**3.1. Line conductor overvoltages due to over-excitation and nonlinear resonance [6,7]**

Figure 3 shows that on Phases A, B, and C there were two overvoltages observed where the second overvoltage was slightly higher than the first. Causes of these 2 overvoltages are detailed as following.

### *3.1.1. First overvoltage (56Hz) – Over excitation*

Figure 4 shows the 2 essential condition for induction motor generating effect: large capacitance and continuous rotating motor. When an induction motor lost its external voltage source, the flywheel with large inertia will keep the motor rotating and the capacitance of transmission line will provide the necessary voltage support for the induction motor to act as a generator. The magnitization curve of the motor and the amount of capacitance will jointly determine the overall motor generating effect as shown in Fig. 5. If the capacitance is too small to provide enough magnetizing current (curve C0 in Fig. 5), the terminal voltage of motor will decay exponentially and the generating effect will not sustain. However, if the capacitance is large enough, the motor generating effect will sustain and the terminal voltage is determined by the intersection of the capacitance and magnetizing curve such as ( V1, C1) and (V2, C2) in Fig. 5.

**Figure 4.** Equivalent Circuit of Motor-Generating Effect.

At "t1" in Fig. 3(a), the last 345kV transmission line connecting to the NPP was tripped on remote end due to a flashover on the line turning the NPP into an electrical island. As the local end of the 345kV line did not trip, a motor generating condition equivalent to Fig. 4 was formed with the 127kM transmission line providing sufficient capacitance to support the voltage of the various motors in the NPP. As can be seen in Fig. 3(b), the terminal voltage is increased to 1.4 p.u. and the overall resultant frequency is 56 Hz.

During this first overvoltage period, the terminal voltage of motor was about 1.4 p.u. (Fig. 3(b)) but the line voltage was about 1.29 times the rated line-to-ground peak voltage (Fig. 3(a)). This implied that the power transformers have saturated. As a result, a lot of harmonics were produced and the zero sequence components of them would be integrated into the neutral voltage resulting in unexpected high neutral voltage. This period ended at "t2" in Fig. 3(a) when the flashover grounded both phase A and B.

**Figure 5.** Relationships between Motor Terminal Voltage, Magnetization Curve, and External Capacitance

Table 1 shows the harmonic contents of B phase voltage between t1 and t2 in Fig. 3(a). The even order harmonics and DC component could be treated as the slight magnetic bias caused by asymmetric fault. At this stage, there was no ferromagnetic resonance in the island system.


**Table 1.** Voltage Harmonic Contents of Phase B between t1 and t2

6 Nuclear Power – Practical Aspects

detailed as following.

**[6,7]** 

**3. Stress mechanism and modeling** 

*3.1.1. First overvoltage (56Hz) – Over excitation* 

magnetizing curve such as ( V1, C1) and (V2, C2) in Fig. 5.

**Figure 4.** Equivalent Circuit of Motor-Generating Effect.

It can be seen from the above that Taipower's 3rd NPP was under sigificant and multiple stresses before and during the Level 2 event. This section explains the mechanisms working

**3.1. Line conductor overvoltages due to over-excitation and nonlinear resonance** 

Figure 3 shows that on Phases A, B, and C there were two overvoltages observed where the second overvoltage was slightly higher than the first. Causes of these 2 overvoltages are

Figure 4 shows the 2 essential condition for induction motor generating effect: large capacitance and continuous rotating motor. When an induction motor lost its external voltage source, the flywheel with large inertia will keep the motor rotating and the capacitance of transmission line will provide the necessary voltage support for the induction motor to act as a generator. The magnitization curve of the motor and the amount of capacitance will jointly determine the overall motor generating effect as shown in Fig. 5. If the capacitance is too small to provide enough magnetizing current (curve C0 in Fig. 5), the terminal voltage of motor will decay exponentially and the generating effect will not sustain. However, if the capacitance is large enough, the motor generating effect will sustain and the terminal voltage is determined by the intersection of the capacitance and

