power system. This directly affects the choice and sizing
of protective and coordination devices used in mine power
systems. The effect of winding temperature is also important,
but the values do not vary too much from values computed
for correctly represented four-bus three-winding transformer
models.

Computer analysis of mine power systems is routinely
utilized to analyze and evaluate mine power systems. Accurate
system modeling of components in the power system is
essential for proper analyses of these systems. The accurate
modeling of three-winding transformers is critical, consider-
ing their widespread use in longwall and continuous miner
sections.

REFERENCES

(1) F.C. Teutt, L. A. Morley, and R. A. Rivell, “Interactive mine power
system analysis, U.S, Bureau of Mines, Washington, DC, Tech. Rep. on
Contract J0199060, 1981.

[2] F. C. Trutt and L. A. Morley, “Mine power system analysis,” /EEE
Trans. Ind. Applicat., vol. 24, pp. 839-845, Sept/Oct. 1988.

(3] F. C. Teutt and J. L. Kohler, “A noniterative approach to mine power
system analysis,” in Conf. Rec. IEEE-IAS Annu. Meeting, 1984, pp.
113-116.

[4] R. C. Degeneff and P. J. McKenney, “A method for constructing reduced
order transformer models for system studies from detailed lumped
parameter models,” IEEE Trans. Power Delivery, vol. 7, pp. 649-655.
Apr. 1992.

{5} V. Brandwajn, H. W. Dommel, and [. 1. Dommel, “Matrix representation
of three-phase N-winding transformers for steady-state and transient
studies,” JEEE Trans. Power App. Syst., vol. PAS-101, pp. 1369-1378,
June 1982.

[6] F. Leon and A. Semlyen, “Reduced order model for transformer
transients.” IEEE Trans. Power Delivery. vol. 7, pp. 361-369, Jan. 1992.

I7) S.J. Chapman, Electric Machinery Fundamenials. New York
McGraw-Hill, 1985, pp. 66-70.

[8] A. E. Fitzgerald, C. Kingsley, and S. D. Umans, Electric Machinery.
New York: McGraw-Hill, 1985, pp. 45-48.

[9] V. E. Mablekos, Electric Machine Theory for Power Engineers. New
York: Harper & Row, 1980, pp. 29-31

[10] W. D. Stevenson, Elements of Power System Analysis. New York:

McGraw-Hill, 1982, pp. 153-155.

IEEE Recommended Practice for Power System Analysis, ANSITEEE
Std 399-1980, Nov. 24, 1980, pp. 65-66.

M. P. Oommen and J. L. Kohler, “An improved model for analyzing
industrial power systems,” in Proc. Ith WVU Int. Mining Electrotech-
nology Conf, 1992, pp. 22-31

my)
(12)

[13] M. J. Gorman and J. J. Grainger, “Transformer modeling for distribution
system studies—Part I: Linear modeling basics,” JEEE Trans. Power
Delivery, vol. 7, pp. 587-574, Apr. 1992.

[14] M. J. Gorman and J. J. Grainger, “Transformer modeling for distribution
system studies—Part Il: Addition of models to Yisus and Zpus." IEEE
Trans. Power Delivery, vol. 7. pp. 567-574, Apr. 1992.

Mathey P. Oommen received the B.Tech, M.S.,
and Ph.D. degrees in mining engineering from The
Pennsylvania State University, University Park, in
1985, 1988, and 1994, respectively.

While at The Pennsylvania State University, he
served as a Graduate Research Assistant irom 1986
to 1994, a Teaching Assistant from 1989 to 1994, a
Software Development/Support and Computer Con-
sultant from 1991 to 1994, and he developed, dis-
tributed, and supported a computer program for
mine power systems analysis while earning his
advanced degrees. Upon graduation, he joined Marston & Marston, Inc. as a
Project Mining Engineer. He is currently the General Manager of the Indonesia
Representative Office, Marston International, Inc. Balikpapan, Indonesia, and
is a past Senior Project Mining Engineer of Marston & Marston, Inc.,
St. Louis, MO.

Dr. Oommen is a member of the Society of Mining, Metallurgy, and
Exploration

Jeffrey L. Kohler (5°74-M’76-SM'88) received
the B.S. degree in engineering science in 1974 and
the M.S. and Ph.D degrees in mining engineering in
1976 and 1983, respectively, from The Pennsylvania
State University, University Park.

He worked as an Electronics Technician and then
as an Electrical Engineering Assistant while an
undergraduate. While working toward the advanced
degrees, he was an Instructor of Mining Engineering
at The Pennsylvania State University. From 1979 to
1982, he was a Senior Associate with Ketron, Inc.

