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In the field of rotor balancing, the traditional influence coefficient method is often employed along with weighted least squares in order to reduce amplitude vibrations, typically at selected rotating speeds such as critical or operating ones. Usually, these weights are manually selected by the operator. In this paper, an automatic procedure for the balancing mass estimation based on robust regression methods is introduced. The analysis is focused on high breakdown-point and bounded-influence estimators. The effectiveness and robustness of the proposed balancing procedure are shown by means of simulations of a 180 MW gas turbo generator of a power plant. [DOI: 10.1115/1.4001842] Keywords: rotor balancing, robust estimation, high breakdown-point estimators, bounded-influence estimators

The design of direct driven turbomachinery is an interdisciplinary task. Standard design procedures propose to split such systems into subcomponents and to design each one individually. This common procedure, however, tends to neglect the interactions between the different components leading to suboptimal solutions. The authors propose an approach based on the integrated philosophy for designing and optimizing gas bearing supported rotors. Based on the choice for herringbone grooved journal and spiral groove thrust bearings, the modeling procedure for predicting their properties and the linking to the rotordynamic behavior of a generic rotor supported on gas lubricated bearings is provided. The global model for gas bearing supported rotors is linked to a multiobjective optimizer for maximizing the dynamic stability and for minimizing the windage losses of the rotor and of the bearings. Two typical rotor layouts have been included in the optimization. The geometry of a proof of concept system, that has been designed previously using the fragmented component view, is represented as a comparison to the proposed integrated approach. It is shown that the integrated solution allows to reduce the windage losses by 25% or to increase the stability margin by 35%, emphasizing the advantage of the proposed integrated design tool. [DOI: 10.1115/1.4001381]

Hydrodynamic flexure pivot tilting pad gas bearings (FPTPGBs) can enable successful operation of oil-free microturbomachinery and FPTPGBs with radially compliant pads permit rotor centrifugal and/or thermal growth to exceed original bearing clearances and achieve higher speeds. This work presents the experimental and analytical study of such bearings and the application of dampers behind the pad radial compliance structure. A time domain orbit simulation method was implemented as the primary analysis tool to predict the rotor-bearing response to imbalance, the presence and location of critical speeds, etc., and to compare with test results. Experiments demonstrate the stable hydrodynamic operation of FPTPGBs with an ~28.6 ram, 0.8 kg rotor above 120 krpm, for the first time. The rotor-bearing system was intentionally destabilized in tests by increasing bearing clearances and the viscoelastic dampers added behind the FPTPGB pads delayed the onset of subsynchronous vibrations (from 43 krpm without damper to above 50 krpm with damper). Midrange subsynchronous vibrations of the destabilized system initiated at ~20 krpm were suppressed by ~25 krpm due to the stabilizing effect of rotor centrifugal growth. The viscoelastic dampers had a negligible effect on suppressing these midrange subsynchronous vibrations in experiments, but this was not demonstrated in simulations, presumed to be due to much lower stiffness contribution of the damper at lower frequencies. [DOI: 10.1115/1.3201831] Keywords: tilting pad gas bearing, damper, rotordynamics, compliant pads

The torque produced by a synchronous reluctance machine (including the permanent-magnet-assisted machine) is studied analytically, with the aim of pointing out the effect of the position of the flux barriers on the torque ripple. It is verified that the position of the flux-barrier ends highly influences the torque waveform. With the aim of reducing torque harmonic contents, a new strategy is proposed based on the choice of couples of flux barriers of different shapes. The flux-barrier geometry is chosen so as to obtain a compensation between the torque harmonics produced by each couple. Experimental results on two prototypes confirm the analytical prediction. Index Terms--Low torque ripple, permanent-magnet (PM)-assisted synchronous reluctance machine, synchronous reluctance machine.

Recently, high-speed axial flux generator (HSAFG) has come to attention because of its some advantages such as high power density and efficiency. This paper presents a modeling and designing procedure of HSAFG with some details. The back iron of the permanent magnet is the main design subject investigated in this paper. Optimized thickness of the back-iron used in the rotor of two ends is determined for a HSAFG by carefully considerations of the terminal voltage, output power, and efficiency. These all vary by thickness of back-iron variation significantly. It is illustrated that a very small thickness of the rotor yoke reduces the terminal voltage and efficiency and a very large value of it increases the rotor inertia, mechanical problems and cost of the machine with no significant improvement of the machine performance characteristics. It is concluded that back-iron thickness of the rotor plays a singular and important role in the HSAFG and requires more carefully attention when designing the machine. Index Terms--Axial flux machine, coreless stator, high speed generator, rotor yoke thickness.

