Direct Phase Quantities Research Articles

Modelling and simulation of faults in synchronous generators for robust numerical protection

When an internal fault occurs in a synchronous generator, the symmetry between the parallel paths of the winding is broken and different currents flow in them, due to unsymmetrical magnetic linkage between the stator windings. The aim of this paper is to present a simulation model to investigate the effect of internal fault on the parallel path currents of a large synchronous generator using direct phase quantities. This model is based on a modified winding function approach where the machine inductances are calculated directly from the machine winding distribution using machine electrical parameters instead of the geometrical ones. The simulation results for different cases of internal faults in salient-pole and non-salient-pole synchronous machines have been obtained. Salient-pole synchronous generator has wave winding distribution while the non-salient-pole generator has lap winding arrangement. Due to different stator winding arrangements, the two machines have been simulated individually. By using the simulated fault data, a suitable numerical protection scheme for synchronous generators can be developed.

Simulation of internal faults in high-voltage cable-wound generators

An accurate determination of internal fault currents is needed for the design of adequate protection schemes for cable-wound high-voltage generators. A model of a synchronous machine in direct phase quantities for an internal single phase-to-ground fault is presented. A single phase-to-ground fault at the first turn near the generator neutral is simulated when the generator is either isolated or connected to a power system network. Simulations are also performed for when a single phase-to-ground fault occurs at different locations along the winding. The simulations are applied on the world's first high-voltage cable-wound generator installed at Porjus, Sweden which is rated at 45 kV and 11 MVA.

Simulation of internal faults in synchronous generators

An internal fault in the armature winding of a synchronous generator occurs due to the breakdown of the winding insulation. In this paper, a method for simulating internal faults in synchronous generators, using direct phase quantities, is described. Simulation results showing the fault currents, during a single phase to ground fault and a two phase to ground fault, are presented.

Synchronous generator internal fault computation and experimental verification

Along with the development of electric power industry, accurate analysis of faulted generators becomes more and more important. The paper presents a method for simulating internal faults in synchronous generators, consisting of a single path per phase, using direct phase quantities. Simulation results showing the fault currents, during single phase to ground faults and two phase to ground faults, are compared with actual fault currents to verify the proposed method.

Analysis of torques in large steam turbine driven induction generator shafts following disturbances on the system supply

The paper first summarises the advantages of steam turbine-driven induction generators over conventional generators such as low cost, less maintenance, rugged and brushless rotors (squirrel cage type, no need for synchronisation, etc.), together with problems concerning excitation (VAr compensation at loads etc). A mathematical model of the induction generator simulated in direct-phase quantities where saturation of the magnetising reactances is simulated and saturation of stator and rotor leakage reactances is ignored is developed and employed for detailed simulation of the machine. Discrete-mass models of the machine shaft where both steam and electrical viscous damping is simulated are employed in comparing transient shaft torsional response evaluated by time domain simulation and frequency domain analysis following incidence and clearance of severe system faults. The paper then investigates torsional response following incidence and clearance of severe supply system disturbances, when the rotor is stationary and when running at close to synchronous speed unexcited, and following malsynchronisation when excited by a controlled VAr source, together with torsional response following bolted stator-terminal short-circuits at full-load and no-load following switching in of the induction generator onto the system supply. It examines precision of predicting torque in turbine-generator shafts by frequency domain analysis not analyzed for induction generators in the literature heretofore following incidence and clearance of worst-case disturbances on the supply. Effect of steam and electrical damping on maximum shaft torques predicted by frequency domain analysis is also illustrated. The results illustrate there is no tendency for shaft torques to become more onerous as the fault clearing time is increased as is the case for shaft torques in large synchronous machines. Three large two-pole machines of rating of up to a few hundred MWs are analysed.

