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오차확률 기반 송전계통 보호계전기 보호도 평가방법 연구
짱원하오*, 최면승*, 이승재* 차세대전력기술연구센터 명지대학교*
Protectability Evaluation of Distance Relay based on a Probabilistic Method for Transmission Network
Wen-Hao Zhang*, Myeon-Song Choi*, Seung-Jae Lee* Next-Generation Power Technology Center Myongji University*
Abstract - In this paper, the protectability of distance relay is furtherly researched. Based on the probabilistic modeling of the measurement errors, the protectability of three zones is presented in detail by considering their different protection aims denoted by sensitivity and selectivity. The optimal setting for the each zone can be obtained to provide a reference for the practical application.
1. Introduction
For transmission system, distance relay plays a very importance role. Many works on the adaptive distance relay setting were presented to meet the practical needs [1, 2]. "Protectability" was first proposed to indicate the protection level of the system or how good the protection system is, given a certain set of settings [3].
In the preliminary research in [4], protectability is defined as an index to denote the protection level of both a single element and the whole system under current relay setting and variable system conditions. For distance relay, its measured impedance was modeled based on the probabilistic method[4, 5]. And protectability is defined including sensitivity and selectivity. Sensitivity is used to denote the ability to operate for the fault within its protection zone while selectivity means for the ability not to operate for the fault without its protection zone or cooperation capability with other zones.
However, the weighting factors of these two parameters can only determined by the practical experience.
In this paper, the sensitivity and selectivity for each zone are explained individually by considering their different protection aims.
And based on their aims, the weighting factors can be reasonably determined so that protectability and optimal setting for each zone can be achieved.
2. Probabilisty based Protectability Evaluation 2.1 Protectability Evaluation for Single Line System Based on the preliminary research, because of the errors, setting has an effective reach which accords with a Gaussian Probability Distribution with that equals 5 %[4].
(1)
<Fig.1> Single Line Model System 2.1.1 Protectability of Zone1
Zone1 of distance relay is aimed to protect its own line, and not overreach the faults beyond the ending bus. So its selectivity should always keep "1" which means there is no mis-tripping for the fault in next line while its sensitivity shows the protection degree of the fault in its own line.
With setting , effective reach is , with a deviation , zone 1’s probability density is:
(2)
Fault located at can be tripped correctly, so conditional probability of correct fault tripping at can be defined by:
∞ (3) Fault location is itself a random variable with probability density function . zone1’s sensitivity can be defined as:
∞ (4) With setting , for the fault at length , zone1 would not trip the fault when effective reach . So its conditional probability of un-tripping fault in L2 and the selectivity of zone1 are shown as:
∞ (5)
(6) The objective function of protectability is given as follows:
(7)
and are the weighting factors with . Here and with the constraint of .
The optimal setting of zone1 would correspond to the setting where its selectivity begins to decline, shown in Fig.2. And with this optimal setting, zone1 can get its maximum sensitivity satisfying the selectivity requirement.
<Fig.2> Sensitivity, Selectivity of Zone1 2.1.2 Protectability of Zone2
Zone2 aims to guarantee the protection of its own line beyond the setting of zone 1, and to provide back up for the neighbor lines[6].
Considering zone2's aim, its sensitivity should be "1" to trip for the fault at its own line and realize full protection. of the whole line. And selectivity of zone2 shows its coordination ability with zone1 of next line. Zone1 of next line adopts 80% of its line.
The mis-tripping conditional probability of zone 2 of relay1:
∞ (8) Ｔhe non-tripping conditional probability of zone1 of R2:
∞ (9) So the incorrect tripping probability and protectability should be:
× (10) 2009년도 대한전기학회 하계학술대회 논문집 2009. 7. 14 - 1 7
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Line Length(L1-L2) Optimal Setting Optimal Protectability
10-10 [11.4,15.4] 1
10-5 [11.4,12] 1
10-2 11.4 0.9848
Line Length(L1-L2-L3) Optimal Setting Optimal Protectability
10-10-10 21.4 0.9920
10-10-5 21.4 0.9844
10-10-2 21.4 0.9702
Line Length(L1-L2-L4) Optimal Setting Optimal Protectability
10-10-10 [11.4, 15.4] 1
10-10-5 [11.4,12] 1
10-10-2 11.4 0.9873
(11) The objective function of protectability is given as follows:
(12)
and are the weighting factors . Here and
with the constraint of .
