Sudden Three-phase Short Circuit Research Articles

Performance Evaluation of Excitation Systems in Stability Enhancement of Power Systems

This paper involves the characterization and the performance evaluation of various types of synchronous generator excitation systems in the transient stability enhancement of power systems. The Investigations are carried out by modelling the typical DC, AC and static excitation systems represented by IEEE types DC1A, DC2A, AC4A, AC5A, ST1A and ST2A attached with a generator connected to the infinite bus. The performance evaluation of these excitation systems is performed in terms of their response ratio and ceiling voltage together with the system settling time and the critical clearing time following a sudden three-phase short-circuit in the system. Each excitation system together with its power system stabilizer is considered in the analysis. 4th order Runge Kutta method is utilized for transient stability analysis of the power system with the 3rd order model for synchronous generator representation. The investigations reveal that the IEEE ST2A Excitation System is better than the other types of excitation systems.

Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis

During transients that occur in an electric network, large currents can flow and large electromagnetic torques can be developed in electric generators. Accurate calculation of currents and magnetic fields during transients is an important element in the optimal design of generators and network parts, as well as mechanical parts of machines and other torque transmission parts. This paper describes the modeling of a sudden three-phase short-circuit on a synchronous generator using the finite element method (FEM) and the dynamic model. The model for simulations that use the FEM was built in the MagNet software package, and the dynamic model is embedded in the MATLAB/Simulink software package. The dynamic simulation model of a part of a network with two identical generators, represented by equivalent parameters, was developed. The results obtained after the simulation of a sudden three-phase fault in the generators by both methods are presented, including three-phase voltages, three-phase currents, machine speeds, excitation voltages, and mechanical power. In particular, the short-circuit current in the phase with the highest peak value was analyzed to determine the accuracy of the equivalent parameters used in the dynamic model. Finally, the results of these two calculation methods are compared, and recommendations are presented for the application of different modeling methods.

Short-Circuit Characteristics of Superconducting Permanent Magnet Generators for 10 MW Wind Turbines

Superconducting permanent magnet generators (SCPMGs) are a potential candidate for 10 MW direct-drive wind turbine applications. This paper presents two 10 MW SCPMG designs using MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> cables for the armature winding and investigates the short-circuit characteristics of the designed SCPMGs. The first part of the results shows that the SCPMGs can double the shear stress of a conventional low-speed permanent magnet (PM) generator (from 65 kPa to 130 kPa) whilst avoiding demagnetization of the PMs in rated-load operation. However, the power factor has to drop to a range of 0.7-0.8. The second part of the results shows that during a sudden three-phase short circuit, the superconducting armature winding is prone to quench and the PMs are likely to be demagnetized in both proposed designs.

Novel approach to calculate electrical currents in stator-, field- and damper-windings at three-phase sudden short-circuit for large synchronous generators

In this manuscript the novel methodology of quick and accurate calculation of the rotor and stator currents during a three-phase sudden short-circuit is presented. The proposed approach consists of two parts. First, the detailed finite element model is developed. It accounts for stator core and winding, rotor yoke and winding, damper winding and conductive rotor surface. Second, the revised analytical formulation of the existing approaches to evaluate transient field current behavior during a three-phase sudden short-circuit is presented. Four phenomenological coefficients are introduced for proper representation of the field winding current. The developed methodology is feasible for solid and laminated rotors, with and without damper bars. It is demonstrated that there is good agreement between the results of our theoretical approach and the factory tests.

Approaching the Processes in the Generator Circuit Breaker at Disconnection through Sustainability Concepts

Nowadays, the electric connection circuits of power plants (based on fossil fuels as well as renewable sources) entail generator circuit-breakers (GCBs) at the generator terminals, since the presence of that electric equipment offers many advantages related to the sustainability of a power plant. In an alternating current (a.c.) circuit the interruption of a short circuit is performed by the circuit-breaker at the natural passing through zero of the short-circuit current. During the current interruption, an electric arc is generated between the opened contacts of the circuit-breaker. This arc must be cooled and extinguished in a controlled way. Since the synchronous generator stator can flow via highly asymmetrical short-circuit currents, the phenomena which occur in the case of short-circuit currents interruption determine the main stresses of the generator circuit-breaker; the current interruption requirements of a GCB are significantly higher than for the distribution network circuit breakers. For shedding light on the proper moment when the generator circuit-breaker must operate, using the space phasor of the short-circuit currents, the time expression to the first zero passing of the short-circuit current is determined. Here, the manner is investigated in which various factors influence the delay of the zero passing of the short-circuit current. It is shown that the delay time is influenced by the synchronous machine parameters and by the load conditions which precede the short-circuit. Numerical simulations were conducted of the asymmetrical currents in the case of the sudden three-phase short circuit at the terminals of synchronous generators. Further in this study it is emphasized that although the phenomena produced in the electric arc at the terminals of the circuit-breaker are complicated and not completely explained, the concept of exergy is useful in understanding the physical phenomena. The article points out that just after the short-circuit current interruption by the generator the circuit-breaker (when the GCB has been subjected at the metal contact terminals to the high temperature of a plasma arc, up to 50,000 K) between its opened contacts, there arises the transient recovery voltage (TRV) which constitutes the most important dielectric stress after the electric arc extinction. Since the magnitude and shape of the TRV occurring across the generator circuit-breaker are critical parameters in the recovering gap after the current zero, in this paper, we model, for the case of the faults fed by the main step-up transformer, the equivalent configurations, with operational impedances, for the TRV calculation, taking into account the main transformer parameters, on the basis of the symmetrical components method.

