Transient Torque Research Articles

Transient performance of eddy-current couplings

Eddy-current couplings are normally used in conjunction with control systems, yet no transient theory for this machine has previously been published. The constant-slip transient performance is calculated from thedesign information, without using experimental data, and is shown to give good results on a test machine. The damping effects of the solid-iron loss member are shown to be negligible over a wide range of slip speed, so that the main timer constants are associated with the field member, which are easily calculated using standard design methods. Test values of load-flux distribution under transient conditions are given. The effectof the index used to represent the magnetisation curve and of the approximation for flux level at various speeds is discussed. The use of the method to calculate large torque transients at low slips and for incremental voltage steps on the field are briefly described.

Switching Transients in Large Deep-Bar Squirrel Cage Induction Motors

A theoretical basis is established for calculating the transient current and torque developed by an induction machine due to switching operations. The method of calculations is similar to that used for synchronous machines. The validity of the theory has been checked with the experimental results on a model induction motor. Formulae presented in this paper can be further simplified by using empirical factors derived from a number of tests on large machines.

Prediction of performance of induction-motor/synchronous-generator combination

The paper describes a digital simulation of an induction-motor/synchronous-generator combination, directly in phase quantities. The equations are developed in phase rather than as d. q quantities, and a digital-computer program is described for their solution. Predictions of the current, voltage and torque transients following a variety of switching operations of a 5.6 kW motor to a 15 kVA generator are shown to compare closely with experimentally obtained results.

Effect of parameter variations on induction-motor transients

Previous work on the transient performance of induction motors has paid little attention to the effect of variations in winding parameters from some assumed stator/rotor allocation. This paper shows that, based on factorialdesign considerations, a response equation may be derived that expresses the severity of the transient current or torque, or the runup time, in terms of a nominal response, together with contributions derived from the parameter variations. The coefficients of the response expressions for the transients that follow several switching and reswitching operations of a 5.6 kW motor are given. The errors introduced by the use of a fractional factorialdesign plan are shown to be small, and mention is made of typical situations in which the technique described may be useful.

Analysis of Transient Torques in Synchronous Machine at Multi-Phase Reclosing

A method is presented which calculates approximately the electrical torque in synchronous machine at multi-phase reclosing, neglecting subtransient saliency and electrical decrements. A new digital simulation program, with some examples of digital calculations, is presented in detail which is used to analyze the transient phenomena accompanying power swings at multi-phase reclosing, after multi open conductors following the fault.

Starting Transients in Induction Motors with Inertia Loads

Direct-on-line starting of the polyphase induction motor coupled to a mechanically resonant load is studied by numerical integration of the nonlinear system equations and is shown to be capable of generating excessively large electromechanical torque peaks during transients. This study is supplemented by the modal approach which identifies the causes to be: (1) the excitation of the line frequency oscillating transient torque component which arises from the interaction of the line currents and the dominant mode currents and, (2) the possibility of mechanical amplification of this oscillating torque component when the resonant frequency of the shaft is close to the line frequency.

Stability of Reluctance Motors from Freely Accelerating Torque Speed Curves

The limits of stability in reluctance machines are known to be narrow, especially in machines of improved design with high reactance ratio. These stability limits can usefully be investigated with the aid of computed and measured freely accelerating torque speed curves. The machine equations are developed using a frame of reference fixed with respeot to the rotor. Machine performance is then simulated on an analogue computer. A large number of freely accelerating torque speed curves are then generated for different values of machine parameters. The model is designed to cope simply with different motors and is based on a per unit system. All parameters can be simply varied, so that their effect on performance can be demonstrated . The torque speed curves that result can be said to be characteristic. of amachine with given parameters and contain information about starting torque, transient torque dips, synchronisation ability and stability. Since changes in parameters cause marked changes in shape of the freely accelerating torque speed curve, it is possible, by matching the results obtained from a practical test with those from a computer study, to determine where the total performance of the machine lies with respect to the optimum and to decide what changes are necessary to improve design.

