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# Single-Phase Series Compensated Network

This example shows frequency-domain and time-domain analysis of a series-compensated transmission system.

G. Sybille (Hydro-Quebec) ### Description

A 735 kV, 300 km line is used to transmit power from bus B1 (735 kV equivalent system) to bus B2 (315 kV equivalent). In order to simplify, only one phase of the system has been represented.

In order to increase the transmission capacity, the line is series compensated at its center by a capacitor representing 40% of the line reactance. The line is also shunt compensated at both ends by a 330 Mvar shunt reactance (110 Mvar /phase). Open the Series Compensation subsystem. Notice that the series capacitor is protected by a metal oxide varistor (MOV) simulated by the Surge Arrester block. The 250 MVA, 735 kV / 315 kV transformer is a Saturable Transformer block simulating one phase of the three-phase 750 MVA transformer. A Multimeter block is used to monitor the fault current as well as the flux and magnetizing current of the transformer.

### Simulation

Transient performance of this circuit can be studied when a 6-cycle fault is applied at node B2. The fault is simulated by the Breaker block. Switching times are defined in the Breaker block menu (closing at t = 3 cycles and opening at t = 9 cycles).

Frequency Analysis

In order to understand the transient behavior of this series-compensated network, a frequency analysis is first performed by measuring the Impedance at node B2. This measurement is performed by the Impedance Measurement block connected at node B2. Open the Powergui and in the Tools menu select 'Impedance vs Frequency Measurement'. Click on Display to compute and display the impedance for the 0 - 500 Hz range. The impedance curves show two main parallel resonances (impedance maxima and phase inversion), corresponding to 15 Hz and 300 Hz modes. The 15 Hz mode is due to a parallel resonance of the series capacitance and the two shunt reactances. The 300 Hz mode is mainly due to resonance of shunt line capacitance and series reactance of the transmission system. These two modes are likely to be excited at fault clearing.

Time Domain Simulation - Fault at Bus B2

Start the simulation and observe waveforms on the two Scopes. At t = 3 cycles, a line-to-ground fault is applied and the fault current reaches 10 kA (trace 1 of Scope2). During the fault, the MOV conducts at every half cycle (trace 2 of Scope1) and the voltage across the capacitor (trace 1 of Scope1) is limited to 263 kV. At t = 9 cycles, the fault is cleared. The 15 Hz mode is clearly seen on the capacitor voltage (trace 1 of Scope1) and bus B2 voltage (trace 3 of Scope1). During fault the flux in the transformer is trapped to around 1 pu. At fault clearing the flux offset and 15 Hz component cause transformer saturation (flux > 1.2 pu, trace 3 of Scope2), producing magnetizing current pulses (trace 2 of Scope2).

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