Tn 1983, he joined the faculty of the Department of Mineral Engineering,

The Pennsylvania State University, where he was an Associate Professor

and Director of the Mine Electrical Laboratory. His teaching and research

interests included elecirical engineering applications in the mineral industries.

He is currently with the National Institute of Occupational Safety and

Health, Pittsburgh Research Laboratory, Pittsburgh, PA, where he is Research

Director.

Dr. Kohler is the Past Chairman of the Mining Industry Committee of the

IEE Industry Applications Society and a member of the Society for Mining

and Exploration.


TABLE I
PERCENTAGE INCREASE IN VOLTAGE MAGNITUDES
‘Companen To INCORRECT MODEL IN CASE I

TABLE Ill
PERCENTAGE INCREASE IN FinsT-CYCL® FAULT
‘CURRENTS COMPARED TO INCORRECT Mopet IN Case I

Bus Case II Case III Bus Case II Case III

1 0.00 0.00 1 0.02 0.01

2 0.02 0.01 2 -0.10 0
52 0.88 0.52 52 16.48
53 1.20 0.44 53 42.08 58.94
62 0.91 0.54 62 10.61 15.89
63 1.21 0.44 63 27.79 36.48
54 1.21 0.44 54 32.38 42.93
55 1.27 0.47 55 10.89 14.30
61 0.94 0.55 61 4.70 7.48
60 2 0.54 60 10.12 15.08
59 “91 0.54 59 10.16 15.13
58 0.91 0.54 58 10.15 15.12
56 1.35 0.50 56 3.34 4.80
37 1.43 0.53 57 0.82 9

TABLE I The results directly affect the protection and coordination of
PERCENTAGE INCREASE IN SYMMETRICAL FAULT .
Currents COMPARED 70 INCORRECT Mopet IN CASE I such a system. For example, the main molded case breaker on
the secondary and tertiary buses will be affected and so will the
Bus Case II Case III instantaneous settings for the distribution system overcurrent
relays.
‘A similar analysis was performed on another longwall

1 0.00 0.00 .

2 0.00 0.00 system to ensure that these results were not peculiar to the
52 24.87 26.32 example under scrutiny. The analysis yielded results similar
53 59.88 61.45 ized in th
62 17.65 19.01 to those summarized in the above results.

63 38.44 40.03

34 S 2 47.28 V. TEMPERATURE EFFECTS AND HIGHER

61 10.47 11.57 ORDER TRANSFORMER MODELS

Hy 36-74 18-08 The previous analysis used manufacturer-supplied data
58 16.74 18.09 which is assumed to be for transformers operating at 170 °C.
56 9.88 10.44 For a transformer at 20 °C, the X/R ratio is expected to be
57 6.61 7.02 about 1.6 times higher than that at 170 °C. Therefore, it is

fault analysis. These results are percentage changes referred
to Case I as the base case.

Given fault currents J), 2, and 3, for Cases I, Il, and Ul,
respectively, the values in Table II were computed as

«100 ©

for Case II, and as

[52 * 100 ie)

ih

for Case III.

It can be seen that there is a significant difference that
can be observed in Cases I and III. The most significant, in
both tables, can be observed at the tertiary bus and the buses
connected to it. Results show that the fault current can be
higher by as much as 60% compared to the incorrect model in
Case 1. The results of the more accurate three-winding model
are higher than those of Case IL

necessary to consider this effect to determine the difference
in maximum fault analysis.

‘An analysis, similar to that in the previous section, was
performed to investigate the effects of temperature. Compared
to the three-winding four-bus model, the values differed by
2% for two systems which were analyzed. These included the
example system and the verification system.

Higher order transformer models can be utilized to incor-
porate the effects of mutual coupling across windings. These
models are typically represented as impedance matrices [13].
These can then be incorporated into the system representation
[14]. The development of such models requires more detailed
information from manufacturers.