This paper presents an invention, the rotor position phase lock loop (PLL), which enables maximum power point (MPPT) tracking of wind by doubly-fed induction generators without needing a tachometer, an absolute position encoder, or an anemometer. The rotor position PLL is parameter variation insensitive, requiring only an estimate of the magnetization inductance for it to operate. It is also insensitive to noise in the electrical measurements. Proof of concept is by: 1) digital simulations and 2) experimental testing of a laboratory prototype. Index Terms--Decoupled P-Q control, doubly-fed induction generator (DFIG), maximum power point tracking, wind turbine generator (WTG).

Sensorless control of permanent-magnet synchronous machines (PMSMs) at low speed and standstill is often based on a difference between q- and d-axis inductances. By determining the inductances, i.e., by evaluating current responses that result from the supply of voltage test vectors, an estimation of the rotor position is obtained. These inductances are dependent on the stator current--because of (cross-)saturation--and on the geometry of the PMSM. Changing inductances strongly affect the accuracy of the rotor position estimation. This paper investigates the influence of geometrical parameters of the rotor on the inductances and on the position estimation. First, for several angles, widths, heights, and radial positions of the buried magnets in the rotor, finite element models (FEMs) calculate the inductances and the torque as a function of the stator current. Second, to study the effect of the variable q- and d-inductances on the position estimator, time-domain simulations are carried out in combination with FEM evaluations. The simulated control is validated on an experimental interior PMSM. The FEM is not needed by the controller in the experiments. Index Terms--Finite element analysis, permanent-magnet synchronous machines (PMSMs).

We have developed a 3-D finite-element mesh modification method for skewed motors with an auto-mesh generator. Meshes modified by the auto-mesh generator are broken as enlarging the skew angel. In order to solve this problem, we have improved the modification method by solving Laplace equation. In this paper, characteristics of the skewed squirrel-cage induction motor are analyzed by changing the rotor skew angle using the meshes created by the improved mesh modification method. Index Terms--Loss, skew, squirrel-cage induction motor, three-dimensional finite element method.

This paper presents the experimental testing of relatively cost-effective expanders in an organic Rankine cycle (ORC) to produce power from low-grade energy. Gerotor and scroll expanders were the two types of expanders tested to determine their applicability in producing power from low-grade energy. The results of the experimental testing showed that both types of expanders were good candidates to be used in an ORC. The gerotor and scroll expanders tested produced 2.07 kW and 2.96 kW, and had isentropic efficiencies of 0.85 and 0.83, respectively. Also the paper presents results of an analytical model produced that predicted improved cycle efficiency with certain changes. One change was the flow rate of the working fluid in the cycle was properly matched with the inlet pocket volume and rotational speed of the expander. Also, the volumetric expansion ratio of the expander was matched to the specific volume ratio of the working fluid (R-123) across the expander. The model incorporated the efficiencies of the expanders and pump obtained during experimental testing, and combined two expanders in series to match the specific volume ratio of the working fluid. The model determined the power produced by the expanders, and subtracted the power required by the working fluid pump and the condenser fan. From that, the model calculated the net power produced to be 6271 Wand the overall energy efficiency of the cycle to be 7.7%. When the ORC was simulated to be integrated with the exhaust of a stationary engine, the exergetic efficiency, exergy destroyed, and reduction in diesel fuel while still producing the same amount of power during 2500 h of operation were 22.1%, 22,169 W, and 4,012 L (1060 U.S. gal), respectively. Consequently, the model presents a very realistic design based on results from experimental testing to cost-effectively use low-grade energy. [DOI: 10.1115/1.3066345]