Demagnetization Analysis of Additional Permanent Magnets in Salient-Pole Synchronous Machines With Damper Bars Under Sudden Short Circuits

To improve output performance of salient-pole synchronous machines, permanent-magnet-assisted salient-pole synchronous machines (PMa-SMs) that have permanent magnets (PMs) between the field poles were previously developed. The PM effect of increasing the output power and the terminal voltage has already been confirmed by finite element analysis (FEA) and experiments under steady states. In this paper, demagnetization in the PMs due to sudden three-phase short circuits is evaluated by FEA. The results show that irreversible demagnetization arises in the PMs of a PMa-SM with relatively smaller circumferential PM length. Effects of the PM shape and damper bars on the irreversible demagnetization are also investigated. The results show that making the PM shape a rectangle and adding damper bars on the outer surfaces of the PMs are effective to reduce the demagnetization, while increasing the number of the conventional damper bars is not effective.

Dynamics of a Turbo-generator Driven by DC Motors During Off-line Three-phase Sudden Short Circuit

This article reports the responses of a turbo-generator driven by separately excited DC motors when the former is subjected to a sudden short-circuit test. Such setups are usually arranged in test rigs of generator manufacturers and electrical machines laboratories, where DC motors are used as the prime mover. Sudden short-circuit tests on turbine generators offer a short-circuit current spectrum that can be used to extract operational impedances and time constants of the generator. The sets of differential equations representing the DC motors, coupling system, and generator are appropriately solved together to obtain the responses. The results show the machine and system dynamics under damped and undamped shaft coupling. Transient parameters of the generator are extracted in each case and compared. The influence of speed departures on shaft torques and current waveforms are also studied. These results suggest that short-circuit tests can be performed at rated voltages if the couplings can be designed so as to absorb the high short-circuit torques developed during sudden short-circuit tests.

Current transients in the small salient-pole alternator during sudden short-circuit and synchronisation events

Small salient-pole machines, in the range 30 kVA to 2 MVA, are often used in distributed generators, which in turn are likely to form the major constituent of power generation in power system islanding schemes or microgrids. In addition to power system faults, such as short-circuits, islanding contains an inherent risk of out-of-synchronism re-closure onto the main power system. To understand more fully the effect of these phenomena on a small salient-pole alternator, the armature and field currents from tests conducted on a 31.5 kVA machine are analysed. This study demonstrates that by resolving the voltage difference between the machine terminals and bus into direct and quadrature axis components, interesting properties of the transient currents are revealed. The presence of saliency and short time-constants cause intriguing differences between machine events such as out-of-phase synchronisations and sudden three-phase short-circuits.

界磁巻線開放時および短絡時の直流試験法による界磁過渡特性を考慮した同期機の等価回路定数算出法

It has been reported that the calculated values of field transient behavior in a synchronous machine differ considerably from the measured values. This discrepancy is caused by the use of equivalent circuit constants in standardized tests provied by JEC2130 and IEC60034-4, in which the mutual leakage reactance between the damper and field windings is not accounted for. The authors have been studying a method for calculating equivalent circuit constants for the accurate simulation of transient behavior including the field winding side, by means of a standstill test with a small-capacity DC power supply (DC decay testing method). The authors have previously presented a calculation method using operational impedances with the field windings opened, shorted, and inserted with an external resistance, obtained by the DC decay test. This paper presents a new method in which the external resistance used in our previous method is no longer needed. Instead, the field winding impedance is determined based on its invariability against slip. The validity of the new method is demonstrated by comparing the calculated and measured values of the armature and field currents during a sudden three-phase short-circuit using 10kVA-200V-31.9A-4P-50Hz test machines.

