del sistema de turbina-generador instalado. Producción. Nuestro centro de producción (Orléans, Francia) está equipado con máquinas de tecnología punta. Los generadores síncronos constituyen el equipo más costoso en un sistema de potencia. Como consecuencia de los posibles fallos que se presentan tanto. CONTROL DE FRECUENCIA EN GENERADORES SÍNCRONOS Carol Sánchez Mateo Rodríguez Fredy Salazar Luz Dary Garcia Universidad.

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Improvement of the third harmonic based stator ground fault protection for high resistance grounded synchronous generqdores. These three different methods are based in voltage measurements at the neutral and terminal connections, and also in the ratio of these measurements. From the results obtained in a real synchronous generator there are advantages of the scheme based on the ratio of the voltages measured at terminals and neutral, in the case of using the voltage threshold strategy.

However, by using the proposed alarm-trip logic, remarkable improvements could be obtained in the case of detecting high impedance ground faults. Finally, this work may help to develop useful protective devices which detect ground faults at the synchronous generator stator windings. Although a aincronos fault normally does not cause any problem, this have to be removed before the occurrence of a second ground fault which could cause severe machine damages and the consequent outage.

Ground faults at the synchronous machine stator are common and these cause current flows through the neutral conductor. The current magnitude depends of the grounding type high, medium and low impedance. The high impedance method is frequently used because in the case of faults the current magnitude is relatively low [1, 2].

A stator ground fault close to the neutral point is not immediately catastrophic because: However an undetected stator ground fault near the neutral could develop into a phase to phase fault or turn to turn fault. Moreover, if a stator ground fault close to the neutral point remains undetected, it bypass the grounding resistor and the conventional protection, and then a second ground fault toward the terminal could lead to catastrophic consequences.

This paper focuses on the application of the third harmonic principle and is devoted to present a comparative analysis and an improvement of three different approaches. First, the basic aspects of the analyzed methods are presented. Then, the main results and a comparative analysis generadodes presented, and finally the main conclusions are presented.

This method uses a comparison of the third order component of the voltage measured at the synchronous generator terminal Vt or at the neutral Vn connections. This harmonic magnitude varies geberadores to the load level, the measurement point and the fault location along the winding.

Figure 1 shows the third harmonic voltage distribution generated along the stator windings during normal operating conditions, considering variations in the machine load [4, 5]. Figure 1 Magnitude of the third harmonic at the stator winding considering non fault situations.

Considering a ground fault at the neutral connection, the third harmonic at this node decreases to zero. However, the value of the third harmonic at terminal is different from zero as it is genwradores in figure 2. Finally and considering a ground fault at the generator terminals, the effect is the opposite of the previously described.

The magnitude of the third harmonic voltage at the neutral connection becomes maximum while in terminals it decreases to zero, as it is presented in figure 3 [4, 8]. Figure 2 Magnitude of the third harmonic at the stator winding considering a ground fault in the neutral.

Figure 3 Magnitude of the third harmonic at the stator winding considering a ground fault in terminals. Undervoltage of the third harmonic component Scheme 1. This scheme is based on the measurement of the third harmonic component sicnronos voltage at the neutral connection of the synchronous generator, as presented in figure 4.

## Electric Machinery Company – Generadores Sincrónicos

In this method, the third harmonic voltage is measured at the neutral. There is a Hz relay tuned to detect third harmonic voltage and a standard 50Hz relay tuned to the fundamental frequency. Overvoltage of the third harmonic component Scheme 2. This scheme is based on the measurement of the third harmonic of voltage at the terminal connection of the generator, see figure 5.

### EST3 – Generadores síncronos estáticos – Google Patents

The two previous schemes normally use a relay 27H able to determine frequencies from to Hz. This relay detects variations at the magnitude of the third harmonic causing alarm or trip. Figure 4 Protective scheme used to detect under voltage of the third harmonic.

