# Decision Algorithm of Neutral Grounding Mode Based on

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```					              Decision Algorithm of Neutral Grounding
Mode Based on Weighted Multi-attribute
Interval Grey Target Theory
Cao Zhenchong, Peng Jian, Xue Zhifang
Guangxi Electric Power Industry Investigation Design and Research Institute Jianzheng Road No.10, Nanning,
Guangxi, 530023, China
caozhenchong@tsinghua.org.cn

Abstract: Neutral grounding mode is important to distribution          mode, which is derived from the grey system theory, the
networks reliability, which has not been calculated                    theory of analytical hierarchy process, and the multi-attribute
quantitatively. Power system is a grey system whose reliability        grey target decision algorithm, which involve many
parameters are statistic, so interval theory should be introduced      disciplines: system engineering, decision theory, and
to analysis the impact of neutral grounding mode to distribution
networks reliability by interval function comparing method
economic theory.
based on relative superiority and extended from interval number           The algorithm proposed is composed of steps as follows: (1)
to interval function. Weighted multi-attribute decision arithmetic     to obtain the fault tripping rate of distribution lines and the
is given to choose distribution system neutral point mode, which       reliability indexes by interval analysis, all of which are the
is based on the analytic hierarchy process theory and more             interval grey numbers and is not capable of being used directly
reasonable, veracious, flexible and applicable. According to           for comparison, synthesis and decision; (2) to construct an
calculation results of examples, resonance grounding device is         optimal objective index that can reflect the integrated
better for the reliability than low value resistor in middle voltage   performance of neutral grounding mode with the grey
distribution overhead line system, in pure cable system or             numbers obtained in former step. Thereby, the major research
cable-overhead line hybrid system, the determinant factor is the
mutual effect between cables when faults occur.
in this paper concentrates on three parts: the analysis on
interval number of fault tripping rate, the decision algorithm
Keywords: Distribution networks; Neutral grounding mode;               based on weighted multi-attribute interval grey target theory,
Reliability; Interval analysis; Multi-attribute weighted grey          and the simulation cases.
target theory
II. INTERVAL ANALYSIS ON FAULT TRIPPING RATE OF
• I. INTRODUCTION
Neutral grounding mode is one of the most key problems                                   DISTRIBUTION LINES
that affect the reliability of distribution system greatly, and           In research filed of power system reliability, the stochastic
many researchers have investigated qualitatively the                   theory is usually applied to quantitative analysis and
characteristics of the distribution system reliability with            evaluation, from which and many effective methods have been
respect to several neutral grounding modes [1-4]. References           developed [7]. In addition, the grey system theory is widely
[5,6] analyzed in detail the influences to fault tripping rate of      used in interval analysis due to the uncertainty of original
power distribution lines by four modes including isolated              reliability parameters.
neutral, neutral point grounded through low-resistance, neutral           Definition 1: assume S is a semi-order set, for a
point grounded through Peterson coil, and neutral point
grounded through adjustable reactance, and emphasized that
( )
given x, x . If x, x ∈ S and x ≤ x , then an interval number