Transient Torque of Steam Turbines in Power Systems

Techniques for the calculation of the transient torque of a steam turbine following step and ramp type displacements of throttle valves are developed. The objective is an improvement in steam turbine representation for digital and other studies of electric power systems under disturbed conditions, including transient stability. The turbine model used as a building block for the transient theory is a length of pipe, representing loop pipe or reheat boiler, followed by a multi-stage turbine. The theory of unsteady flow of compressible fluids is applied to the problem and this, together with throttle, nozzle and steam turbine equations, allows the transient torque to be calculated. A digital computer programme has been developed which could be used as a sub-routine in an overall transient stability programme. The dominant transient feature is a transport lag and not an exponential time delay, as is commonly assumed. Moreover this transport lag, being associated with the local sonic velocity rather than the steam particle velocity, has a value about one-tenth of the usually assumed exponential time lag in mass-flow. Methods are indicated for extending the transient response obtained for the above turbine model to multi-cylinder turbines. The conclusion to be drawn is that, for any fast turbine control or transient condition (on a time-scale of seconds rather than tens of seconds), the conventional assumption of an exponential time constant will be substantially in error. Such fast disturbances will almost certainly have their origins on the power system side. It is from the power system point of view that this paper is written.

Plugging an Induction Motor

Plug stopping a low-inertia squirrel-cage induction motor can provide a very quick stop, but the motor draws high peak currents from the power system and delivers high transient torques to the driven machinery. This engineering phenomena is well documented, yet the potential pitfalls of plugging applications are often not appreciated. The induction motor is so widely used in industry that a review of its plugging characteristics may be useful.

Transient negative torques in induction motors due to rapid reconnection of the supply

The first part of the paper deals with a combined experimental and analytical study on a 5 hp laboratory set. It establishes the way in which the transient negative-torque peak ↑R− varies with the residual voltage on the machine terminals at the time of reconnecting the supply, and the phase angle that could exist between this voltage and the supply voltage which is being reconnected. An approximate expression for the peak negative torque is developed, which helps to explain why the characteristics showing how ↑R− varies diverge significantly from what would be expected by simple reasoning. A 100hp motor is then considered, and the variation of ↑R− with the time delay td in reconnecting is established. The effects of the load at which the motor is operating at the instant of supply disconnection and of external inertia are examined. Finally, for a range of machines from 100 to 2700hp, operating at various loads and with various external inertias, patterns of ↑R−/td are computed and reduced to a single normalised curve, from which the largest possible value of ↑R− for any machine, under any operating conditions, can quickly be assessed for any selected delay in reclosing. The application of this normalised curve is illustrated for three motors not already used, and the results are compared with values obtained from complete-transient solutions.

Dynamic performance of induction motors in control systems

The paper analyses the behaviour of induction motors in control systems in response to sinusoidally varying torque distrurbances by using a 2-coil rotor model. It is found that induction motors exhibit resonance and possibilities of instability in response to torque disturbances, and transient torques substantially greater than the steady-state peak torque of the motor may be generated in the region of resonance. It is also observed that, in certain frequency ranges, the speed may be considered as leading the torque disturbances. Extension of previous frequency-response analysis in response to excitation-frequency variations and applicability of the present analysis to constant-net-flux operation are also given.

Torsional Response of Systems

Torsional resonance in coupled rotating systems such as multiunit turbine-gear-compressor trains is sometimes a serious problem and several shaft failures have been reported. Often it is desirable to know the magnitude of vibration in or near resonance. A procedure is developed whereby an alternating exciting torque of known magnitude and frequency is applied at any required point in the system and a digital computer solution is obtained for the resulting steady-state, torque in each shaft and deflection of each inertia. Use of this in the analysis of test data is illustrated. Methods are also developed whereby the foregoing steady-state solution is used to obtain approximate transient torques appearing in shafts when an a-c machine is short-circuited, and during acceleration through resonance. Correlation of computations with acceleration test data is shown.

Constant-speed solutions applied to the evaluation of induction-motor transient torque peaks

The paper outlines the derivation of a constant-speed transient torque solution for a polyphase induction motor for any switching condition. A representative selection of computed torque/time patterns is given, for a 5hp motor, including all torque components. These are compared with actual experimental results. Also for this motor, the way in which the transient negative torque varies with speed is shown for the speed range zero to three times synchronous speed. For speeds above synchronous value, it has been found necessary to use values of rotor parameters corrected for the skin effect of the speed-frequency transient currents.Simple approximate expressions are given for evaluation of the maximum positive torque peak during starting from test and the maximum negative peak when the supply is connected when the rotor is rotating at some finite speed. The results given by such expressions are compared with values obtained from both computed and recorded torque/time patterns for motors up to 100hp.

