Selection of the measuring data window

For accurate fault location computation the currents and voltages must exhibit as steady a state as possible. The selected data window may therefore not contain any abrupt changes due to fault condition changes or switching. For the fault location computation, a data window containing at least one but not more than three cycles of sampled values is used. The data window selection is carried out automatically by the algorithm. In the event of system disturbances that cause tripping by the device, the data window is positioned around the instant of the trip command. It ends shortly after the circuit breaker opens, immediately prior to interruption of the current. The start of the current and voltage data window is positioned such that the length of the data window is preferably three cycles without any abrupt changes of the current wave form. In the event of very short system faults, or short intervals until the fault condition changes, the measured window may be as short as one system, cycle for the computation. (Figure 6) Sometimes it is also desirable to indicate impedance measured value and fault locator data when there is only a fault detection by the protection and no trip command. In this case the data window is positioned at the end of the first fault detection data window. The end of the first fault detection data window is either determined by the re-set of the protection fault detection or by a change of the fault type.

Synchronization of the phasors

The "two ended" fault locator uses current and voltage phasors of all three phases from both line ends. The numerical filters are designed so that the fault location calculation is done based on the fundamental component. The current and voltage phasors are provided with a time stamp, the actual system frequency and data window length information is added and then transmitted via the digital communication link to the corresponding device at the other line terminal. Protection device A therefore receives the values from protection device B and vice versa. With the time stamp, system frequency and data window length the phasors can then be synchronized to a common reference. Using the time stamp, the phasors are then checked to see if they belong to the same condition during the system disturbance.

Only if they both refer to an identical interval of the fault will the computation based on the "two-ended" method be done.

Two ended fault locator computation with positive and negative sequence values

The here presented two ended fault location is based on the principle that the voltage decays along the line up to the fault location. By means of the currents and voltages measured at one line end, the voltage along the line may be calculated using an RLC line model. If the cause of the voltage is now calculated from both line ends, a fault location may be indicated at the location where both voltages have the same value. In Figure 7 this is given by the intersection of the two curves.

To achieve high accuracy also for long overhead lines and cable sections, the voltage calculation is done based on the homogenous line impedance. The relationship of voltages and currents is given by the hyperbolic function



whereby:

V (x) voltage at the position x

V _m , I _m measured value at the corresponding line end

x distance from the beginning of the line

g propagation constant of the line



Z characteristic impedance of the line



At the fault location, the voltages calculated from both ends of the line must be the same.

The set of non-linear equations is solved by determining the smallest voltage difference:

e(x) = V _l (x) - V _r (x) whereby:

e(x) error voltage (ideally equals zero)

V _l (x) course of the voltage calculated from the left hand line terminal

V _r (x) course of the voltage calculated from the right hand line terminal

Using proven mathematical techniques the fault location can be determined by means of the sum of the least squares in the symmetrical component system (least-square' estimation according to Clarke-Transformation)/2/.

The measuring technique contains several plausibility checks. They are:

- Faulty or missing communication telegrams are detected and eliminated

- Measured values that deviate extensively from the sinusoidal wave form are detected and not used for the fault location computation. A CT saturation detector additionally ensures that no gross errors in the fault locator are indicated.

- Short circuit locations outside the protected feeder can by principle not be calculated by the two ended technique.

- Multiple ground faults at different locations on the protected feeder can by definition also not be calculated with the two ended method.

Only when the measured results are plausible, will the two ended fault locator indicate a result. To provide the user with some assistance in locating the fault, an indication based on the single ended impedance measuring technique which is similar to the distance protection measurement, is provided.



Non-symmetrical overhead lines

In connection with the fault location calculation it is often neglected to consider that the individual conductors of the three phase system are not spaced equally with respect to each other and ground. It is generally assumed that the impedance in all three phases is the same. By neglecting the existing physical non-symmetry of the conductors, the fault locator result will in practice vary, depending on the faulted phase. Ideally, the nonsymmetrical inductive coupling between the three phases should be considered in the fault location algorithm. Setting all six coupling impedances would however be very complicated and not practical for the user.

In the two ended fault locator there is therefore a function that allows for the non-symmetry of the impedances of a non-transposed overhead line. When commissioning the fault locator, the central conductor must be defined. Particularly good results are obtained with tower geometries having horizontal or vertical conductor spacing. In the following diagram the "central conductor is Phase B. If the conductors are properly transposed (refer to 3) no central conductor is defined.