IEEE Std 115-2009

IEEE Guide for Test Procedures for Synchronous Machines

Part I—Acceptance and Performance Testing

8. Sudden short-circuit tests

8.1 Mechanical integrity of machine

One of the purposes of short-circuit testing is to verify the mechanical integrity of the machine. During its
lifetime of service, depending upon its use either as a generator or as a large industrial-size motor, the
machine will be subject to sudden changes in load, due to faults on the power system (or industrial system)
or due to full load rejection, or subject to sudden requirements for increases or decreases in power output
due to governor action.

Thus, in addition to meeting the mechanical stresses due to (usually) three-phase short-circuit tests, the
mechanical capability of the machine is measured in a qualitative manner.

Before performing tests for mechanical integrity, the manufacturer should be consulted. The machine must
be carefully inspected to see that the bracing of the stator coil ends is satisfactory, the foundation is in good
condition, and the hold-down bolts are tightened to the applicable specification. The rotor must be
inspected to see that all keys and bolts are in place and properly tightened.

8.2 Electrical integrity of machine

Insofar as the electrical integrity of the machine is concerned, there are insulation and other types of
overvoltage tests to quantify the electrical operation performance, per IEEE Std 4 and IEEE Std 43.

During short-circuit testing, certain precautions are required in preparing the electric connections because
of the abnormal conditions that attend a sudden short-circuit test. Very high current flows, particularly on
large machines, result in great forces on the test conductors. To prevent damage movement, test conductors
should be securely braced.

The armature circuit should be solidly grounded at a single point using a conductor of size comparable to
the leads from the machine terminals. There are two choices for the location of this ground connection: the
neutral of a wye-connected armature winding or the point common to the three contacts of the shorting
circuit breaker. If shunts are used in measuring the currents, their common point should be where the
ground connection is made. This setup minimizes the risk of hazardous voltages at the oscillograph or
recorder in case of a mishap. If current transformers are used in measuring armature current, the point
common to their primaries should be where the ground connection is made, unless they are insulated to
withstand full line-to-line armature voltage. If the armature circuit is not solidly grounded, then high-
voltage insulation equipment should be used between the shunts or current transformers and the data
recording devices.

All protective relays that could cause the field circuit breaker to trip should be made inoperative. A
discharge resistor of sufficiently low value should be used so that if the field circuit breaker were to trip,
the voltage across the field winding would not be excessively high.

The electric or mechanical integrity of the machine is not a major consideration during standstill frequency
response (SSFR) testing. Those factors, which experience has shown should be at least recognized, are
spelled out in Clause 12 on SSFR testing.

89
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

IEEE Guide for Test Procedures for

Synchronous Machines
Part II—Test Procedures and Parameter
Determination for Dynamic Analysis

9. Applications of machine electrical parameters

9.1 General

The original background work on IEEE Std 115 was published in 1945, and the first “official” version of
the standard is dated 1965. Prior to the period from 1945 to 1965, synchronous machine transient and
subtransient quantities had been originally developed and applied to determine fault currents under both
balanced and unbalanced conditions.

Some of these short-circuit “parameters” were also converted for use in stability studies by using analog (of
network) computers, starting in the 1930s and continuing up to the 1950s. These relatively simple analogue
studies considered a synchronous machine’s stability response to be provided by a constant voltage behind
a transient reactance. This simplification provided suitable answers to a majority of power system analysts.
Exceptions to this practice were studies conducted using mechanical or electronic differential analyzers.

The advent of high-initial-response excitation systems, along with the development of digital computers,
brought forth more sophisticated modeling of the dynamic properties of both machines and their associated
excitation controllers. In addition to time-domain digital simulations, small-signal, linear eigenvalue
analyses became prevalent for synchronous machines connected through power system networks.

All this analytical activity commencing around the time of the first publication of IEEE Std 115
accentuated the requirements for additional methods for determining synchronous machine stability or
electrical quantities. Such features as determining characteristic quantities (time constants and reactance) or
stability (network) models for both direct-axis and quadrature-axis representation became the norm. While
second-order models were used extensively from 1945 to 1965, third-order (or higher order) models
appeared to be required for some types of excitation-system studies. These requirements led to IEEE
Std 115A (incorporated in the 1995 edition of the guide) for describing SSFR testing. This supplement
dealt with testing of turbo alternators, particularly for parameter determination and third-order direct-axis
and quadrature-axis model development.

Clause 10 discusses the synchronous machine quantities required for system studies and analysis of steady-
state operation.

90
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

Procedures for testing and parameter determination methods for short-circuit tests are given in Clause 11,
while similar tests and stability model development through SSFR methods are given in Clause 12.

