0.9ZAB J 1
This error correction is successful if the error level described by equations (6) and (7) is constant. But for wind farms this is a functional relation. The arguments of the function are, among others, the impedance of WF ZWF and a fault current Iwf. These parameters are dependent on the number of operating wind turbines, distance from the ends of the line to the WF connection point (point M in Fig. 12a), fault location and the time elapsed from the beginning of a fault (including initial or steady fault current of WF).
As mentioned before, the three-terminal line connection of the WF in faulty conditions causes shortening of reaches of all operating impedance characteristics in the direction to the line. This concerns both protections located in substation A and WF. For the reason of reaching reduction level, it can lead to:
• extended time of fault elimination, e.g. fault elimination will be done with the time of the second zone instead of the first one,
• improper fault elimination during the auto-reclosure cycles. This can occurs when during the intermediate in-feed the reaches of the first extended zones overcome shortening and will not reach full length of the line. Then what cannot be reached is simultaneously cutting-off the fault current and the pick-up of auto-reclosure automation on all the line ends.
In Polish HV distribution networks the back-up protection is usually realized by the second and third zones of distance protections located on the adjacent lines. With the presence of the WF (Fig. 13), this back-up protection can be ineffective.
As an example, in connecting WF to substation C operating in a series of lines A-E what should be expected is the miscalculation of impedances in the case of intermediate in-feed in substation C from the direction of WF. The protection of line L2 located in substation B, when the fault occurs at point F on the line L3, "sees" the impedance vector in its second or third zone. The error can be obtained from the equation:
ZpB = ^ = Il 2 ^ +(t +IWF )Zcf = Zbc + Zcf +aZpb (11)
UpB - positive sequence voltage on the primary side of voltage transformers at point B, IpB - positive sequence current on the primary side of current transformers at point B, IL2 - fault current flowing by the line L2 from system A, IWF - fault current from WF,
Zbc - line L2 impedance,
Zcf - impedance of segment CF of the line L3
and the error AZpB is defined as:
It must be emphasized that, as before, also the impedance reaches of second and third zones of LWF protection located in substation WF are reduced due to the intermediate in-feed. Due to the importance of the back-up protection, it is essential to do the verification of the proper functioning (including the selectivity) of the second and third zones of adjacent lines with wind farm connected. However, due to the functional dynamic relations, which cause the miscalculations of the impedance components, preserving the proper functioning of the distance criteria is hard and requires strong teleinformatic structure and adaptive decision-making systems (Halinka et al., 2006).
Overlapping of the operating and admitted load characteristics
The number of connected wind farms has triggered an increase of power transferred by the HV lines. As far as the functioning of distance protection is concerned, this leads to the increase of the admitted load of HV lines and brings closer the operating and admitted load characteristics. In the case of non-modified settings of distance protections this can lead to the overlapping of these characteristics (Fig 14).
The situation when such characteristics have any common points is unacceptable. This results in unneeded cuts-off during the normal operation of distribution network. Unneeded cuts-off of highly loaded lines lead to increases of loads of adjacent lines and cascading failures potentially culminating in blackouts.
The impedance area covering the admitted loads of a power line is dependent on the level and the character of load. This means that the variable parameters are both the amplitude and the phase part of the impedance vector. In normal operating conditions the amplitude of load impedance changes from Zpmin practically to the infinity (unloaded line). The phase of load usually changes from cos^ = 0.8ind to cos^ = 0.8cap. The expected Zpmin can be determined by the following equation (Ungrad et al., 1995), (Schau et al., 2008):
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