Swing Curves Research Articles

Application of Interline Power Flow Controller to Increase Transient Stability of Power System

Problem statement: The Interline Power Flow Controller (IPFC) is a novel device which can increase transient stability of power system. To verify the capability of the effect of IPFC on stability improvement of power system, the suitable mathematical model and control strategy of IPFC are needed to be presented. Approach: This study presented the mathematical model and control strategy of IPFC. The multi-series converters of IPFC are represented by multi-series voltage sources with associate transformer leakage reactance. The parameters of IPFC are modeled into power flow equation and thus it is used to determine control strategy. This study used Bang-Bang control strategy. The swing curves of the three phase faulted power system without and with an IPFC are tested and compared in various cases. Results: The swing curve of system without an IPFC get increased monotonically and thus the system can be considered as unstable whereas the swing curves of system with an IPFC can return to stable equilibrium point. Conclusion: The presented model of IPFC can help us to comprehend the effect of IPFC on transient stability improvement of power system. From simulation results, the IPFC can increase transient stability of power system.

Power System Stability Enhancement Using Unified Power Flow Controller

Problem statement: The enhancement of transient stability of the power system is one of the most challenging research areas in power engineer. Approach: This study presents the method to enhance transient stability of power system by Unified Power Flow Controller (UPFC). The mathematical model of power system equipped with a UPFC is systematically derived. The parameters of UPFC are modeled into power flow equation and thus it is used to determine control strategy. The swing curves of the three phase faulted power system without and with a UPFC are tested and compared in various cases. Results: The swing curve of system without a UPFC gets increases monotonically and thus the system can be considered as unstable whereas the swing curves of system with a UPFC can return to stable equilibrium point. Conclusion: From the simulation results, the UPFC can enhance transient stability of power system.

Improvement of Transient Stability of Power System by Thyristor Controlled Phase Shifter Transformer

Problem statement: The improvement of transient stability of the power system was one of the most challenging research areas in power engineer. Approach: This study presents the method to improve transient stability of power system by Thyristor Controlled Phase Shifter Transformer (TCPST). The mathematical model of power system equipped with a TCPST was systematically derived. The parameters of TCPST are modeled into power flow equation and thus it was used to determine control strategy. The swing curves of the three phase faulted power system without and with a TCPST are tested and compared in various cases. Results: The swing curve of system without a TCPST gets increases monotonically and thus the system can be considered as unstable whereas the swing curves of system with a TCPST can return to stable equilibrium point. Conclusion: From the simulation results, the TCPST can increase transient stability of power system.

Influence of a voltage compensation type active superconducting fault current limiter on the transient stability of power system

We have proposed a voltage compensation type active superconducting fault current limiter (SFCL). In this paper, the influence of the SFCL on the transient stability of power system is investigated. For the typical one-machine infinite-bus system, the power-angle characteristics of generator with SFCL are studied in different working conditions, and the transient physical process is analyzed. Using MATLAB SIMULINK, the power-angle swing curves are simulated under different current-limiting modes, fault types and fault clearance times. The results show that the proposed SFCL can effectively reduce the transient swing amplitude of rotor and extend the critical clearance time under mode 1, compared with mode 2 and mode 3 having few effects on enhancing the transient stability.

Generator Coherency Using the Hilbert–Huang Transform

Coherency between generators is tracked, by examining the instantaneous phase differences among interarea oscillations and swing curves in disturbed multiarea power systems. Huang's empirical mode decomposition is applied to extract dominant oscillatory modes from interarea oscillations/swing curves. Hilbert transform on these modes yields their instantaneous phase. The coherency is thus revealed by the temporal evolution of the phase difference among interarea oscillations/generator swing curves. The technique is illustrated using simulations on a test system, as well as actual wide-area measurements.