Synchronous machine electrical parameters are used in a variety of power system problems. In the steady
state, a knowledge of the direct-axis synchronous reactance, Xdu, and the quadrature-axis synchronous
reactance, Xqu, is required to determine, after appropriate adjustments for saturation, the maximum value of
reactive power output, Q, for certain armature terminal conditions. Such maximum reactive power outputs
are basically a function of the field excitation. Calculation of field excitation using saturated values of Xdu
and Xqu is discussed in Clause 5. The reactive-power output capabilities of generators are used in load-flow
studies for control of power systems (grid) voltages and supply of load reactive powers. As a corollary to
this, the above mentioned synchronous reactances are used to determine the approximate values of reactive
power, which can be absorbed by a synchronous machine. This is sometimes studied in load-flow studies
under system minimum-load conditions.

The transient or subtransient reactances whose derivation is discussed in Clause 11 are used in relay
application studies of system protection. Included in this area of analysis are circuit-breaker fault
interruption requirements. The effect of magnetic saturation on synchronous reactance must also be
accounted for. For the purposes of specification and/or test, the values of transient or subtransient reactance
shall be determined for one or more nominal conditions, i.e., rated voltage or rated current. This is also
discussed in IEEE Std 1110.

Since the correction for other conditions is usually not large, the nominal values may be used, or the
correction may be estimated or determined approximately from empirical curves based upon tests of typical
machines. However, when agreed upon, values for other conditions may be determined by test, as described
in Clause 10, Clause 11, or Clause 12.

Synchronous machine reactances in general are substantially equal in magnitude to their corresponding
impedances and are usually so considered in interpreting test results, with the resistance components
disregarded.

In all of the above-mentioned clauses, the distinction between test procedures and parameter determination
has been stressed.

9.2 P.U. quantities

9.2.1 Comments

Subsequent clauses of this guide provide methods for determining machine reactances and resistances in
per unit because this form is the most often desired by the user and may constitute the basis for guarantees
when included in contracts. Time constants are evaluated in seconds. (See IEEE Std 86-1987.)

To avoid error in the use of p.u. quantities, care should be used in defining clearly the p.u. base used for
each quantity and making sure all base quantities are consistently chosen. The preferred procedure is to
select only three base quantities and to derive the others from these three. The three normally chosen are
base three-phase power, SNΔ, base line-to-line voltage, ENΔ, and base frequency, fN. Each physical
measurement is expressed in per unit when so desired by dividing the physical value by the corresponding
base quantity, expressed in the same units. Conversely, any quantity in per unit can be converted to
physical units by multiplying by the base value. Any p.u. quantity expressed on one base can be converted
to another base by multiplying by the old base quantity and dividing by the new.

P.U. quantities may be expressed in either peak or rms values. In this guide, rms values are normally used.

9.2.2 Base power

For a generator, base three-phase power (SNΔ) is taken as the rated kilovoltampere output of the machine.

91
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

For a motor, base three-phase power is taken as the apparent power input to the machine when operating at
rated voltage and power factor and delivering rated load.

The base power is usually expressed in kilovoltamperes, but multiple or submultiple units, such as
megavoltamperes and voltamperes can be used, with appropriate modifications in the equations (see 9.2.4).

Single-phase power measurements, as may be needed in a test procedure, are normally expressed in per
unit of the base power for one phase. Base single-phase power, SN, is derived from the base three-phase
power, SNΔ, by Equation (9-1).

S NΔ
SN = base single-phase power, in kilovoltamperes, or megavoltamperes (9-1)
3
where

SNΔ is the base three-phase power, in kilovoltamperes, or megavoltamperes

9.2.3 Base voltage and current

Base line-to-neutral voltages and other single-phase voltages, as may be specified in this guide, are
expressed in per unit by dividing by the base line-to-neutral voltage, EN. The base line-to-neutral voltage is
obtained from the base line-to-line voltage by Equation (9-2).

E NΔ
EN = base line-to-neutral voltage, in volts or kilovolts (9-2)
3

where

ENΔ is the base line-to-line voltage, in volts or kilovolts

Base line-to-line voltage, ENΔ, is normally selected equal to the rated line-to-line voltage, E(LL). Both the
volt and kilovolt (rms) are in common use as the unit in which the base voltage is expressed. In this guide,
the volt (rms) will normally be used, but the kilovolt (or other multiple) will be used with appropriate
modifications in the equations. A line-to-line voltage (whether alternating or direct) is expressed in per unit
by dividing its value by the base line-to-line voltage, expressed in the same units.

For balanced sinusoidal conditions, the p.u. values of corresponding line-to-line and line-to-neutral voltages
are the same.