VI. SUMMARY

This paper has presented the impact of accurate, three-
winding transformer models in the analysis of mine power sys-
tems. Although the disparity in voltage regulation is minimal,
the enhanced representation of three-winding transformers
seriously affects the results of both steady-state and first-cycle
fault analysis, Fault current magnitudes could be underesti-
mated by as much as 60% at strategic locations in the mine



Effect of Three-Winding Transformer Models on the
Analysis and Protection of Mine Power Systems

Mathew P. Oommen and Jeffrey L. Kohler, Senior Member, IEEE

Abstract—Computer-aided loadfiow and fault analyses of mine
power systems are routinely conducted to ascertain system per-
formance and also to provide information to assist in the protec-
tion and coordination of these systems. Three-winding transform-
ers are frequently encountered in mining applications, typically
at continuous miner and longwall sections where there exists
a need for dual utilization voltages. These transformers are
often modeled as a three-bus system neglecting the secondary to
tertiary winding impedance and the effect of base changes. This
paper analyzes the impact of more accurate transformer models
on voltages and fault currents which are realized from loadflow
and fault studies of mine power systems.

Index Terms—Fault analysis, load flow analysis, power system
analysis, power system modeling, transformer models.

1. INTRODUCTION

HE design of a mine power system should always be

supported with computer analyses, including loadflow,
fault, and machine starting. Engineers now have access to
a variety of loadflow and fault analysis programs [1]-[3].
However, the availability of such tools does not eliminate the
need for accurate system modeling. Oftentimes, these tools are
used without an appropriate understanding of their capabilities
and limitations.

System modeling is a key component in the proper eval-
uation of any power system. This, for example, includes the
representation of cables, loads, correction devices, and trans-
formers. The results from the analysis of mine power systems
will only be as accurate as the model that is represented by
the user, Most programs in use today can assist the user in
easily specifying most of the components encountered in a
mine power system, However, the representation of three-
winding transformers and the effect of inaccurate models is
not well understood in the context of mine power systems.
The need for accurate representation is all the more important
since more systems are utilizing dual voltages at longwall and
continuous miner power centers.

Paper PID 98-01, presented at the 1993 Industry Applications Society
Annual Meeting, Toronto, Ont., Canada, October 2-8, and approved for
publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the
Mining Industry Committee of the IEEE Industry Applications Society.
Manuscript released for publication February 17, 1998.

M. P. Oommen was with the Department of Mineral Engineering, The
Pennsylvania State University, University Park, PA 16802 USA. He is now
with Marston Intemational, Inc., St. Louis, MO 63021 USA.

J. L. Kohler was with the Department of Mineral Engineering, The
Pennsylvania State University, University Park, PA 16802 USA. He is now
with the National Institute of Occupational Safety and Health, Pittsburgh
Research Laboratory, Pittsburgh, PA 15236 USA.

Publisher Item Identifier S 0093-9994(99)03859-1

Utilities have long appreciated the need for accurate trans-
former models. There is a variety of models one could use
for intricate modeling of transformers to accurately delineate
their performance under steady-state and transient conditions
(4]16). Unfortunately, mine power systems analysis, for the
most part, has not considered the impact of even simpler
representation and its effects on mine power system design
and protection.

Tl, THREE-WINDING TRANSFORMERS

Transformer equivalent circuits are typically based on the
parameters obtained from open- and short-circuit tests [7]-{9].
‘An approximate model is often obtained by neglecting the
shunt admittance.

Both the primary and secondary windings of a two-winding
transformer have the same kilovoltampere rating. However,
all three windings of a three-winding transformer may have
different kilovoltampere ratings. The impedances of each
winding of a three-winding transformer may be specified as a
percent or in per-unit based on the rating of its own winding,
or could be referred to a common base.

In the case of three-winding transformers, the impedances
may be measured by the standard short-circuit tests and could
be represented as follows [10]:

Zp leakage impedance measured in primary with sec-
ondary short circuited and tertiary open;

Zp leakage impedance measured in primary with tertiary
short circuited and secondary open;

Z.. ‘leakage impedance measured in the secondary with

tertiary short circuited and primary open.
If these impedances are referred to the primary circuit, the
impedances of each individual winding can be computed as
follows [10], [11]:

1

Ly = 5 Lan + Lie — Zoe)
1

2, = 5 (lpn + Zus — Zs)
1

Zea 3!

The individual impedances referred to the primary circuit are
related to the leakage impedances as follows:

Zs + Zoe — Zps). a)

Zys = Bp + Zs
Zp = Zp +2

Zp = Zs + Zr. Q)



Fig. 1

Single-phase equivalent of three-winding transformer.

The impedances of the windings computed in (1) can
be represented as a Y single-phase equivalent of the three-
winding transformer with the magnetizing current neglected
This representation is shown in Fig. 1. The neutral point (’)
is a fictitious neutral that has no physical meaning, but is
necessary in the representation.