This paper presents a new numerical technique for simulating two-dimensional wind turbine flow. The method, denoted as the 2D actuator surface technique, consists of a two-dimensional Navier-Stokes solver in which the pressure distribution is represented by body forces that are distributed along the chord of the airfoils. The distribution of body force is determined from a set of predefined functions that depend on angle of attack and airfoil shape. The predefined functions are curve fitted using pressure distributions obtained either from viscous-inviscid interactive codes or from full Navier-Stokes simulations. The actuator surface technique is evaluated by computing the two-dimensional flow past a NACA 0015 airfoil at a Reynolds number of [10.sup.6] and an angle of attack of 10 deg and by comparing the computed streamlines with the results from a traditional Reynolds-averaged Navier-Stokes computation. In the last part, the actuator surface technique is applied to compute the flow past a two-bladed vertical axis wind turbine equipped with NACA 0012 airfoils. Comparisons with experimental data show an encouraging performance of the method. [DOI: 10.1115/1.3027502]

This study evaluates the potential benefits that fixed but deployable trailing-edge flaps may have on a low-twist hovering rotor using a blade-element method combined with two-dimensional and three-dimensional computational fluid dynamics. Low blade twist is beneficial in terms of forward-flight performance, which, combined with a deployable flap, could also offer good hover performance, resulting in an overall better design in comparison with a plain twisted blade. To evaluate this concept, a parametric study of flap configurations was conducted using a simple blade-element method based on computational-fluid-dynamics-generated two-dimensional aerodynamics. This simple model indicated that up to 6 deg of blade twist could be recovered at high rotor thrust by using an optimized flap configuration. Performance improvements were also obtained for outboard slotted-flap configurations. The optimum slotted-flap designs were also evaluated using three-dimensional computational fluid dynamics, which confirmed that an inboard flap combined with a low-twist (-7deg) rotor blade matched the performance of a plain blade with -13deg of twist. A blended-flap configuration was also applied and evaluated. This simpler design demonstrated the equivalent performance of a clean rotor with 10 deg of blade twist, providing further evidence of the potential of the fixed inboard flap concept.

This paper presents a case study of a design for a complete microair vehicle thruster. Fixed-pitch small-scale rotors, brushless motors, lithium-polymer cells, and embedded control are combined to produce a mechanically simple, high-performance thruster with potentially high reliability. The custom rotor design requires a balance between manufacturing simplicity and rigidity of a blade versus its aerodynamic performance. An iterative steady-state aeroelastic simulator is used for holistic blade design. The aerodynamic load disturbances of the rotor-motor system in normal conditions are experimentally characterized. The motors require fast dynamic response for authoritative vehicle flight control. We detail a dynamic compensator that achieves satisfactory closed-loop response time. The experimental rotor-motor plant displayed satisfactory thrust performance and dynamic response. DOI: 10.1061/(ASCE)0893-1321(2009)22:1(85) CE Database subject headings: Aerodynamics; Robotics; Dynamic response.

High-frequency current responses of a permanent magnet synchronous machine (PMSM), with and without considering eddy current effects, are significantly different. This paper investigates the eddy current effects on rotor position estimation. A compensation method is developed to improve the high-frequency-injection-based rotor position estimation of a PMSM at zero and low speeds. The paper also contributes to an improved magnetic pole identification based on space vector pulse width modulation for an arbitrary initial rotor position. The estimation and sensorless control method of PMSM, considering eddy current effects, has been verified by experimental results. Index Terms--Eddy current effects, initial rotor position, magnetic pole identification, permanent magnet synchronous machine (PMSM), rotor position estimation, sensorless control, space vector pulse width modulation (SVPWM).

The study of dynamic whirl behavior of air bearings is fundamental for an adequate rotordynamic analysis and future validation of numerical predictions. This work shows the dynamic response of the air film on a three-lobe bearing under asynchronous whirl motion. One-dimensional multifrequency orbits are used to characterize the bearing rotordynamic coefficients. The test rig uses two magnetic bearing actuators to impose any given orbits to the journal. The dynamic forces are measured on the test bearing housing by three load cells. Journal whirling excitation is independent of the rotating speed, thus allowing asynchronous excitations. The multifrequency excitation is applied at each rotating speed up to 11,000 rpm, allowing the asynchronous characterization of the air film. The experimental procedure requires two linearly independent excitation sets. Thus, vertical and horizontal one-dimensional multifrequency orbits are applied as perturbations. Results show the synchronous and asynchronous dynamic coefficients of the air bearing. Asynchronous experimental results are compared to numerical estimation of the bearing force coefficients through solution of the isotropic ideal gas journal bearing Reynolds equation. Numerical dynamic coefficients are obtained as the effective coefficient values of the bearing when subject to a given orbit. A full characterization of the asynchronous rotordynamics coefficients of the bearing is presented in three-dimensional maps. [DOI: 10.1115/1.2772635] Keywords: gas bearings, asynchronous response, dynamic coefficients