Induction-motor reswitching transients

The transient behaviour of an induction motor when disconnected from the supply and reswitched to the same or to a different supply before the complete decay of rotor currents is investigated. A digital-computer program is described for calculating the internal voltage generated by the decaying rotor currents and the transient torques and currents produced on reswitching. Experimental measurements of the transients experienced by a 7 5hp motor following reconnection to the same supply, plugging and dynamic braking are compared with computed results. Tests were made both at rated and at reduced supply voltage, and better agreement between theory and measurement is obtained at the lower voltage.

Transient performance of the induction motor

Numerical and analytical solutions of equations describing the transient performance of an induction motor are investigated. A digital-computer program is described for the numerical evaluation of the transient currents and torque following connection to the supply, and the components of the transients are investigated using an analytical method. Experimental measurements using a 3hp induction motor confirm the theoretical predictions.

Transient torques in induction motors, due to switching of the supply

An experimental study of transient torques in induction motors, due to application of the supply, is described. The transient-torque recordings were obtained by means of a 2-phase induction generator, used as an accelerometer, and apply to the free-rotor, i.e. unloaded, condition. Point-on-wave switching was used to obtain selective transient-torque patterns. Results are given for 3-phase and single-phase motors. In the former case, the effects of nonsimultaneous switching, and of connecting the motor to the supply while the rotor is still rotating, are shown. The results confirm the assumption that the transient torques are due mainly to the interaction between transient asymmetrical flux and alternating currents.

Relation between structural compliance and allowable friction in a servomechanism

In a great many control systems, error is primarily caused by transient load torques, often the result of static friction. To keep the error due to transient load torques small a high output inertia, and high values of gain crossover frequencies are required in the control loops. Integral networks that increase the static stiffness of the control system generally have negligible effect against transient load torques. The maximum error produced by a step of torque is approximately as follows for a rate feedback system: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\theta_{e} = \frac{T}{J \omega_{c}\omega_{r}}</tex> (1) where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</tex> is the magnitude of the step of torque, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> is the output intertia, ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> , is the gain-crossover frequency of the position loop, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega{r}</tex> is the gain-crossover frequency of the rate loop. Thus, if the error is to be kept within a given bound <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\theta_{e}</tex> , the maximum allowable friction torque T <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</inf> is given by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_{f} \leq \theta_{e}J\omega_{c}\omega_{r}</tex> (2) Structural compliance is a severe limitation upon the allowable values of gain-crossover frequency. The maximum value of rate loop gain-crossover frequency ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> in practice is usually about half the natural frequency of the structure ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> . The position loop gain-cross-over frequency is usually at least a factor of three below that of the rate loop. Therefore one can assume that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{r} \leq \frac{\omega_{n}}{2}</tex> (3) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{c} \leq \frac{\omega_{r}}{3} \leq \frac{\omega_{n}}{6}</tex> (4) Substituting (3) and (4) into (2) gives <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_{f} \leq (1/12)J\omega_{n}^{2}\theta_{e}</tex> (5) Equation (5) shows that regardless of the type of control system used, there is a maximum possible value of friction torque that is related only to the allowable error, the output inertia, and the structural natural frequency. Although this limitation is derived in terms of a specific servo configuration, it also holds approximately for other configurations, and cannot be improved by integral networks.

Transient Torques in 3-Phase Induction Motors during Switching Operations

Transient torques developed in 3-phase induction motors, during switching operations, i.e., during starting, during reconnection to the line, and during plugging are studied. A mathematical analysis for torque is given for each case. The expressions are obtained in the normalized form and are studied for various numerical values of the parameters of the machine. An experimental verification is given for the case of starting. Based on theoretical and experimental studies conclusions are drawn.

Transient torque and load angle of a synchronous generator following several types of system disturbance

The paper develops theoretical methods of calculating the variation of torque and load angle of a synchronous machine connected to a fixed supply voltage. In order to supplement and explain the results of recent full-scale tests the following conditions are considered:(a) Condition after a sudden short-circuit.(b) Condition after switching in a reactance between the generator and the supply.(c) Asynchronous operation.(d) Resynchronization after asynchronous operation.In a companion paper experimental equipment for measuring the variations of torque and load angle of a small synchronous machine is described. The equipment has been used to verify the theoretical results for each of the above conditions. The machine tested was a model alternator or ‘micro-alternator’ which simulates a typical large machine. The special laboratory equipment is of great value for studying in detail the factors governing the performance of large alternators.

Transient torque and load angle in disturbed conditions

Transient torque and load angle in disturbed conditions