Il. SYSTEM MODELING

In a computer-aided analysis of a mine power system
containing a three-winding transformer, the points p, s, and
tin Fig. 1 are connected to the buses designating the primary,
secondary, and tertiary, respectively. However, in a system
representation, the values of Z, and Z, must be referred to
their individual kilovoltampere bases.

For example, given Zps, Zpt, and Z referred to the
transformer's primary kilovoltampere base (consistent with the
respective winding voltages), one could apply (1) to compute
values for Z,, Z,, and Z,. These values, however, are based
on the primary kilovoltampere rating.

Given that the kilovoltampere rating of the primary, sec-
ondary, and tertiary winding are kVA), kVA,, and kVA;,
respectively, the following base transformations have to be
made to prepare the model for computer analysis:

kVA,
a4 (im)

kVA,
at (Se): ey
°

This base change is necessary, since all impedances during
analysis will be converted to a uniform system base.

Fig. 2(a) shows the often used inaccurate representation
of three-winding transformers ignoring the second-to-tertiary
impedance. Fig. 2(b) depicts the more accurate four-bus model
developed in this section.

TV. SYSTEM ANALYSIS

The previous sections have introduced and developed the
modeling aspect of three-winding transformers. However, to

Ww WwW ,
AWW 78 MW 7
| |

@)

WW

—“
whw ww

zy

Mts MW

ob)

Fig. 2. (a) Innacurate representation of three-winding transformer. (b) Cor-
rect three-winding transformer winding.

compare the two models, it is necessary to perform an analysis
of a typical mine power system containing a three-winding
transformer. Fig. 3 shows a typical longwall section employing
a three-winding transformer.

The program used to evaluate the mine power system
is called MPAP and was developed at the Mine Electrical
Laboratory, The Pennsylvania State University, University
Park. The program provides a single platform for performing
loadflow analysis, symmetrical fault analysis, and first-cycle
(transient) fault analysis. Details of the program may be found
in [12].

‘The analysis was performed on three cases.

1) Case I is the base case, where the transformer is repre-
sented as a three-bus system, ignoring the secondary-to-
tertiary impedance. Furthermore, it is assumed that Zp.
and Zpt are not converted to their individual winding
capacities (kilovoltamperes).

2) Case II also employs a three-bus representation, but the
necessary base changes are performed to convert Z,5
and Zp. to their respective kilovoltampere bases.

3) Case III uses the complete four-bus model of the three-
winding transformer with the appropriate base changes.

In all cases, it is assumed that the manufacturer-specified
values for leakage impedances are referred to the primary
circuit of the transformer.

The values used for the analysis are as follows:

Zps = 3.5% (X/R = 4)
Zoe = 5.5% (X/R = 6)
Zu. = 3.0% (X/R= 4).

The utility short-circuit capacity is assumed to be 280 MVA
at 7.2 kV.

A. Loadflow Analysis

Table I summarizes the results from the three cases. The
values shown are percentage differences of Cases II and III as
compared to the base case.



@

Utility Short Circuit WW 7.5 MVA 5%
Capacity : 280 MVA 23.1: 7.2 kV
sk 11,000"
4/0 MPF

WW
AWN 3 Winding XFMR

3500 kVA

Primary
| | Bus
WW 2000 Kva WWW 1800 Kva
7200:2400 V NWA 7200:1040 v
Seconda: | (2) ® | Tertiary
Bus ” 8) Te Bus
2/0 | 150°
850" water Y 4/0
4/0 Pump 850"
125 hp Hydraulic 4/0
Pumps
Longwall
pongwall 150 hp 150 hp
100'| Box @) Shearer
100°} 2/0 Control
2/0 Crusher 625° Box
100° 200 hp 2/0
2/0 8) Mid—Face
1150" Stage Loader @) Gonnection
2/0 160 bp 875°
AFC Heag Motors Connected To 2/0
Secondary Bus Are Shearer
600 hp The Secondary Shearer

2300V & Those Connected To
The Tertiary Bus Are 995V

— 1
ye
Fig. 3. Example of longwall power system

Given voltage values V;, V2, and V3 for Cases I, II, and Hl,

respectively, the values in Table I were computed as

(Va-V1)

a) +100 (4)

for Case II, and as

6)

for Case Til.

It can be easily seen that the relative change is minimal in
both cases. There is, however, a small improvement in voltage
regulation. This can be explained by the drop in line impedance
between transformer buses due to the base change in Case II
and due to the effective transformation to smaller impedances
in the three-winding representation in Case II.

B. Fault Analysis

Table I shows the comparative results of symmetrical fault
analysis, and Table III shows the results from symmetrical