD) controller in AGC. Controller gains in the two-area system are optimized using classical approach whereas in the three and five area systems controller gains and governor speed regulation parameters ( R i) are simultaneously optimized by using a more recent and powerful evolutionary computational technique called bacterial foraging (BF) technique. Investigations reveal on comparison that Integral (I), Proportional–Integral (PI), Integral–Derivative (ID), or Proportional–Integral–Derivative (PID) controllers all provide more or less same response where as Integral–Double Derivative (IDD) controller provides much better response. Sensitivity analysis reveals the robustness of the optimized IDD controller gains and R i of the five area system to wide changes in inertia constant ( H), reheat time constant ( T r), reheat coefficient ( K r), system loading condition and size and position of step-load perturbation.

A simple expression for fluid inertia force acting on micro-plates undergoing squeeze film damping

Squeeze film damping in systems employing micro-plates parallel to a substrate and undergoing small normal vibrations is theoretically investigated. In high-density fluids, inertia forces may play a significant role affecting the dynamic response of such systems. Previous models of squeeze film damping taking inertia into account do not clearly isolate this effect from viscous damping. Therefore, currently, there is no simple way to distinguish between these two hydrodynamic effects. This paper presents a simple solution for the hydrodynamic force acting on a plate vibrating in an incompressible fluid, with distinctive terms describing inertia and viscous damping. Similar to the damping constant describing viscous losses, an inertia constant, given by ρL 3 W / h (where ρ is fluid density, L and W are plate length and width, respectively, and h is separation distance), may be used to accurately calculate fluid inertia for small oscillation Reynolds numbers. In contrast with viscous forces that suppress the amplitude of the oscillation, it is found that fluid inertia acts as an added mass, shifting the natural frequency of the system to a lower range while having little effect on the amplitude. Dimensionless parameters describing the relative importance of viscous and inertia effects also emerge from the analysis.

Postbuckling analysis of beams of arbitrary cross section using BEM

In this paper, the postbuckling analysis of beams of arbitrary cross section is presented taking into account moderate large displacements, large angles of twist and adopting second order approximations for the deflection–curvature relations. The beam is subjected to the combined action of the arbitrarily distributed or concentrated axial, transverse and torsional loading, while it is supported by the most general boundary conditions including elastic support or restraint. Starting from a displacement field without any simplifying assumptions about the angle of twist amplitude and based on the total potential energy principle, four highly coupled nonlinear governing differential equations are derived taking into account the shortening and warping effects and the Wagner’s coefficients due to the asymmetric character of the cross section. The arising four boundary value problems with respect to the transverse displacements, to the axial displacement and the angle of twist are solved using the Analog Equation Method, a BEM based method. The geometric, inertia, torsion and warping constants of the arbitrary beam cross section are evaluated employing only boundary integrals. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint–Venant’s torsional constant. Numerical examples are worked out to illustrate the efficiency, accuracy and range of applications of the developed method. Conclusions of great practical interest are drawn.

On-line designed hybrid controller with adaptive observer for variable-speed wind generation system

Abstract This paper presents a wind-driven induction generator system with a hybrid controller, which combines the advantages of the integral–proportional and the sliding mode controllers. The proposed controller is designed to adjust the turbine speed to extract maximum power from the wind. The integral–proportional speed controller can be designed on-line according to the estimated rotor parameters, and the observed disturbance torque is feed-forward to increase the robustness of the system. The designed integral switching surface with integral–proportional due to on-line tuning produced a new sliding surface to implement the control, and can ensure the robustness under noisy environment. The rotor inertia constant, friction constant, and the disturbed mechanical torque of the induction generator are estimated by a proposed adaptive observer, which is composed of the recursive least square algorithm and a torque observer.

Robust transient stabilisation problem for a synchronous generator in a power network

The robust transient stabilisation problem (with stability proof) of a synchronous generator in an uncertain power network with transfer conductances is rigorously formulated and solved. The generator angular speed and electrical power are required to be kept close, when mechanical and electrical perturbations occur, to the synchronous speed and mechanical input power, respectively, while the generator terminal voltage is to be regulated, when perturbations are removed, to its pre-fault reference constant value. A robust adaptive nonlinear feedback control algorithm is designed on the basis of a third-order model of the synchronous machine: only two system parameters (synchronous machine damping and inertia constants) along with upper and lower bounds on the remaining uncertain ones are supposed to be known. The conditions to be satisfied by the remote network dynamics for guaranteeing ℒ2 and ℒ∞ robustness and asymptotic relative speed and voltage regulation to zero are weaker than those required by the single machine-infinite bus approximation: dynamic interactions between the local deviations of the generator states from the corresponding equilibrium values and the remote generators states are allowed.