Evaluation of First Swing Stability of a Large Power System With Various FACTS Devices

This paper presents a simple method of evaluating the first swing stability of a large power system in the presence of various flexible ac transmission system (FACTS) devices. First a unified power flow controller (UPFC) and the associated transmission line are considered and represented by an equivalent pi-circuit model. The above model is then carefully interfaced to the power network to obtain the system reduced admittance matrix which is needed to generate the machine swing curves. The above pi-circuit model can also be used to represent other FACTS devices (SSSC and STATCOM) by selecting appropriate values of control parameters of the UPFC. The complex voltage at two end buses of the pi-circuit model is also evaluated during simulation to implement various existing control strategies of FACTS devices and to update the reduced admittance matrix. The effectiveness of the proposed method of generating dynamic response and hence evaluating first swing stability of a power system in the presence of various FACTS devices is tested on the ten-machine New England system and the 20-machine IEEE test system. The results obtained with various FACTS devices are also compared and discussed.

Determination of swing curve “shifts” as a function of illumination conditions: Impact on the CD uniformity

The use of a wide range of optical illumination settings may generate significant shifts in the photoresist (PR) swing curves. For technologies where critical dimension controls of few nanometers are required, the impact of these shifts on the critical dimension uniformity must be taken into account. In this paper, we have reproduced and quantified the shift of different swing curves (dose-to-clear and critical dimension) with a 248 nm positive PR. The impact of such shift on critical dimension uniformity has been determined on Deep UV Scanner.

A hybrid approach in the study of UPFC effects on transient stability of multi machine power systems

In this paper, a novel method for investigation of unified power flow controller (UPFC) effects on transient stability of a multi machine power system has been introduced. Based on the combination of output results of time domain simulation (TDS) and transient energy function (TEF) analysis, the study of power system transient stability is converted to the study of transient stability of only one machine, the so called critical machine. The effects of UPFC in three basic control modes, namely, in-phase voltage control (IVC), quadrature voltage control (QVC) and shunt compensation control (Sh.C), on the transient stability margin and for various fault clearing times has been studied. Based on acquired results, it can be seen that in-phase and quadrature voltage controls are the most effective on the improvement of transient stability margin. Also, ivc is more robust than other control modes against the increase of fault clearing time. The proposed method determines the critical machine based on the swing curves resulting from TDS, and then provides a stability margin (SM) of the critical machine with trivial computation by use of machine speeds and inertia constants. The method does not need to include a UPFC description equation in the transient energy function. The proposed method was successfully demonstrated on the 7-machine CIGRE test system.

Impact of exposure induced refractive index changes of photoresists on the photolithographic process

In many commercial and noncommercial photoresists the real and the imaginary parts of the refractive index are changed during exposure. Using a finite-difference beam-propagation algorithm, we analyze the impact of these nonlinear optical effects on the photolithographic process. Changes of the real part of the refractive index have a considerable impact on dose latitudes, sidewalls, swing curves, iso-dense bias and other process parameters. These effects become more dominant as the thickness of the resist layer increases.

Critical dimension control optimization methodology on shallow trench isolation substrate for sub-0.25 μm technology gate patterning

The impact of shallow trench isolation (STI) chemical mechanical polishing on gate critical dimension (CD) control for submicron technology was studied. The CD depends on the STI process scheme, whether it is recessed or elevated STI. We investigated the surface topography for both STI schemes at different stages of patterning and how it affected the CD control. Surface topography affected organic bottom antireflective coating (BARC) and resist thickness uniformity, led to variation in the effective exposure dose and caused CD nonuniformity across the wafer [C. A. Mack, Appl. Opt. 25, 1958 (1986)]. We used an atomic force microscope surface scan to study substrate topographical variations. The solution is to optimize BARC and resist thickness by using simulations of topographical swing curves and CD error contour plot. Excellent agreement was found between simulation and experimental results.

Concept of two-dimensional swing curves for critical dimension prediction and optimization of resist/antireflective coating bilayers in topographic situations