At "t1" in Fig. 3(a), the last 345kV transmission line connecting to the NPP was tripped on remote end due to a flashover on the line turning the NPP into an electrical island. As the local end of the 345kV line did not trip, a motor generating condition equivalent to Fig. 4 was formed with the 127kM transmission line providing sufficient capacitance to support the voltage of the various motors in the NPP. As can be seen in Fig. 3(b), the terminal

During this first overvoltage period, the terminal voltage of motor was about 1.4 p.u. (Fig. 3(b)) but the line voltage was about 1.29 times the rated line-to-ground peak voltage (Fig.

voltage is increased to 1.4 p.u. and the overall resultant frequency is 56 Hz.

behind these stresses and provide basic principles how to model them.

#### *3.1.2. Second overvoltage (45 Hz) - Nonlinear resonance*

Figure 6 shows the four essential conditions for a ferroresonance to occur: voltage source, capacitance, nonlinear inductance (ferromagnetic and saturable), and low losses. The R in the RLC resonant circuit in Fig. 6 is very large due to the "low losses" condition and can often be ignored. The nonlinear inductance L is the magnetizing curve of the motors and transformers in the system and the capacitance is provided by the transmission line.

At "t3" in Fig. 3(a), all the motors on the 4.16 kV system were tripped by undervoltage relay. Between t3 and t4, the flashover grounding of phases A and B were cleared and the motor generating effects mentioned above picked up again gradually re-establishing the line voltage. At "t4" in Fig. 3(a), most motors in 13.8 kV system were also tripped by undervoltage relay with the exception of two largest ones. With the capacitance provided by the transmission line now need only to support the terminal voltage of 2 motors, we would

expect the terminal voltages to be higher than those during the first overvoltage stage according to Fig. 5. However, due to deep saturation of the motors and transformers, the overvoltage magnitude in Fig. 3(b) during the 2nd overvoltage is only slightly higher than the previous stage. This can be further seen from the fact that at the beginning of "t4" in Fig. 3(a), there were no overvoltage and no distortion of waveforms. As line voltage increased, the harmonics increased and after a few cycles the amplitude of voltage remained but voltage waveform distorted dramatically. Figure 7 shows the waveform at 4 cycle prior to t5 with its Fourier components summarized in Table 2 [10].

Power System Protection Design for NPP 9

order Phase A Phase B Phase C

**Table 2.** Fourier Analysis of Fig. 7

**3.2. Neutral voltage transfer [10]** 

point[7].

capacitances.

0 175.068 0.429 48.279 0.113 71.93 0.017 1 408.273 1.0 427.991 1.0 413.726 1.0 2 108.386 0.265 47.287 0.11 39.829 0.096 3 179.679 0.44 179.734 0.42 195.357 0.472 4 41.29 0.101 28.313 0.066 24.702 0.06 5 28.13 0.069 30.829 0.072 65.626 0.159 6 13.036 0.044 10.364 0.024 22.34 0.054 7 12.562 0.031 22.126 0.052 37.579 0.091 8 15.84 0.039 28.219 0.066 7.708 0.019 9 14.315 0.035 8.207 0.019 39.509 0.095 10 9.428 0.023 16.289 0.038 6.203 0.015 11 18.092 0.044 14.962 0.035 27.434 0.066 12 18.805 0.046 27.966 0.065 25.323 0.061 13 15.387 0.038 11.466 0.027 22.233 0.054 14 15.717 0.038 10.323 0.027 24.685 0.06 15 13.897 0.037 24.991 0.058 13.998 0.034 16 1.992 0 36.961 0.086 12.173 0.029