Maiden Application of Bacterial Foraging-Based Optimization Technique in Multiarea Automatic Generation Control

A maiden attempt is made to examine and highlight the effective application of bacterial foraging (BF) to optimize several important parameters in automatic generation control (AGC) of interconnected three unequal area thermal systems, such as integral controller gains (K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ii</sub> ) for the secondary control, governor speed regulation parameters (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ) for the primary control and frequency bias parameters (B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> ), and compare its performance to establish its superiority over genetic algorithm (GA) and classical methods. Comparison of convergence characteristics of BF, GA, and classical approach reveals that the BF algorithm is quite faster in optimization, leading to reduction in computational burden and giving rise to minimal computer resource utilization. Simultaneous optimization of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ii</sub> , R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> parameters which surprisingly has never been attempted in the past, provides not only best dynamic response for the system but also allows use of much higher values of R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> (than used in practice), that will appeal to the power industries for easier and cheaper realization of governor. Sensitivity analysis is carried out which demonstrates the robustness of the optimized K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ii</sub> , R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , and B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> to wide changes in inertia constant (H), reheat time constant (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ), reheat coefficient (K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ), system loading condition, and size and position of step load perturbation.

Analysis of delta-omega and fuzzy logic power system stabilizers under several operating conditions

Power system stabilizers (PSSs) have become very common in the operation of large electric power systems. The stability of electric power systems is increased by the use of power system stabilizers. It is a challenging task to design a stabilizer that delivers good performance in a wider range of operating conditions and under disturbances. This paper presents a fuzzy logic power system stabilizer (FLPSS) and demonstrates the good performance of this stabilizer under a wide range of operating conditions and disturbances. The performance of FLPSS is compared with that of a speed deviation (delta-omega) PSS in the variation of four different operating conditions, i.e., inertia constant (H), automatic voltage regulator (AVR) gain (Ka), internal reactance (Xe), and reactive power (Q).

Flexural–torsional postbuckling analysis of beams of arbitrary cross section

In this article, the postbuckling analysis of axially compressed elements of arbitrary cross section is presented taking into account moderately large displacements, moderately large angles of twist and employing nonlinear relationships between bending moments and curvatures. The elements are supported by the most general boundary conditions including elastic support or restraint. Based on Galerkin’s method and approximating the displacement field of the element by polynomial expressions the governing differential equations lead to a nonlinear algebraic system. The geometric, inertia, torsion and warping constants of the arbitrary beam cross section are evaluated employing the boundary element method. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint–Venant’s torsional constant. Both the Wagner’s coefficients and the shortening effect are taken into account, while their influence is examined and discussed. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method.

Transient stability simulation of wind generator expressed by two‐mass model

AbstractRecently, wind power generation is increasing worldwide. In wind power stations, induction machines are mostly used as generators. Since induction generators have a stability problem similar to the transient stability of synchronous machines, it is important to analyze the transient stability of power systems including wind generators. Although there have been some reports analyzing the transient stability problem, wind turbine and wind generator are, in most cases, modeled as a one‐mass shaft system having total inertia constant. This paper presents simulation analyses of transient stability of power system including induction generator which is expressed by a two‐mass shaft model and analyzes an effect of shaft system modeling on the transient stability characteristics. Simulations are performed by PSCAD/EMTDC in this study. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 162(3): 27–37, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20394

Rovibrational Spectra for the HCCCN·HCN and HCN·HCCCN Binary Complexes in 4He Droplets