In microlithography, the necessity of using bottom antireflective coatings (BARCs) to reduce linewidth variations resulting from reflective notching and thin film interference effects has been largely demonstrated. We report a new methodology, based on a 2-D swing curve concept, to predict the lithographic performance of resist/BARC bilayers in a topographic situation to optimize the critical dimension (CD) range. Due to inherent planarization effects when coating on topography, both the resist and organic BARC thicknesses vary, as do the final reflectivity and CDs. As a consequence, it is not easy to determine the optimal BARC thicknesses and to predict the lithographic performance, taking into account topography effects over the whole chip. Usually, lithographic performance (CD swing curves) is measured or calculated using modeling over plane wafers. Over the topography of a real chip, however, the resist thickness can cover up to four periods of the swing curve, which means that lithographic performance over a real chip cannot be predicted using swing curves calculated or measured on plane wafers. We therefore propose a new method of representing the reflectivity and CD swing curves in two dimensions to evaluate the lithographic performance of the BARC/resist bilayer. A simulation algorithm is performed that enables the determination of both the optimal BARC thicknesses and the lithographic performance window over the whole chip. Practical examples are given demonstrating the role of such a simulation.

Data analysis for photolithography

This paper will propose standard methodologies for analyzing common lithographic data in three areas: photoresist contrast curves, swing curves, and focus-exposure matrices. For each data type, physics-based algebraic equations will be proposed to fit to the data. The equations will be fit to the data using standard non-linear least-squares fitting algorithms with standard statistical tests for removing data flyers and options for weighting the data. Analysis of the resulting curve fits will provide important information about the data.

200nm Deep-UV lithography using Step-and-Scan

This paper reports the performance of deep-UV resists on a new high-NA Step-and-Scan system. The study highlights the requirements for the printing of 200nm lithography using single-layer resists. Results are reported for resist systems such as TOK, APEX and ARCH2. SEM profiles are used to demonstrate key performance parameters of depth of focus and resolution for grouped and isolated line features.Data on linewidth control, measured at 195 points in a 26 × 32.5mm field using electrical- probe technique, is presented. The effects of exposure level on linewidth control are measured. Linewidth linearity measurements for grouped features and isolated features for the studied resist systems are used to assess the resolution capabilities of the resist systems.The measured performances of the resists are compared with resist simulations computed using PROLITH/2. The impact of resist properties on 200nm lithography is explored. Swing curves are measured for the resist systems on the high-NA, laser-illuminated Step-and-Scan system.The importance of quadrupole illumination in enhancing the depth of focus for grouped features is discussed. The effect on pattern-feature linearity is measured. The enhancement of the depth of focus for both grouped and isolated line features is analyzed. Quadrupole aperture design calculations are indicated.

Dimensional control of sub-half-micron polysilicon gate structures at DUV exposure

Results of dimensional control of sub-half-micron polysilicon gates which pass over LOCOS egdes are presented. Calculations, at duv exposure, using a chemically amplified resist, with and without top and bottom anti-reflective coatings, are performed using SOLID. Results are presented in terms of “swing curves” so that a range of dimensions may be predicted for any linewidth.

Transient stability assessment for network topology changes: application of energy margin analytical sensitivity

Developments in direct transient stability assessment using the Transient Energy function (TEF) method have included the exit point technique to determine the controlling unstable equilibrium point (u.e.p.). In this paper, analytical sensitivity of the energy margin is coupled with the exit point based TEF method to assess system stability when there is a change in system parameters: plant generation or network configuration. The principal features of this paper include: introduction of a very fast sensitivity technique to account for network configuration changes; elimination of the assumption that the mode of disturbance of the controlling u.e.p. does not change; and correlation of the sensitivity results with time simulation through swing curves. The technique is tested on the 50-generator IEEE test system and the 161-generator Northern States Power (NSP) system. >

Critical-cluster identification in transient stability studies

A method is proposed for identifying the critical cluster of machines, i.e. the machines responsible for loss of synchronism in a power system following a large disturbance. It is based on the conjecture that the loss-of-synchronism condition can be recognised by, first, considering ‘near-critically cleared trajectories’ of the machines and, secondly, observing how they are organised near the system's unstable equilibrium point. The term ‘near-critically cleared trajectories’ is meant to imply the swing curves of the system in the postfault-phase and is computed for a fault-clearing time that is slightly larger than the actual critical clearing time. To realise the above, the method uses the extended equal-area criterion. This direct criterion makes it possible to assess a convenient clearing time for computing the swing curves; to determine the system's unstable equilibrium point with great ease; and to select the critical machines by observing them at the time corresponding to this unstable equilibrium point. It also makes the speed of critical-cluster identification compatible with real-time requirements. Examples are given using the IEEE test system to illustrate the essential features: reliability in correctly identifying the critical clusters, robustness with respect to its capacity to do so under very stringent conditions, and effectiveness concerning its ability automatically to identify critical clusters of any size, i.e. irrespective of the number of machines that they contain.