the reliability of entire distribution system can’t be evaluated                                         {                }
can be defined as: [ x] = [ x, x] = x ∈ S | x ≤ x ≤ x , where x
accurately only by fault tripping rate of lines. Actually, the
reliability should be analyzed according to the specific grid          is called lower extreme point, and x upper extreme point.
structure of distribution system in terms of reliability indexes       Furthermore, if x = x , [ x ] will regress as a real number [8].
such as CAIDI (Customer Average Interruption Duration
As shown in Fig. 1, it is an actual 6kV distribution system
Index), ASAI (Average System Availability Index), SAIDI
with n lines including k cables and n-k overhead lines, each of
(System Average Interruption Duration Index), SAIFI (System
which corresponds to one load point. Before calculation, some
Average Interruption Frequency Index), and ENS (Energy Not
Supplied).
However, there is still no systematic theory and algorithm          1) When a single-phase-to-ground fault occurs at the ith
that can be employed to compare the advantages and                          cable line, if the arc extinction unsuccessful or the fault
disadvantages of different neutral grounding modes                          line is not tripped out, the accident spreads and
quantitatively, which is subject to the reliability index of                endangers the near line, which consequently leads to
distribution system. In this paper, the decision algorithm based            tripping of this line and the near m cables.
on weighted multi-attribute interval grey target theory is
proposed to solve the decision problem of neutral grounding
2)   When the fault occurs at overhead line and even if the
[ g ni ]=[λi ](1+ km / n )                              (1)
accident can’t be cleared in time, the near lines will not
be affected.                                                    2)   Similarly, in system with neutral grounding through
Peterson coil, assume the probability that arc can be
extinguished is [α ] . the fault tripping rate of distribution
system is derived below,
[ g pi ]=[ λi ](1−[α ][η ][δ ])+[ λi ][η ](1−[α ][δ ]) km / n                 (2)
3)   As for system with low-resistance neutral point, when
fault occurs, relay protection maybe fails to trip out the
fault line, due to the mismatch between relay protection
and low-resistance. This condition is described by
probability [ β ] , then the fault tripping rate is,
[ g ri ]=[ λi ](1+[ β ][λi ][η ]km / n )                       (3)
4)   For neutral grounding through adjustable reactance,
Fig. 1 Schematic diagram of a distribution system
assuming the probability that reactance extinguishes arc
3)   For the neutral grounding through Peterson coil, if the              is [σ ] , and the probability that the reactance can’t match
coil can extinguish the arc of single-phase transient fault,         the relay protection to successfully trip out the fault line
relay protection only records the action event of                    is [ζ ] , the fault tripping rate is,
extinction coil. If the coil can’t eliminate the fault, it
quits and the system degenerates as an isolated neutral               [ g ci ]=[ λi ](1−[σ ][η ][δ ]) +[ λi ][η ]{1−[σ ][δ ]+ (1−[δ ][ζ ])}km / n   (4)
system. Finally, relay protection sends the warning signal
and records the fault event.                                       As discussed above, the fault tripping rate of distribution
lines is usually related to the influencing degree that the fault
4) For the neutral grounding through low-resistance, relay           line affects its near lines, which is described by an influencing
protection sends tripping command and records the fault         factor γ = km / n .
event.
III. DECISION ALGORITHM BASED ON WEIGHTED
5) For the neutral grounding through adjustable reactance, if
the arc of single phase transient fault can be extinguished,         MULTI-ATTRIBUTE INTERVAL GREY TARGET THEORY
relay protection only records the action event of               A. Interval Number of ReliabilityIndex
adjustable reactance. Otherwise, relay protection sends
directly the over-current quick-break signal used for              Typical reliability indexes of distribution system includes
tripping and records the fault event.                           ASAI, CAIDI, SAIDI, SAIFI, and ENS, which are determined
by both neutral grounding mode and many other factors such
6) The faults caused by other elements in distribution               as elements (generator, transformer, bus, and breaker), main
system are not taken into account.                              connection and grid structure of system[9-11]. Whereas, the
7) The        probability    that     the     fault    type     is   influence of neutral grounding mode is relatively independent
single-phase-to-ground fault is [η ] , among which the          of that of other factors, and this paper only investigates the
probability of transient type is [δ ] . The faults including    former.
two-phase- to-ground, two-phase or three-phase short               Setting the schedule repair rate [λi' ] and combining the fault
circuit can be eliminated successfully by relay protection.     tripping rate of distribution line as shown in Eqs. (1)~ (4), it is
Based on the above assumptions, the influence of neutral           ready to obtain the outage rate [Gi ] and annual outage time
grounding mode on fault tripping rate is discussed as below:         [U i ] of the ith line:

1)   In isolated neutral system, the fault rate of the ith line                                      [Gi ]=[ gi ]+[ λi' ]                                (5)
is [λi ] . According to the technical code, the line with                                                ' '
[U ] = [ g ][ r ] + [ λ ][ r ]      (6)
single-phase-to-ground can operate for 2 hours until                                i       i i          i i
tripping out. Therefore, the fault tripping rate is [λi ] for     where the general representations [Gi ] , [ gi ] and [U i ]
overhead line, and [ λi ](1+ m ) for cable. In hybrid           can be specialized by adding subscripts n , p , r , and c ,
distribution system consisting of cable and overhead line,      which identify respectively the four neutral grounding modes.
the probability of being cable fault is k / n , so the fault       According to the interval inversion rule [12], the reliability
tripping rate of distribution system initiated by the ith       indexes of distribution system can be expressed below,
line is calculated by,                                                            [CAIDI ]=φ ( ∑ [Gi ] Ni , ∑ [U i ] Ni )
i∈R             i∈R
(7)
[ SAIFI ] = φ ( ∑ [Gi ] Ni , ∑ Ni )                                                                                             n

i∈R              i∈R
(8)                      [c j , d j ] = [ kij ]                  ∑ [k ], w      ij               j
∈ [c j , d j ]                                                       (13)
[ SAIDI ]=φ ( ∑ [U i ] Ni , ∑ Ni )                                                                                             i =1

i∈R           i∈R
(9)          In further, by utilizing the weight shown in Eq. (13), the
'
[ ASAI ] = ( ∑ 8760 Ni − ∑ [U i ] Ni ) ∑ 8760 Ni                               normalized decision matrix R                                                                         is transformed into the
(10)
i∈R            i∈R                    i∈R                         weighted normalized decision matrix R = ([ rij , rij ]) m× n .
[ ENS ] = ∑ [ Pai ][U i ]
i∈R
(11)
[ rij , rij ] = [c j , d j ] [ rij , rij ]
'            '
(14)
where [ Ni ] is the customer number at load point i, [ Pai ]
the average load at load point i. For different distribution                                   where ri = ([ ri1 , ri1 ],[ ri 2 , ri 2 ], L ,[ rin , rin ]), i = 1, 2, L , m , is
systems, the importance of one reliability index varies when
compared with the others. To select neutral grounding mode                                the ith row vector of R, here called the effect vector of drafted
from the point of view of the reliability, the decision algorithm                         decision scheme Si .
based on weighted multi-attribute interval grey target theory is                               Definition 3:
used.
Let r = max
j
o
{( r + r )
ij           ij                                               }
2 | 1 ≤ i ≤ m , j = 1, 2, L , n , and its

B. Decision Algorithm Based on Interval Grey Target Theory                                    corresponding decision value in R is written as [ ri j , ri j ] ,                                                                             o       o

Definition 2: for m-dimension interval numbers
o
A = [( a11 , a12 ), K , ( am1 , am 2 )] and B = [(b11 , b12 ), K , (bm1 , bm 2 )]             then r is called the optimal effect vector of multi-attribute
grey target decision, also named bull’s eye.
} = {[r                                                                                               }
where ai1 ≤ ai 2 , bi1 ≤ bi 2 , i=1,2,L,m , then L p ( A, B ) is called
{
ro = rj , rj , L , rj
o       o              o
io 1
, ri 1 ],[ ri 2 , ri 2 ], L ,[ ri n , ri n ] .
o               o           o                        o       o
the distance from A to B. Especially, L2 ( A, B ) is called
When constructing the optimal effect vector, if there are

(r                       )/2
Euclidean distance.
1                                                                 two or more decision schemes whose values                                                                                                             + ri
Lp ( A, B) =      [( a11 − b11 ) + ( a12 − b12 ) + L
p               p                                                                                                                                                                               io j            o
j