Figure 5 Protective scheme using over voltage of the third harmonic. Ratio of the third harmonic components Scheme 3. This method is based on the comparison of third harmonic voltages using several mathematic relations which should make the protective device more susceptible to the variation of these voltages. In this paper, three different relations as the presented from 1 to 3 are analyzed. In the above equations, V 3n corresponds to the third harmonic voltage at the generator neutral and V 3t is the third harmonic voltage at the generator terminals.

In figure 6 the ratio scheme is presented [7, 11, 12]. Figure 6 Protective scheme of third harmonic voltage using the ratio method. Theoretical evaluation of the non-faulted and faulted models.

The three previously described protective schemes are here analyzed according to two models, previously developed to represent the stator winding equivalent circuit [7]. The first model is the equivalent scheme of the system under normal condition operation while the second one is equivalent to the system working under fault conditions.

The equivalent circuit developed for non fault conditions is presented in figure 7. As is mentioned before, the third harmonic voltage appears as zero-sequence quantities. Then the third harmonic voltage produced by the synchronous generator is distributed between the terminal and the neutral shunt impedances governing the zero-sequence.

In figure 8 it is possible to see this zero-sequence circuit obtained from figure 7where Rn is the grounding resistor, Cg is the phase capacitance to ground of the generator stator winding, Cp is the total external phase capacitance of the system as seen from the generator, and E 3 is the generated third harmonic voltage.

Finally, figure 9 is obtained as a simplification of figure 8. Figure 7 Equivalent synchronous generator model considering non fault conditions. Following, from figure 9 and using the proposed equations presented in 4 and 5 it is possible to obtain the impedances at the terminal and neutral nodes, respectively. Where i indicates the imaginary operator and f is the power frequency. Solving circuit proposed in figure 9equations 6 and 7 are then obtained for the voltage at the neutral and terminals, respectively.

The equivalent circuit developed to consider under faulted conditions is presented in figure This circuit was solved according to the Millman theorem properties, and it is graphically presented in figure 11 [13].

From figure 11V 1 and V 2 are the equivalent voltages as seen from the left and the generzdores sides of E3n at the faulted winding. Similarly, the admittances Y gneradores and Y 2 have the same meaning. Additionally, E 3n corresponds to kE 3 and E 3t is associated to 1-k E 3where both are the third harmonic voltages produced by the stator winding between the generator neutral and the ground-fault location k, and between the generator terminal and the ground fault location krespectively.

Cg is the phase capacitance of the generator stator winding to ground; Cp is the total external phase capacitance of the system as seen from the generator.

Figure 10 Equivalent synchronous generator model considering fault conditions. Finally, Cn corresponds to Cgwhile Ct is equivalent to 1-k Cg. Both are the phase capacitances to ground of the generator stator winding between the ground-fault location gensradores and the generator neutral, and between the generator terminal and the ground-fault location krespectively.

Rn is the ground resistor. As described before, equations from 8 to 11 are obtained by applying the Millman theorem to the system presented in figure The flowing current I is then obtained as it is presented in Figure 12 shows an equivalent circuit obtained from figure 11where Va is the equivalent voltage obtained at generdores right side of the source E 3n.

From the proposed equivalent, voltages at the neutral Vn and terminal Vt under fault conditions are obtained as it is presented in 14 and Figure 12 Equivalent circuit used to find Vt and Vn. This corresponds to a proposed improvement of the classical voltage threshold alternatives. All of the possible variations of the third harmonic voltage due to changes on the connected load and errors in the meters are considered for this analysis.

The logic used to determine the presence of trip or alarm for sincroos, under and overvoltage of the third harmonic component schemes 1 and genetadores, respectivelyis presented in figure 13, and it is based on the comparison of the values of the third harmonic of the voltage measured denoted with the additional subindex m and those normal values as the present generaddores figure The behavior of the third harmonic voltage is described by curves as shown in figure 14 [7, 10].