相互漏れリアクタンスを考慮した制動巻線付き同期機の等価回路定数算出法

The mutual leakage reactance between the d-axis damper and field windings is ignored in the conventional d-axis equivalent circuit. It has been pointed out that the calculated value of the field transient current differs considerably from the measured value when this reactance is not taken into account. A method to determine this reactance has been reported previously, but this method has problems concerning measurement precision. The authors have previously presented a calculation method for equivalent circuits, adapting a DC decay testing method, using two synchronous machines of the same specifications (one with damper winding, the other without). Yet, this method is not practical because of the use of two machines. This paper presents a calculation method for equivalent circuit constants taking into account the mutual leakage reactance to accurately represent the field transient current using a single machine. The proposed method determines equivalent circuit constants by calculating the physically correct d-axis transient reactance from the operational impedances when the field winding is shorted and when the field winding is shorted with an external resistance. The validity of the proposed method is demonstrated by comparing the measured values with the calculated values of field and armature currents at sudden three-phase short-circuit. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 167(2): 71–78, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20891

A calculation method of field current of synchronous machines at sudden short‐circuit

AbstractThe mutual leakage reactance between D‐axis damper and field windings is ignored in conventional D‐axis equivalent circuits. It has been pointed out, however, that the calculated value of the field current differs considerably from the measured value if this reactance is not taken into account. This is due to the difficulty of determining the physically correct damper winding impedance value. A method of determining the equivalent circuit constants using the mutual leakage reactance has been reported previously, where the D‐axis damper winding time constant is measured from the upper and lower envelopes of field current at sudden three‐phase short‐circuit. Yet there are machines for which the upper and lower envelopes of field current are not readily established, and in this case the method is unsatisfactory. The authors describe a method to accurately identify the equivalent circuit constants taking into account the mutual leakage reactance, using a standstill test with a small‐capacity DC power supply (DC decay testing method). The field current at sudden short‐circuit can be simulated accurately using these equivalent circuit constants. The validity of the proposed method is demonstrated by implementation results on two salient‐pole synchronous machines at the same specifications (one with damper winding, the other without). Furthermore, the dependent relation between the armature leakage reactance and mutual leakage reactance, as well as its influence on the calculation of field transient currents, are made clear. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 151(3): 61–70, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20113

Calculation of Sudden Three-Phase Short-Circuit Current of Turbine Generator by 3D Magnetic Field Analysis

Sudden three-phase short circuit current of a turbine generator was calculated by a three-dimensional magnetic field analysis. That analysis takes into account the rotation, magnetic saturation, and eddy current at a rotor part. To compare test results and calculated results, we proposed a method for short-circuit phase estimation at sudden three-phase short-circuit test by line voltage waveform of the test results. The calculated results of short-circuit current waveform are good agreement with the test results.

A Calculation Method of Field Current of Synchronous Machines at Sudden Short-circuit

The mutual leakage reactance between d-axis damper and field windings is ignored in conventional d-axis equivalent circuits. It has been pointed out, however, that the calculated value of the field current differs considerably from the measured value if this reactance is not taken into account. This is due to the difficulty of determining the physically-correct damper winding impedance value. A method to determine the equivalent circuit constants using the mutual leakage reactance has been reported previously, where the d-axis damper winding time constant is measured from the upper and lower envelopes of field current at sudden three-phase short-circuit. Yet there are machines for which the upper and lower envelopes of field current are not readily established, in which case this method is unsatisfactory. The authors describe a method to accurately identify the equivalent circuit constants taking into account the mutual leakage reactance, using a standstill test with a small-capacity DC power supply (DC decay testing method). The field current at sudden short-circuit can be simulated accurately using these equivalent circuit constants. The validity of the proposed method is demonstrated by implementation results on two salient-pole synchronous machines with the same specifications (one with damper winding, the other without). Furthermore, the dependent relation between the armature leakage reactance and mutual leakage reactance, as well as its influence on the calculation of field transient currents, are made clear.

Analysis of magnetic saturation in a salient‐pole synchronous machine after sudden three‐phase short circuit

AbstractIn order to evaluate magnetic saturation under subtransient and transient states of a large‐sized salient‐pole synchronous machine, the currents and leakage inductances after sudden three‐phase short circuits are analyzed by a two‐dimensional nonlinear transient finite element method (FEM). The currents are calculated both by direct and indirect methods. The direct method uses the FEM and considers fluctuation of the magnetic saturation after the short circuit. The indirect method solves Park's differential equations without fluctuation. Results of the direct method agree well with measurements. When the preshort voltage is large, fluctuation of the leakage inductances after the short is large and it greatly affects values of the short‐circuit currents. As the preshort voltage becomes large, the damper leakage inductances saturate at first, then the field leakage inductances, and finally the armature leakage inductances saturate. Although the indirect method considers saturation under the preshort condition, it gives inaccurate results and they are nearly the same as the results by the linear FEM. In general, it is thought that saturation of the leakage flux should be considered when subtransient conditions with large disturbance are analyzed. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 145(4): 46–55, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10240