1/ p
2                                                        (12)      with respect to one or more indexes are equal, then the optimal
+ ( am1 − bm1 ) + ( am 2 − bm 2 ) ]
p                        p 1 p
effect can be realized. In this case, to select the upper limit
Given that the multi-attribute decision problem has m                                rij as evaluation standard can solve the above problem.
evaluation objects or drafted decision schemes, belonging to                                                                              (n)
Definition 4: R is n-dimensional grey target with bull’s
the set S = {S1 , S 2 , L , S m } ; and the index set                                          o
eye r and radius R, written as:
A = { A1 , A2 , L , An } is composed of n evaluation indexes or
{
1           ⎡   (r − r )
2
(n)
= ([ ri 1 , ri 1 ], [ ri 2 , ri 2 ], L , [ rin , rin ]) | R =
2
R
attributes. Writing the attribute of scheme Si with respect to                                                                                                                                              2
1/ 2
⎣       i1      io 1

(13)
Aj     as [ xij , xij ] , all of which form a decision sample
(              )                       (                    ) + (r − r )                             ⎤ ⎫
1/ 2
2                                            2                                2

⎦ ⎬
+ ri 1 − ri 1              + L + rin − ri n
⎭
o                                             o
in        io n

matrix X = ([ xij , xij ]) m× n , i = 1, 2, L , m ,                   j = 1, 2, L , n .
Because the index set A includes both optimistic and                                           Definition 5:
pessimistic indexes, it is necessary to transform A into the                                                                                                                                                                                            (n)
Let effect vector ri = ([ ri1 , ri1 ],[ ri 2 , ri 2 ], L ,[ rin , rin ]) ∈ R                                                                                     ,
[12]
: R = ([ rij , rij ]) m× n .
'          '     '
normalized decision matrix
then call ε i the off-target distance of ri .
The weight w j owned by each element in index set A can’t
ε i = ri − ro
be assigned exactly, being able to be described by the
(( i1 i 1 )    )
⎡ r − r 2 + r − r 2 +L+ r − r
(                    ) (                             )           ⎤
1/ 2
1                                                                                                                    2
following: w j ∈ [c j , d j ] , 0 ≤ c j ≤ d j ≤ 1 , w1 + w2 + L + wn = 1 .
2
=                                                                                                                                + rin − ri n
2 ⎢   ⎣ i1 i 1                                                                                                                                                   ⎥
⎦
1/ 2                     o
in  i n                         o                                                o                                o

According to the meaning of importance standard degree in
.
analytical hierarchic theory [13], an importance degree matrix
The value of off-target distance reflects the bad or good
can be constructed, written as K = ([ kij ]) m× n , which is a             property of effect vector: the smaller it is, the better the
consistent matrix with the following properties (proof omitted): decision scheme Si is; and vice versa.
[ kij ] > 0 , [ kij ] = 1 [ k ji ] , and [ kii ] = 1 .By normalizing every    This section illustrates the basic principle of decision
column of the importance degree matrix K, the weight of each               algorithm based on weighted multi-attribute interval grey
target theory, which also can be seen in reference [8] for
element in the index set A can finally be obtained:
detailed derivation process. Essentially, the algorithm is a                applications of the algorithm proposed not only in the decision
generalization of decision algorithm multi-attribute interval               problem of neutral grounding mode, but also in the optimal
grey target theory from real space to interval number space,                reconfiguration of power system grid, and the optimal design
and can comprehensively consider the weight problem of                      of power system high-voltage transmission line.
every index. Compared with traditional decision algorithms,
this algorithm takes more advantages of flexibility, rationality,
IV. STUDY CASES AND RESULT ANALYSIS
and universality: the flexibility is embodied by that all
decision indexes with different meanings, dimensions, and                     Three study cases were performed to validate the algorithm
properties can be evaluated in same decision system, thus                   proposed.
expanding the select range of decision indexes to make it more                Case 1: given the electric parameters of a real distribution
comprehensive of considering the influencing factors on                     system    [14-15]
: [λi ] = [0.05, 0.1] ,   [λ ' ] = [0.5,1] ,    i
decision-making; the rationality by that the importance degree
[ηi ] = [0.8, 0.9]   ,         [δ i ] = [0.7, 0.8]   ,   [α ] = [0.9, 0.95]   ,
of every decision index indicated by its importance weight is
reflected in the decision process, as seen in the process of                [ β ] = [0.05, 0.1] ,           [σ ] = [0.9, 0.95] ,       [γ ] = [0.05, 0.1] ,
transforming the normalized decision matrix into the weighted               [ ri ] = [1.0, 2.0] , [ ri ] = [1.0,1.5] , k = 57, n = 57, m = 1.
'