Measured rotordynamic force coefficients (stiffness, damping, and added mass) and static characteristics (eccentricity and attitude angle) of a pressure-dam bearing are presented and compared to predictions from a Reynolds-equation model, using an isothermal and isoviscous laminar analysis. The bearing's groove dimensions are close to the optimum predictions of Nicholas and Allaire (1980, 'Analysis of Step Journal Bearings-Infinite Length and Stability,' ASLE Trans., 22, pp. 197-207) and are consistent with current field applications. Test conditions include four shaft speeds (4000 rpm, 6000 rpm, 8000 rpm, and 10000 rpm) and bearing unit loads from 0 kPa to 1034 kPa (150 psi). Laminar flow was produced for all test conditions. A finite-element algorithm was used to generate solutions to the Reynolds-equation model Excellent agreement was found between predictions and measurements for the eccentricity ratio and attitude angles. Predictions of stiffness and damping coefficients are in reasonable agreement with measurements. However, experimental results show that the bearing has significant added mass of about 60 kg at no-load conditions, versus zero mass for predictions from the Reynolds-equation model and 40 kg using Reinhardt and Lund's (1975, 'The Influence of Fluid Inertia on the Dynamic Properties of Journal Bearings,' ASME J. Lubr. Technol., 97, pp. 159-167) extended Reynolds-equation model for a plain journal bearing. The added mass quickly drops to zero as the load increases. Measured results also show a whirl frequency ratio near 0.36 at no-load conditions; however, a zero whirl frequency ratio was obtained at all loaded conditions, indicating an inherently stable bearing from a rotordynamics viewpoint. [DOI: 10.1115/1.2906173]

Seeking relevant criteria for testing the quality of turbulence models, the scale of turbulence and the gust factor have been estimated from data and compared with predictions from first-order models of these two quantities. It is found that the mean of the measured length scales is approximately 10% smaller than the IEC model for wind turbine hub height levels. The mean is only marginally dependent on trends in time series. It is also found that the coefficient of variation of the measured length scales is about 50%. 3 s and 10 s preaveraging of wind speed data are relevant for megawatt-size wind turbines when seeking wind characteristics that correspond to one blade and the entire rotor, respectively. For heights exceeding 50-60 m, the gust factor increases with wind speed. For heights larger than 60-80 m, present assumptions on the value of the gust factor are significantly conservative, both for 3 s and 10 s preaverages. The usually applied value of [k.sub.p] [approximately equal to] 3 should probably be reduced. [DOI: 10.1115/1.2931511]

To reduce the level of uncertainty associated with current rotor aerodynamics codes, improved understanding of rotor aerodynamics is required. Wind tunnel measurements on model rotors contribute to advancing our knowledge on rotor aerodynamics. The combined recording of blade loads and rotor wake is desired, because of the coupled blade and wake aerodynamics. In general, however, the small size of model rotors prohibits detailed blade load measurements; only the rotor wake is recorded. To estimate the experimental blade flow conditions, a measurement analysis tool is developed: the inverse vortex wake model. The rotor wake is approximated by a lifting line model, using rotor wake measurements to reconstruct the vortex wake. Conservation of circulation, combined with the Biot-Savart law, allows the induced velocity to be expressed in terms of the bound circulation. The unknown bound circulation can be solved for, since the velocity is known from rotor wake measurements. The inverse vortex wake model is subsequently applied to measurements on the near wake of a model rotor subject to both axial and yawed flow conditions, performed at a TUDelft open jet wind tunnel. The inverse vortex wake model estimates the unsteady experimental blade flow conditions and loads that otherwise would have remained obscured. [DOI: 10.1115/1.2931508]

The work detailed in this paper is focused on updating and refining a coning rotor wind turbine concept. The coning rotor combines the load shedding properties of flapping hinges with gross change in rotor area, via large coning angles, to affect increased energy capture at nominally constant system cost. Previous studies have indicated that the large cost of energy reductions is possible, compared to the state-of-the-art machines then, particularly for abundant but presently uneconomic low-wind sites. Almost ten years later, the fundamentals of the design remain sound, but bear reevaluation relative to current machines, both exploiting modern power electronics and control technology. The coning rotor was never optimized in its own right, so an integrated design tool suitable for human and computer refinement of the design has been developed. Incorporated into the tool is a corrected blade element momentum method that more properly accounts for coned rotor aerodynamics. A discussion of the development of coning rotors is presented, along with a comparison to present operational strategies. Results obtained for nondimensionalized rotors and specific machine optimization studies are presented, followed by a discussion of further issues to be addressed. [DOI: 10.1115/1.2931497]