Modeling of the cage induction motor for symmetrical and asymmetrical modes of operation

This paper presents a numerical model of the three-phase, cage induction motor. This model has been represented as a system of differential equations for flux linkages and angular velocity determination. The differential equations for the flux linkages of the stator windings have been expressed in phase coordinates, while the differential equations for the flux linkages of the rotor circuits have been expressed in orthogonal coordinates, which are fixed in respect with the stator of the motor. The skin effect in the rotor deep bars has been taken in account by representing the rotor as two parallel-connected resistive–inductive circuits. Using the developed model the starting, restarting, running-down modes and three-phase, line-to-line, line-to-ground short-circuits as well as the steady-state conditions can be analyzed. The modes of sudden three-phase short-circuit at the motor terminals, sudden single line-to-ground fault at the high-voltage side of the power supply system and the motor starting process followed by steady-state conditions have been computed.

Finite Element Time-Stepping Method for the Prediction of Small Alternator Transient Response

This paper describes a method of predicting the transient response of a small salient pole alternator during a sudden three-phase shortcircuit using a time-stepping, two-dimensional, nonlinear finite element field model in conjunction with circuit equations. Alternator parameters are deduced from the predicted response and compared with practical measurements and data published by the alternator manufacturer. The method is also used to predictthe response following the sudden application of a resistive load.

Analysis of Magnetic Saturation in a Salient-Pole Synchronous Machine after Sudden Three-Phase Short Circuit

In order to evaluate magnetic saturation at sub-transient and transient states of a large-sized salient-pole synchronous machine, the currents and leakage inductances after sudden three-phase short circuits are ana-lyzed by a two-dimensional non-linear transient finite element method (FEM). The currents are calculated both by direct and indirect methods. The direct method uses the FEM and considers fluctuation of the magnetic saturation after the short circuit. The indirect method solves the Park's differential equations without the fluctuation. Results of the direct method agree well with measurements. When the pre-short voltage is large, fluctuation of the leakage inductances after the short is large and it greatly affects values of the short-circuit currents. As the pre-short voltage becomes large, the damper leakage inductances become saturated at first, then the field leakage inductances and finally the armature leakage inductances. Although the indirect method considers saturation at the pre-short condition, it gives inaccurate results and they are nearly the same as the results by the linear FEM. In general, it is thought that saturation of the leakage flux should be considered where sub-transient conditions with large disturbance are analyzed.

Measurement and analysis of 70 MW superconducting generator constants

The constants of a superconducting synchronous generator (SC-generator) were measured to prove its design method and electromagnetic analysis. This paper describes the test results related to the measurements of synchronous machine constants, and the comparison between the test results and the values which are calculated by a 3 dimensional finite element method (3D-FEM) for the electromagnetic analysis of SC-generator. The test items compared with the analysis are no load saturation curve of armature voltage at rated speed, armature current of steady state short circuit, air gap magnetic flux to add the armature current and synchronous reactance (Xd). The constants for the transient state of SC-generator were measured by three-phase sudden short circuit current. The effect to improve the electric power system stability is analyzed by decreasing Xd of SC-generator and by comparing the stability of a conventional generator for the same power system disturbances.

Analysis of the field current after three-phase sudden short-circuit of turbogenerators using equivalent circuits

An analysis of the influence of equivalent circuits which represent the phenomena occuring in the solid rotor of a turbogenerator on the waveform of the field current at three-phase sudden short-circuit has been performed. The results have been compared with the waveform of the field current determined on the basis of electromagnetic field theory with the use of Fourier's inverse transformation, and differences have been discussed.

A Method to Predict Transient Constant for Synchronous Machine.

It is impossible to determine subtransient (transient) reactance and subtransient (transient) short-circuit time constant of middle and large synchronous machines from the sudden three-phase short-circuit test, because it needs a large capacity of equipment to determination of quantities from the test.Thus, this paper describes a new method which is wield to measures these constants by a simple test using a small D. C. power supply.The key points of this method are summarized as follows:(1) D. C. voltage is applied to the armature winding (two terminals with the third one open) of a stationary synchronous machine through a resistance. When two terminals are closed, the winding is short-circuited and the current in the armature winding decays. The whole process of decaying current is recorded.(2) The value of transient phenomena of the winding calculated from circuit equations (circuit of armature, field winding and damper winding) is compared with actual data, and the unknown equivalent circuit constants can be identified by the least square method.(3) Transient phenomena of the sudden three-phase short-circuit are calculated by two-reaction theory using identified constant. As a result these transient constants are calculated.Transient constant of the synchronous machine by the new method almost agrees with the observed values.