<Fig.3> Sensitivity and Selectivity of Zone2 Seen from the Fig.3 and Table 1, the sensitivity equals "1"
to satisfy the full protection of whole L1, and the optimal setting does not change with L2. For a long adjacent line, with no mis-coordination with next zone1, there would be a optimal setting band which satisfy both sensitivity and selectivity perfectly. However, with the decrease of L2 length, the selectivity would decrease because of larger probability of mis-coordination with zone1 in next line.
<Table 1> Protectability of Zone2
2.1.3 Protectability of Zone3
Zone3 is decided to provide the maximum back to the neighbor lines, but without intersecting the zones 3 of their own primary relays. With similar evaluation process, its protectability should be determined by the selectivity with the constraint of sensitivity "1"
and the zone2 setting of next line adopts 120% of its line. Seen from Table 2, for the same L1 and L2, its optimal setting does not change with L3. However, with the decrease of L3, protectability decreases because of larger probability of mis-tripping.
<Table 2> Protectability of Zone3
2.2 Protectability of Multiple Lines System
<Fig.5> Model System with Multiple Lines
For zone1, the multiple neighbor lines do not affect its protection.
For zone2 and zone3, their sensitivity share same meaning with single line system, however, the selectivity evaluation must consider all the neighbor relays. Here we take zone2 for example. In Fig.5, the non-tripping probability of zone1 of R4 also need to be considered.
(13) So the incorrect probability is:
× (14) Here, , . These two rates are inversely proportional to their lengths because shorter line has higher probability of mis-tripping.
<Fig.4> Sensitivity and Selectivity of Zone2 In Fig.4 and Table 3, we can notice that similar to the single line system, with the same L1, optimal setting does not change according with the neighbor lines. However, selectivity would decrease corresponding with the L4 length since the mal-operation probability increases if its length decreases.
<Table 3> Protectability of Zone2 of multiple neighbor lines
3. Conclusion
In this paper, protectability of distance relay is evaluated and the optimal setting can be got through an objective function including sensitivity and selectivity with reasonable weighting factors by considering about the protection aim of each zone. A full description of the developed procedures and analysis are also presented. With the optimal setting achieved could provide a good reference for the practical application.
[Acknowledgements]
Supported by the ERC program of MOST/KOSEF (NPTC) and Korea Research Foundation Grant funded by the Korean Government (MEST)" (KRF-2007-211-D00044).
[References]
[1] M.Kezunovic, J.T.Cain, B.Perunicic, S.Kreso, "Digital Protective Relaying Algorithm Sensitivity Study and Evaluation," IEEE Transactions on Power Delivery, Vol.3, No.3,pp.912-922, July,1988 [2] Mladen Kezunovic, Bogdan Kasztenny, "Design Optimization and
Performance Evaluation of the Relaying Algorithms, Relays and Protective Systems Using Advanced Testing Tools", IEEE Trans. On Power Delivery, Vol15. No.4, Oct.2000
[3] S.J.Lee,et al, "Protection Levels Evaluation of Distribution systems Based on Dempster-Shafer Theory of Evidence", Power Engineering Society Winter Meeting, 2000. IEEE, Vol.3, pp.1894-1899, Jan.2000
[4] W.H.Zhang, M.S. Choi, S.J.Lee, et al." A Probabilistic Method Based Protectability Evaluation of Distance Relay in Transmission Networks", JEET, Vol.3, No.3, pp.246-353 ,2008
[5] J.Pinto de Sa, J.Afonso, "A Probabilistic Approach to Setting Distance Relays in Transmission Networks", IEEE Transactions on Power Delivery, Vol.12,No.2, pp.681-686, April 1997