Sensorless control of a permanent-magnet synchronous machine at low and zero speed is based on the injection of an oscillating high-frequency carrier signal. A particular demodulation technique serves to eliminate the estimation error introduced by pulsewidth modulation delay and the nonlinear characteristics of the inverter. Before the drive is started, the initial rotor position and the magnet polarity are detected. The initialization is performed by injecting an ac carrier and two short current pulses in a sequence. Index Terms--Initial rotor position, permanent magnet (PM) synchronous motor, sensorless control, zero-speed operation.

The relationship between the deviation of spin axis and the reflective optical intensity modulation and some related factors are analyzed. The results have shown that under the cryogenic environment the method using optical intensity modulation to measure spin-axis deviation is feasible.

A conceptual design of a superconducting rotor based on Mg[B.sub.2] conductor is designed for a synchronous machine. The overall machine design and parameters have shown a promising High Temperature Superconducting (HTS) flux pump excited double-helix design for synchronous machines.

Forced oscillations in the vicinities of both the major and the secondary critical speeds of a continuous asymmetrical rotor with the geometric nonlinearity are discussed. When the self-aligning double-row ball bearings support the slender flexible rotor at both ends, the geometric nonlinearity appears due to the stiffening effect in elongation of the shaft if the movements of the bearings in the longitudinal direction are restricted. The nonlinearity is symmetric when the rotor is supported vertically, and is asymmetric when it is supported horizontally. Because the rotor is slender, the natural frequency [p.sub.fn] of a forward whirling mode and [p.sub.bn] of a backward whirling mode have the relation of internal resonance [p.sub.fn]: [p.sub.bn] = 1 : (-1). Due to the influence of the internal resonance, various phenomena occur, such as Hopf bifurcation, an almost periodic motion, the appearance of new branches, and the diminish of unstable region. These phenomena were clarified theoretically and experimentally. Moreover, this paper focuses on the influences of the nonlinearity, the unbalance, the damping, and the lateral force on the vibration characteristics.

This paper presents the modeling procedure for a high-velocity rotor system (RS) combined with sliding bearings. The equations for motion of the RS parts were derived based on the model of a rotating elastic medium. Lubrication layers have been calculated with the use of the Reynolds equations. The discretization of the RS model has been carried out using three-dimensional contact finite element method and two-dimensional method of finite differences. The integration with respect to time is performed by an absolutely stable step-by-step method. The paper also compares and discusses computed and experimental amplitude-frequency characteristics of the self-oscillating turbocharger's RS. The values of dynamic loads in parts, as well as reactions, clearances, and losses in bearings, computed based on the presented modeling procedure make the RS designing more accurate and reliable. Keywords: rotor system, sliding bearing, rotating elastic medium, finite element simulation, lubrication layer, self-sustained modes, turbocharger

A voltage-behind-reactance formulation of a synchronous machine model is set forth, which incorporates saturation and cross-saturation, and is general enough to encapsulate a variety of rotor structures by use of arbitrary linear networks instead of equivalent circuits. Specifically, the model's equations--originally expressed in the qd-axes framework--are rewritten in such a way as to allow the actual abc stator windings to be represented by inductive branches, which can then be naturally connected in the desired circuit topology, e.g., to a rectifier. The model's predictions are validated against experimental results. Index Terms--Electric machines, modeling, rotating machine transient analysis, simulation, synchronous generator transient analysis, synchronous machines, transfer functions.

This paper presents the modeling and steady-state performance of a novel dual-winding reluctance generator (DWRG) that uses a multiple-barrier (MB) rotor. A simple math-ematical model was developed, and the effects of external parameters (speed, field current, and load) on the steady-state performance were analyzed. Experimental results conducted on a prototype machine were also provided to justify the theoretical approach and performance calculations. The developed model takes into account the magnetic saturation and core loss and enables a quantitative prediction of load characteristics from the no-load test data. Index Terms--Core loss, dual winding, equivalent circuit, magnetic saturation, multiple-barrier (MB) rotor, reluctance generator.