As the inductances in the systems are now deeply saturated, there is a possibility that ferroresonance can occur. (Note: Ferroresonance is nonlinear resonances in power system where the voltage and current may change from normal steady state to another steady state with large harmonic distortion.) The phenomenon can be best understood from a circuit perspective using Figure 6 as example. In Fig. 6, the total equivalent impedance of the circuit is (jXL - jXC). When the inductance is saturated and current further increases, it will drive the inductor into deeper saturation where the inductor impedance jXL will reduce when current further increases. A critical point will be reached at Point B in Figure 8 when (jXL - jXC) becomes zero. Any current increase beyond Point B will cause the total impedance change from a positive value to a negative value causing resonance effects near this operating

Based on analysis of all available data, it is believed that the 2nd overvoltage from t4 onward is on the boundary to be ferroresonance therefore the 2nd overvoltage is caused by a

It can be seen from Figure 3 that overvoltage can be observed not only on the line conductor but also on the neutral conductor as well. In order to understand this phenomenon we need to look at Fig. 9 where the equivalent circuit of a transformer is shown including its stray

combination of motor-generating effect and nonlinear resonance.

Vpeak %fund. Vpeak %fund. Vpeak %fund.

**Figure 6.** Equivalent RLC Circuit

**Figure 7.** Zoom-in of The 4 Cycles prior to t5

It can be seen from Table 2 that the voltage of fundamental frequency was about 1.5 times the rated line-to-ground peak voltage, which is slightly larger than the previous overvoltage. The large DC and even-order harmonics indicate the deep saturation of the start-up transformer. In Table 2 the total of 3rd harmonics is 554.7 kVpeak (Note: The 3rd harmonics are in-phase therefore can be added up directly.) Comparing this figure with the neutral voltage of 626 kVpeak in Fig. 3(a), this indicates that 3rd harmonics is the main source of neutral voltage during the second overvoltage period.


**Table 2.** Fourier Analysis of Fig. 7

8 Nuclear Power – Practical Aspects

**Figure 6.** Equivalent RLC Circuit

**Figure 7.** Zoom-in of The 4 Cycles prior to t5

of neutral voltage during the second overvoltage period.

with its Fourier components summarized in Table 2 [10].

expect the terminal voltages to be higher than those during the first overvoltage stage according to Fig. 5. However, due to deep saturation of the motors and transformers, the overvoltage magnitude in Fig. 3(b) during the 2nd overvoltage is only slightly higher than the previous stage. This can be further seen from the fact that at the beginning of "t4" in Fig. 3(a), there were no overvoltage and no distortion of waveforms. As line voltage increased, the harmonics increased and after a few cycles the amplitude of voltage remained but voltage waveform distorted dramatically. Figure 7 shows the waveform at 4 cycle prior to t5

It can be seen from Table 2 that the voltage of fundamental frequency was about 1.5 times the rated line-to-ground peak voltage, which is slightly larger than the previous overvoltage. The large DC and even-order harmonics indicate the deep saturation of the start-up transformer. In Table 2 the total of 3rd harmonics is 554.7 kVpeak (Note: The 3rd harmonics are in-phase therefore can be added up directly.) Comparing this figure with the neutral voltage of 626 kVpeak in Fig. 3(a), this indicates that 3rd harmonics is the main source As the inductances in the systems are now deeply saturated, there is a possibility that ferroresonance can occur. (Note: Ferroresonance is nonlinear resonances in power system where the voltage and current may change from normal steady state to another steady state with large harmonic distortion.) The phenomenon can be best understood from a circuit perspective using Figure 6 as example. In Fig. 6, the total equivalent impedance of the circuit is (jXL - jXC). When the inductance is saturated and current further increases, it will drive the inductor into deeper saturation where the inductor impedance jXL will reduce when current further increases. A critical point will be reached at Point B in Figure 8 when (jXL - jXC) becomes zero. Any current increase beyond Point B will cause the total impedance change from a positive value to a negative value causing resonance effects near this operating point[7].

Based on analysis of all available data, it is believed that the 2nd overvoltage from t4 onward is on the boundary to be ferroresonance therefore the 2nd overvoltage is caused by a combination of motor-generating effect and nonlinear resonance.