These variations are particular for each one of the generator machines generadoress are due small imperfections in the winding distribution during the fabrication process, which cause small voltage unbalances [9]. Finally, the alarm-trip logic used in the case of scheme 3 is based on the definition of the maximum non trip voltages at the neutral and the terminals defined by the schemes 1 and 2, and by using one of the equations presented form 1 to 3.

### GENERADORES SINCRONOS by Jorge Rosas on Prezi

Figure 13 Alarm-trip logic used for the undervoltage scheme 1 or overvoltage scheme 2 of the third harmonic component. Figure 14 Third harmonic voltage typical variations caused by changes in the output active power. To obtain the proposed comparison, a real generator machine is used in tests and these parameters generadroes the presented in table 1. Table 1 Typical values for a unit-connected generator. Validation of the proposed third harmonic generator models.

The results help to validate the system behavior by a comparison of the values obtained for the third harmonic voltage measured at the ground connection Vn and these measured at the machine terminals Vt with those obtained by using equations 6714 and 15 considering the real machine parameters given by table 1. Fault resistance estimation using the voltage thresholds. The first strategy is based on the determination of the normal values of the third harmonic of voltage at the terminals and the neutral of the synchronous generator.

Considering that the third harmonic voltages are strongly related to the generator load as it is graphically presented in figure 14it is important to determine how this dependence affects the detectable values of the fault resistance in all of the analyzed protection schemes. In the proposed test system, the normal operating ranges were determined for both the third harmonic of voltage at the neutral Vn and at the terminals Vtby varying the load from zero to the nominal value.

The normal operating intervals for the third harmonic voltage measured at the neutral is [ Using the classical thresholds strategy to determine the maximum fault resistance to be detected in the case of the undervoltage scheme, different fault situations were analyzed using the circuit presented in figure Sincronoz all of the situations, sincrinos voltage at the neutral Vn was measured and these values which are lower than minimum voltage normal operating conditions correspond to faults which could be detected in the case of scheme 1.

A similar strategy is used to determine those faults that could be detected using the overvoltage scheme, but considering values of terminal voltage Vt which are higher than the maximum voltage during normal sinceonos conditions. In the case of the ratio scheme, the values of the third harmonic measured during faults are compared with those obtained in the case of non fault situations, and as a consequence the dependence on the load is greatly reduced considering the division of the voltages at the sincroos and the terminals as proposed from generdaores 1 to 3.

According to preliminary test performed in the proposed real synchronous generator, the obtained values for the maximum fault resistances which are detectable by using generadorse one of the three proposed schemes are presented in table 2.

In the case of the overvoltage of the third harmonic scheme 2there is not possible to detect any ground fault because the overlapping of the normal operation range values of the third harmonic and those values measured in case of faults.

Finally, the alternative which uses the ratio of the third harmonic components scheme 3 as it is presented from equation 1 to 3due its high sensibility to the voltage variations could detect high resistance faults. Table 2 Maximum fault resistance values detectable by the analyzed protective methods using the voltage thresholds Undervoltage, overvoltage and ratio of the third harmonic of voltage.

Fault resistance estimation using the alarmtrip logic. As proposed improvement of the protection method, the alarm-trip logic previously explained is considered to determine the maximum values of fault resistance which could be detected in the case of ground faults. Figure 15 Maximum fault resistance values detectable by the protective methods using the alarmtrip logic Undervoltage, overvoltage and ratio of the third harmonic of voltage.

In the case of the scheme 3 ratio of the third harmonicthe relation presented in equations 12 and 3 were tested, as it is present in figure 15 as scheme 3 1scheme 3 2 and Scheme 3 3respectively. Finally, the different schemes were tested in the case of nine values of third harmonic voltage nine different load conditions to cover all variation range. The obtained results shows small variations in the maximum fault resistance detected, showing the reduced dependence of the proposed protection strategy and the synchronous generator load condition.