Computation Of Maximum Earth Current In Substation Switchyards

This paper presents recent developmental advances for the computation of maximum ground potential rise of grounding structures or alternatively maximum earth current in substation grounding systems. An advanced methodology for short circuit analysis is presented. The methodology is based on modeling of power system elements in direct phase quantities. Coupled with equivalency techniques, it provides an extremely efficient algorithm for performing numerous sequential short circuit analyses. An easy to use computer program has been developed under EPRI sponsorship. The computer algorithm uses the methodology to search for the fault condition which yields the maximum earth current in a substation grounding system. The methodology has been validated with actual system measurement on a Georgia Power Company Substation. Validation results are presented. Typical results as well as program utilization factors are discussed. The results demonstrate that the worst fault location is highly dependent on system parameters and cannot be predicted with simple rules.

Frequency-domain digital simulation of synchronous generators operating under faulted conditions

The paper details a method by which the equations describing a 3-phase synchronous machine may be transformed into the frequency domain to provide a means of digitally simulating faults at the generator terminals. Evaluation of the Fourier integrals involved in determining the machine response is achieved by means of the fast-Fourier-transform algorithm, and numerical results are presented together with the criteria necessary to achieve an accuracy comparable with that attainable using direct-phase quantities. The methods provide a basis for combining synchronous sources with transmission lines having frequency-variant parameters, and which are not therefore amenable to simulation using other than frequency-domain techniques. Studies using the new method indicate that, when predetermining the armature currents of a faulted machine, considerable economies in computing time may be effected, and the possibility of improving the simulation to simulate more accurately rotor eddycurrent effects by utilising the direct- and quadrature-axis frequency response emerges.

Digital simulation of an AC/DC system in direct-phase quantities

This paper describes a mathematical model for the simulation of an AC/DC system using direct-phase quantities. This system consists of an AC/DC converter station connected to a synchronous generator at its terminals as well as to an infinite bus-bar through a short transmission line. The proposed model in direct-phase quantities enables the study of the effects of the generated harmonics of the DC transmission on AC systems in general and on the behavior of synchronous machines in particular. The paper describes also a numerical solution using a digital computer for the mathematical model of this AC/DC system. The usefulness and versatility of the computer program are demonstrated by applying it to different AC/DC system configurations. The paper gives results of some studies concerning the effects of the generated harmonics on the behavior of synchronous machines with or without filters in the system.

Unified control for synchronous-machine stabilisation

This paper describes the theory and procedure for the design of a unified control to improve the stability of a synchronous machine whenever a major disturbance occurs. Using a nonlinear state-space model in directphase quantities, a direct-optimisation technique has been used to derive the unified controls that are effective for the most common types of balanced and unbalanced faults. Practical considerations such as the relative frequency of occurrence of various faults are taken into account. It is shown that the unified controls give an improved system performance over that obtained with the use of conventional controls.

Simulation of a synchronous generator connected via a delta—star transformer

A mathematical model of a 3-phase synchronous machine, connected to the infinite bus through a delta?star transformer and a transmission line, is given. Symmetric and asymmetric faults on the low-voltage side and on the high-voltage side of the transformer are analysed by using 3-phase variables. Since the simulation is in terms of the direct-phase quantities, the digital-program solution can very easily simulate simultaneous fault conditions as well as sequential faults on either side of the power transformer. By applying proper constraint conditions, the model can be readily used to include symmetric and asymmetric faults for an unloaded alternator, and power-frequency transients following the closure of the generator circuit breaker. The validity of the analysis developed is examined by comparing the digital results with the theoretical results for 3-phase faults on a generator on open circuit, and with a number of experimental results. Versatility is demonstrated by the range of experimental results considered and by further studies.

Digital simulation of a synchronous generator in direct-phase quantities

The paper describes a mathematical model for the simulation of a 3-phase synchronous machine using direct-phase quantities, thus obviating the need for any transformation. Numerical solution using a digital computer has also been described, and compared with digital simulation in transformed d-q-0- and α-β-0-axes models of a synchronous machine. The proposed model in direct-phase quantities enables a unified approach to be adopted in the study of both symmetrical and asymmetrical conditions. Since the constraints to be imposed are direct operating conditions, asymmetrical operating conditions can be studied very easily. Modifications required in the model to simulate various types of faults are described. Versatility of the proposed model is illustrated by the study of a single-line-earth fault with single-phase opening and automatic reclosure. It is shown that this type of fault can be studied as simply as, say, a 3-phase fault.