normalized decision matrix; the universality by the
generalization of decision algorithm multi-attribute interval                 Case 2: m = 4, and the rest is same as Case 1.
grey target theory from real space to interval number space,                  Case 3: m = 8, and the rest is same as Case 1.
thus making the algorithm can deal with more complicated                      The results are shown in TABLE I ~III respectively for
decision problems. The above feature promotes the wide                      Case 1~3.

TABLE I
CALCULATION RESULT OF CASE 1

Grounding Mode             CAIDI / h         SAIFI / time/a       SAIDI / h/(a.c)                 ASAI             ENS / MV.A              ε
isolated           [6.000,27.000]      [0.0600,0.1000]      [0.5600,1.7000]     [0.99981,0.99994]           [16.993,64.819]         0.102

Peterson coil        [13.063,100.430]     [0.0152,0.0415]      [0.5152,1.5829]     [0.99982,0.99994]           [15.635,60.354]         0.034

low-resistance        [10.569,51.603]      [0.0302,0.0523]      [0.5302,1.6045]     [0.99982,0.99994]           [16.090,61.178]         0.061

adjustable-reactance    [18.197,146.680]     [0.0104,0.0291]      [0.5104,1.5581]     [0.99982,0.99994]           [15.487,59.410]         0.037

TABLE II
CALCULATION RESULT OF CASE 2

Grounding Mode             CAIDI / h         SAIFI / time/a       SAIDI / h/(a.c)                 ASAI             ENS / MV.A              ε
isolated          [3.0000,12.0000]     [0.1500,0.2500]      [0.6500,2.0000]     [0.99977,0.99993]           [19.724,76.258]         0.159

Peterson coil        [6.4705,48.1250]     [0.0325,0.0914]      [0.5325,1.6828]     [0.99981,0.99994]           [16.159,64.163]         0.074

low-resistance        [9.4746,50.4500]     [0.0310,0.0590]      [0.5310,1.6180]     [0.99982,0.99994]           [16.112,61.692]         0.067

adjustable-reactance   [12.9330,117.1000]    [0.0130,0.0419]      [0.5130,1.5838]     [0.99982,0.99994]           [15.568,60.388]         0.01

TABLE III
CALCULATION RESULT OF CASE 3

Grounding Mode            CAIDI / h         SAIFI / time/a        SAIDI / h/(a.c)                 ASAI               ENS / MV.A                ε
isolated           [2.1111,7.5556]     [0.2700,0.4500]      [0.7700,2.4000]      [0.99973,0.99991]            [23.365,91509.0]        0.173

Peterson coil        [4.1646,28.9980]     [0.0556,0.1580]      [0.5556,1.8160]      [0.99979,0.99994]             [16.858,69.242]        0.098

low-resistance       [8.3529,48.9920]     [0.0319,0.0680]      [0.5319,1.6360]      [0.99981,0.99994]             [16.141,62.379]        0.061