Rovibrational spectra are measured for the HCCCN*HCN and HCN*HCCCN binary complexes in helium droplets at low temperature. Though no Q-branch is observed in the infrared spectrum of the linear HCN*HCCCN dimer, which is consistent with previous experimental results obtained for other linear molecules, a prominent Q-branch is found in the corresponding infrared spectrum of the HCCCN*HCN complex. This Q-branch, which is reminiscent of the spectrum of a parallel band of a prolate symmetric top, implies that some component of the total angular momentum is parallel to the molecular axis. The appearance of this particular spectroscopic feature is analyzed here in terms of a nonsuperfluid helium density induced by the molecular interactions. Finite temperature path integral Monte Carlo simulations are performed using potential energy surfaces calculated with second-order Möller-Plesset perturbation theory, to investigate the structural and superfluid properties of both HCCCN*HCN(4He)N and HCN*HCCCN(4He)N clusters with N < or = 200. Explicit calculation of local and global nonsuperfluid densities demonstrates that this difference in the rovibrational spectra of the HCCCN*HCN and HCN*HCCCN binary complexes in helium can be accounted for by local differences in the superfluid response to rotations about the molecular axis, i.e., different parallel nonsuperfluid densities. The parallel and perpendicular nonsuperfluid densities are found to be correlated with the locations and strengths of extrema in the dimer interaction potentials with helium, differences between which derive from the variable extent of polarization of the CN bond in cyanoacetylene and the hydrogen-bonded CH unit in the two isomers. Calculation of the corresponding helium moments of inertia and effective rotational constants of the binary complexes yields overall good agreement with the experimental values.

Mechatronic systems identification using an impulse response recursive algorithm

A recursive identification algorithm is used to identify mechatronic systems using impulse response data. The algorithm is based on an auto regressive moving average (ARMA) model with a steepest descent method to minimize the least square error between the original and predicted outputs. Two mechatronic systems are tested: DC motor and gyroscope. Impulse voltage input is used to excite the system and the angular speed output is measured. In both systems, the torque and angular velocity outputs are dependent on the voltage and current inputs. This relationship is governed by characteristics such as inductance, resistance, moment of inertia, friction, load, and system constants. Once the ARMA model is constructed, the transfer function is realized. Then the input voltage is varied and the identified model results are compared with the original system. Simulation results using Simulink and experimental results using Labview with data acquisition card (DAQ) are presented. Results show that the recursive identification algorithm is able to identify the two systems with minimal error.

Estimating wind turbines mechanical constants

The performance of wind turbines during transient situations such as the soft-starting process or in transient stability studies is strongly influenced by a broad set of mechanical parameters involved in the turbine dynamics, mainly the inertia constant, self and mutual damping and torsional stiffness. The values of these parameters use to be difficult to find because the wind turbine manufacturer/supplier usually do not supply this information. So researchers are usually forced to use vague estimated values to simulate these transients. This communication presents an analysis of the mechanical component that models the wind turbine rotor, as well as its mechanical coupling to the generator shaft. A discussion will be introduced to question how to calculate approximate but realistic values for the wind turbine inertia time constant, preferably as a function of the blade mass and length, but also the rated wind turbine power. The dependence of the remaining mechanical wind turbine parameter values will be also provided.

Motor planning of arm movements is direction-dependent in the gravity field

In the present study we analyzed kinematic and dynamic features of arm movements in order to better elucidate how the motor system integrates environmental constraints (gravity) into motor planning and control processes. To reach this aim, we experimentally manipulated the mechanical effects of gravity on the arm while maintaining arm inertia constant (i.e. the distribution of the mass around the shoulder joint). Six subjects performed single-joint arm movements (rotation around the shoulder joint) in both sagittal (upward, U, versus downward, D) and horizontal (left, L, versus right, R) planes, at different amplitudes and from different initial positions. Under these conditions, shoulder gravitational torques (SGTs) significantly varied when arm movements were performed in the sagittal but not in the horizontal plane. Contrary to SGTs, arm inertia remained constant and similar for both horizontal and sagittal planes since subjects performed arm movements with only one degree of freedom. All subjects, whatever the movement direction, appropriately scaled shoulder joint kinematic parameters according to movement amplitude. Furthermore, peak velocity and movement duration were equivalent for both horizontal and sagittal planes. Interestingly, some kinematic parameters significantly differed according to U/D but not L/R directions. Specifically, acceleration duration was greater for D than U movements, while the opposite was true for peak acceleration. Consequently, although vertical and horizontal arm movements shared a general common strategy (i.e. scaling law), the kinematic asymmetries between U and D arm movements, especially those that reflect central planning process (i.e. peak acceleration), indicated different motor intentions regarding the direction of the upcoming movement. These findings indicate that the interaction of the arm with the dynamics of the environment is internally represented during the generation of arm trajectories.