In this paper, the definitions of rigid and flexible rotors, the rotor-dynamic analysis procedure, and the design criteria defined in the American Petroleum Institute (API) standard 541 are reviewed and compared to API 684. The definition of the quasi-flexible rotor is introduced, as it is not covered by the standards. The influence on critical speeds and response to unbalance of the parameters in the rotor-bearing system including foundation stiffness, bearing-support-structure stiffness, bearing-oil-film characteristics, and shaft design are analyzed for each type of rotor. The advantages and disadvantages of each type of rotor manufacturing, initial cost, maintenance, and possible site problems are also analyzed. Numerical results and test data are presented as study cases. The conclusion shows that it is important to know the operation conditions of the machine, specifically the operating-speed range and how the machine will be installed in order to select the most economical and reliable design for the particular case. If the machine will be constant speed, the question is less complex. The conclusion confirms that, in general, low-speed induction machines using standard plain cylindrical bearings and slower (up to 7000 kW) four-pole and high-speed (below 1000 kW) two-pole machines are well suited for rigid rotor design. Larger machines, particularly two-pole, are more practical to design as a flexible rotor. Adjustable-speed-drive machines introduce special concerns for the operation of flexible rotors when there is a critical speed in the operating range. Several design solutions are presented and discussed in terms of initial cost, maintenance, and performance. Index Terms--Flexible rotors, induction motors, rotor dynamic design.

This paper proposes a coordinated control of the rotor side converters (RSCs) and grid side converters (GSCs) of doubly-fed induction generator (DFIG) based wind generation systems under unbalanced voltage conditions. System behaviors and operations of the RSC and GSC under unbalanced voltage are illustrated. To provide enhanced operation, the RSC is controlled to eliminate the torque oscillations at double supply frequency under unbalanced stator supply. The oscillation of the stator output active power is then cancelled by the active power output from the GSC, to ensure constant active power output from the overall DFIG generation system. To provide the required positive and negative sequence currents control for the RSC and GSC, a current control strategy containing a main controller and an auxiliary controller is analyzed. The main controller is implemented in the positive [(dq).sup.+] frame without involving positive/negative sequence decomposition whereas the auxiliary controller is implemented in the negative sequence [(dq).sup.-] frame with negative sequence current extracted. Simulation results using EMTDC/PSCAD are presented for a 2 MW DFIG wind generation system to validate the proposed control scheme and to show the enhanced system operation during unbalanced voltage supply. Index Terms--Control design, converter, doubly-fed induction generator (DFIG), modeling, unbalance, wind turbine.

A small rotor designed to simulate a miniature turbojet engine or turbocharger rotor mounted on compliant foil bearings was tested at speeds in excess of 150,000 rpm and temperatures above 260[degrees]C (500[degrees]F). The simulator rotor-bearing system was operated while positioned in various orientations and was subjected to transient shock impacts exceeding 35g. Subsequent testing was completed to demonstrate the capabilities of miniature thrust foil bearings as well. The tested rotor weighed approximately 400 g and used 15 mm diameter foil journal bearings and a multipad 25 mm diameter double acting thrust foil bearing. Results of the rotor-bearing system dynamics are presented along with experimentally measured natural frequencies, rotor displacements, and thrust load carrying ability. A good correlation between measurement and analysis is observed. Very short rotor acceleration times from rest to maximum speed were also measured. A parallel test simulator has been used to accumulate over I000 start-stop cycles to demonstrate the life of the bearing and coating. Based on this successful testing, it is expected that the goal of developing oil-free turbochargers and small turbojet engines that operate at high speeds with long life will be achieved.

This paper describes a novel generation rescheduling method to reduce the generator rotor shaft impacts induced by transmission loop closures. The rotor shaft impact constraints, at the instant of transmission loop closure, are explicitly modeled into an interior point optimal power flow. This method represents a considerable improvement on the conventional redispatch for reducing the standing phase angle of the closing breaker. Optimal power flow and transient stability results are provided for a tutorial four-bus and the IEEE 118-bus test systems. Index Terms--Benders decomposition, interior point methods, line closure, MW redispatch, optimal power flow, rotor shaft impact, standing phase angle, system restoration, transient stability, transmission loop.