BECKWITH ELECTRIC M-0420, Инструкция

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A–7
Theory of Operation – Appendix A
Implementation of Inverse Time Overcurrent
Relay Curves
The time current characteristic of an induction
type overcurrent relay can be modeled as:
f f
(I)dt
P
K
t
0
t
(19)
Where I is the current in multiples of tap setting,
K is the time-dial setting and function ƒ deter-
mines the shape of the curve. In the above equation
the integration process begins when the current
exceeds the tap setting and the relay operates
when the integral exceeds K.
The digital implementation of (19) is used in this
relay. Let
I
k
be the current magnitude in multi-
ples of the tap setting and consider the following
integration with an initial sum (
U
0
) set to zero:
U
k
= U
k-1
+ƒ(I
k
) (20)
and if we say the relay is operated when the
running sum reaches a threshold value (
K
tv
), then
the relay operating time ( T
0
) for a constant mag-
nitude of current is given by:
T
0
=
K
tv
T
f
(I
k
)
(21)
where T = 4.17 ms is the time interval used for
the integration.
Four independent integrators – three for phase
elements and one for neutral element – are used.
The integration function allows the overcurrent
relay to coordinate with existing electromechani-
cal relays. The integration function provides cor-
rect relay operation for dynamic fault currents.
The relay actuating quantity can be selected as
the rms current or the fundamental frequency
rms current.
The function ƒ(I
k
) in (20) is approximated as a
piece-wise quadratic polynomial as follows [7,9]:
ƒ' (I
2
) = A
0
+ A
1
(I
2
) + A
2
(I
2
)
2
(22)
where ƒ' is a weighted least-squares approxima-
tion of ƒ, and
A
0
, A
1
, and A
2
are the polynomial
coefficients. The variable in the approximating
function is selected as
I
2
instead of I to avoid
the square root computation.
A.4 Acknowledgements
Beckwith Electric Company is pleased to ac-
knowledge the financial support of the Gas Re-
search Institute, Consolidated Edison Company
of New York and Rochester Gas and Electric
Company in the development of this product.
A.5 References
[1]
Grid Interconnection Performance Require-
ments and Current Practice. Gas Research
Institute, Topical Report 87-0117, 1986.
[2]
IEEE Guide for Interfacing Dispersed Stor-
age and Generations Facilities with Electric
Utility Systems. ANSI/IEEE Std. 1001-1988.
[3]
Intertie Protection of Consumer—Owned
Sources of Generation, 3 MVA or Less. IEEE
Publication 88TH0224-6-PWR.
[4]
Microprocessor Relays and Protection Sys-
tems. IEEE Tutorial Course Text,
88EH0269-1-PWR.
[5] A. G. Phadke, J. S. Thorp and M. G. Ad-
amiak, “A New Measurement Technique for
Tracking Voltage Phasors, Local System
Frequency, and Rate of Change of Frequency.”
IEEE Transactions on PAS, vol. PAS-102,
No. 5, May 1983, pp. 1025–1038.
[6] Authors’ closure discussion to [5].
[7] Murty V.V.S. Yalla, “
Design and Implemen-
tation of Digital Relays for Power System
Protection,” Ph.D. Dissertation, University
of New Brunswick, Canada, Nov. 1987, (Chap-
ter 3).
[8] Murty V.V.S. Yalla, “
A Digital Multifunction
Protective Relay,” IEEE Transactions on
Power Delivery, Vol. 7, No. 1, January 1992,
pp. 193–201.
[9] Murty V.V.S. Yalla and W.J. Smolinski, “
De-
sign and Implementation of Versatile Digital
Directional Overcurrent Relay”, Electric Power
Systems Research, Volume 18, No. 1, Jan-
uary 1990, pp. 47–55.