Lithographic tolerances based on vector diffraction theory

The classic rules for scaling lithographic resolution derive from scalar models of image formation in air, and must be reexamined as numerical apertures (NAs) increase beyond 0.5. This article describes a vector image code (VIC) based on plane wave decomposition of the radiation that propagates from the exit pupil, and a modified thin film treatment of propagation into the photoresist. Tolerances on resolution, depth-of-focus (DOF), and source polarization can be derived from VIC simulations. The strongest vector diffraction effects arise from polarization in the illumination, producing nonscalar effects in exposure-to-clear curves (‘‘swing curves’’), as well as orientation-dependent asymmetries in printed patterns. Modeling shows that the small asymmetries previously reported [D. Flagello, A. E. Rosenbluth, C. Progler, and J. Armitage, Microcircuit Engineering 1991 (Elsevier, New York, 1991)] at 0.55 NA increase rapidly for NAs beyond 0.7. Resolution increases more slowly than NA−1 at high NA, even with unpolarized illumination and perfect focus control. The contrast loss can largely be ascribed to the in-plane or parallel component of the E field within any image slice; the out-of-plane or perpendicular component actually shows a slight contrast increase. Snell’s law reduces the angular range of E orientations in the resist, so the contrast loss in resist is much less than in air. At high NA, the aerial image loses its relevance as a predictor of lithographic performance. Snell’s law also implies spherical aberration in the refracted field, reducing DOF in thick resist layers. Further, focal tolerances calculated with the traditional ±λ/2 NA2 criterion are shown to be optimistic, since this criterion is derived from the paraxial form for defocus.

Sub-0.5 micron lithography with i-line acid-hardened negative resists

Detailed lithographic data has been obtained for a series of high resolution i-line acid-hardened negative photoresists. These resists consist of a phenolic polymer, an acid-activated crosslinker, a photoacid generator (PAG), and an i-line sensitizer. Imaging to 0.40 μm has been achieved for both a dyed and an undyed version of this resist at exposure doses <100 mJ/cm2 using a 0.45 NA i-line exposure tool. This has been demonstrated in a variety of developers, including 2.38% TMAH. Using the dyed resist, 0.5 μm lines with straight sidewalls have been imaged on aluminum substrates. Swing curves and linearity data, as well as focus and exposure latitudes, are reported.

Analysis of electrical machines using Symphony

The application of Symphony spreadsheet programs to electrical machine analysis is described. Seven typical examples are presented, namely steady-state performance of a DC shunt generator, speed control of a DC shunt motor, magnetizing current waveform of a transformer, steady-state performance of a three-phase induction machine, frequency control of a three-phase induction motor, induction motor run-up, and swing curves of a synchronous generator. Advantage is taken of the spreadsheet environment for such operations as tabular calculation, table lookup, numerical integration, and what-if analysis. Extensive use is made of the integrated graphics facilities of Symphony for producing good quality screen displays on a personal computer, which proves very convenient and useful for computer-aided instruction. Certain features of Symphony are described in the context of the applications described.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of coherent generators for power system dynamic equivalents using unstable equilibrium point

A new technique for identifying coherent generators in dynamic equivalencing of large power systems is presented. Coherency of generators in the early part of the transient period is determined by directly checking the relative rotor angle deviations. This requires the prefault angles, faulted angles and the angles at the unstable equilibrium point corresponding to the expected mode of system instability. The faulted angles are estimated by the Taylor series expansion and the unstable equilibrium point is computed by the Davidon-Fletcher-Powell method in the centre of angle reference frame. The method also requires a checking on the admittance distances between the generators to maintain coherency for the later part of the transient period. The proposed method was tested on two power networks and the results obtained were perfectly matched with those found from direct examination of swing curves. The results obtained by the proposed method were also compared with some other reported methods.