Lyapunov-based Design of Adaptive Sliding Mode Controllers

The results of field tests have shown, that the behaviour of the restriking earthfault in a cable is completely different in isolated and well-tuned compensated networks. In this paper, the differences will be considered in detail and the impact on the earthfault detection and the control of the Petersen-Coil will be explained. Due to the different behaviour, there are new possibilities to reduce the current via the fault location. Actually the control of the Petersen-Coil is a preventive action during the healthy network operation. On the other side the control of the Petersen-Coil is currently blocked during the earth-fault. Therefore a change of the network-size during the earthfault will increase the current via the fault location. In this paper the new method “faulty phase earthing“ will be presented,which finally allows the correct tuning of the Petersen-Coil even under earth-fault conditions. In addition, the earth fault detection will be influenced by this new method. These influences and the new demands on the earth fault detection will be presented in detail. 1 Physic of the earthfault The characteristic impedance of the lossless line (surge impedance) has a value of about 335 Ohm for overhead lines and about 40 Ohm for cables. This surge impedance limits the discharge current via the fault location in a cable to about 400 A (Fig. 1). Fig. 1 Discharge current of a loaded cable (11.5 kV * sqrt(2), 20km, NA2XS2Y 150mm2 ) 2 Restriking earthfault in a cable-section Fig. 2 shows a line-to-ground-fault (LG-fault) in a cable. Due to the fault, an air-channel is developing with higher pressure. The isolation level of the air gap is smaller than the one of the dielectric. Fig. 2 LG-fault in a cable section. 2.1 Results of field tests The increasing restrikes at the beginning of the earthfault record shown in Fig. 3 are due to the slow earth-faultswitch. After few seconds the detuning of the Petersen-Coil started. It is also remarkable, that at certain detuning the restriking pulses all have the same polarity. Details will be explained in the paper Fig. 3 Restriking fault at damaged high voltage cable and tuning of the Petersen-Coil 0 1 2 3 4 5 6 7 -400 -300 -200 -100 0 100 200 300 400 500