adjustable-reactance    [9.4746,92.4490]     [0.01658,0.0590]     [0.5166,1.6180]      [0.99982,0.99994]          [15676.000,61692.0]       0.004
[6]    Cao Z C, Yang X C, Wu Z S. A novel adjustable TCR arc suppression
Cases 1~3 calculated the reliability indexes of the                                 coil [C]. Proceedings of the XIVth International Symposium on High
distribution system as shown in Fig. 1, comparing four neutral                         Voltage Engineering, Tsinghua University, Beijing, China, August
grounding modes by the algorithm proposed.                                             25-29, 2005, 305.
From the results shown in Tables 1~3, the neutral                            [7]    Billinton R, Allan R N. Reliability Evaluation of Power Systems [M].
Boston, MA, USA: Pitman Advanced Publishing Program, 1996.
grounding mode imposes an extreme impact on the reliability                     [8]    Cao Z C. Research on Reliability and Decision Arithmetic of
indexes of distribution system. The performance of isolated                            Distribution System Neutral Point Mode and Calculation of
neutral point is worst, and all the remained three modes can                           Overvoltage [D]. Beijing, China: Tsinghua University, 2006
improve the reliability of distribution system to some extent,                  [9]    Zhang P，Guo Y J. Interval method for power station and substation
affected considerably by the fault influencing coefficient m.                          reliability evaluation [J]. Automation of Electric Power Systems, 2004,
28(19): 48-52. (in Chinese)
the smaller the influencing coefficient m is, the more                          [10]   Zhang P, Wang S X. Interval analysis based multi-objective network
remarkable improvement the low-resistance can improve;                                 reconfiguration for distribution system reliability improvement [J].
otherwise, low-resistance and adjustable reactance can                                 Automation of Electric Power Systems, 2004, 28(21): 22-26. (in
improve the reliability remarkably. Because adjustable                                 Chinese)
[11]   Guo Y J. Power system reliability analysis [M]. Beijing, China:
reactance has the ability of extinguishing the arc of                                  Tsinghua University Press, 2001
single-phase transient fault and avoiding unnecessary                           [12]   Dang Y G, Liu S F, Liu B. Study on the multi-attribute decision model
tripping-out of line, it can improve the reliability of                                of grey target based on interval number [J]. China Engineering Science,
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[13]   Saaty T L. The analytical hierarchy process [M]. Pittsburgh PA: RW S
As discussed above, the algorithm proposed can unite many                           Publications, 1996.
reliability decision indexes with different meanings,                           [14]   Allan R N, Billinton R, Sjariefi I, et al. A reliability test system for
dimensions, and weights into a reasonable decision system,                             educational purposes- basic distribution system data and results [J].
and the decision result is in the form of off-target distance,                         IEEE Transactions on Power System, 1991, 6(2): 813-820.
[15]   Billinton R, Jonnavithula S. A test system for teaching overall power
which is in agreement with practical decision process.                                 system reliability assessment [J]. IEEE Transactions on Power System,
1996, 11(4): 1670-1676.

V. CONCLUSIONS
1)    The neutral grounding mode affects reliability of
distribution system considerably, so is necessary to take
into account the neutral grounding mode in reliability
analysis of distribution system.
2)    In the distribution system only consists of overhead lines
or in the cable distribution system where the fault cable
would not affect the near normal operating cables,
Peterson coil grounding can improve the system
reliability in the maximal degree.
3)    In cable system where the fault cable affects severely the
near normal operating cables, low-resistance and
adjustable reactance are beneficial to the improvement of
system reliability.
4)    From the point of view of improving system reliability,
the decision algorithm based on weighted multi-attribute
interval grey target theory can effectively evaluate the
grounding modes.

REFERENCES
[1]   Yao H N. Practical experiences of EdF (Electricite de France) in using
resonance grounding for neutrals of medium voltage power network [J].
Power System Technology, 1998, 22(4): 50-53. (in Chinese)
[2]   Yi D F. Research on neutral grounding in 6~10kV power networks [J].
Power System Technology, 1998, 22(7): 27-30. (in Chinese)
[3]   Wu Q Y, Shen P, Chen L M. Neutral grounding in urban power
distribution system [J]. High Voltage Engineering, 2002, 28(6): 50, 58.
(in Chinese)
[4]   Yao H N, Cao M Y. On neutral grounding modes of cable network.
Power System Technology, 2003, 27(2): 84-89. (in Chinese)
[5]   Cao Z C, He J S, Yang X C, Zhi X, etc. Interval analysis about
Influence on Reliability of Power Distribution Lines With Various
Grounded Neutral [J]. Guangxi Electric Power, 2007, 30(5): 5-7. (in
Chinese)

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