Base line current, IN, is obtained from the base power and base voltage and is equal to the current per line
when the circuit is carrying base power at base voltage. It may be derived either from the base three-phase
power and base line-to-line voltage or from the base single-phase power and base line-to-neutral voltage by
Equation (9-3). For wye-connected machines, a p.u. base current for one phase of the wye winding denoted
by IN would be as expressed in Equation (9-3).

1000S NΔ 1000 S N
IN = = base line current amperes (9-3)
3E NΔ EN

where

SNΔ is the base three-phase power, in kilovoltamperes

SN is the base single-phase power, in kilovoltamperes

92
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

ENΔ is the base line-to-line voltage, in volts

EN is the base line-to-neutral voltage, in volts

Alternatively,

S NΔ
IN = base line current kiloamperes (9-4)
3E NΔ

where

SNΔ is the base three-phase power, in megavoltamperes

ENΔ is the base line-to-line voltage, in kilovolts

For delta-connected machines, a base current for one phase of the delta winding, denoted by INΔ, would be
appropriate for expressing individual winding currents in per unit. If needed, it would be found from
Equation (9-5).

S NΔ
I NΔ = base delta current kiloamperes (9-5)
3E NΔ

where the quantities are expressed in the same units as in Equation (9-4).

Each current is expressed in per unit by dividing its value by the corresponding base, in the same units.

If instantaneous currents or voltages are to be expressed in per unit, it is recommended that the same base
values be used as for rms currents and voltages. If this practice is followed, the usual relations between
instantaneous, average, and rms currents or voltages will apply regardless of whether the results are
expressed in physical values or in p.u. values.

9.2.4 Base impedance

E ⎛ EN ⎞⎛ E N ⎞ (E N ) 2

Z N = N base impedance, ohms = ⎜⎜ ⎟⎟⎜⎜ ⎟⎟ = (9-6)

IN ⎝ IN ⎠⎝ E N ⎠ EN I N

The base impedance is the value of impedance that would allow base line current to flow if base line-to-
neutral voltage were impressed across it, as expressed by Equation (9-6).

The results can also be expressed in terms of the base power and base voltage by substituting from
Equation (9-2) and Equation (9-3) into Equation (9-6), as shown by Equation (9-7).

ZN =
(E NΔ )2 =
(E N )2 base impedance, ohms (9-7)
1000S NΔ 1000S N

where the quantities are expressed in the same units as in Equation (9-3).

The same base shall be used regardless of whether the impedance is a resistance, a reactance, or any
combination.

93
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

9.2.4.1 Additional comments on stator and rotor base impedances

In the latter part of this subclause, the nomenclature used for stator p.u. voltage is Ea, and the nomenclature
for stator p.u. current is Ia. This practice corresponds to the nomenclature used in IEEE Std 1110. It is
also used in 5.2.2.1 of this guide. Note also that base voltage is expressed in 9.2.3 as ENΔ or EN
[see Equation (9-2)]. Base current is expressed as IN [see Equation (9-3)]. An alternate expression
to Equation (9-7) for stator base impedance, applied especially for larger size machines, is given in
Equation (9-8).

ZN =
(E NΔ )2 base impedance, ohms (9-8)
S NΔ

where

E NΔ is the machine stator terminal base, in kilovolts, line to line

S NΔ is the three-phase of the machine, in megavoltamperes
Z N can also be expressed in a single phase basis as follows:

ZN =
( EN )
2
, base impedance, ohms (9-9)
SN

where

EN is the machine stator terminal base, in kilovolts, line-to-neutral

SN is the single-phase of the three-phase machine, in megavoltamperes

The base impedance ZN is in terms of single phase, line-to-neutral ohms. This practice holds true
irrespective of whether one is calculating on a single-phase, line-to-neutral basis or calculating on a three-
phase, line-to-line basis.

In some of the issues being discussed in Clause 12, the field circuit base, in ohms, referred to the stator is
given as shown in Equation (9-10).

machine voltamperes (three phase) 3( E N I N )

Z fdbase = = ohms (9-10)
(i fdbase )
2
(i fdbase )
2

where

EN and IN are as defined in Equation (9-2) and Equation (9-3)

The ifdbase is the field current excitation, in amperes, required to induce a p.u. voltage Ea on the open-circuit
air-gap line of the machine equal to Ia Xadu. Ea is in per unit of ENΔ or EN kV. Ia is 1.0 p.u. stator current on
the machine stator current base of IN. Xadu in per unit is defined in 10.2.1.

The convention is to per-unitize field circuit and the rotor-equivalent circuit resistances and inductances
and to refer these physical resistance and inductance values to p.u. values as viewed from the stator
terminals. In so doing, direct-axis and quadrature-axis stability models can be readily applied and analyzed
in large power system studies.

94
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

There is a relationship between the ifdbase and the more commonly encountered Ifdbase. This relationship was
originally discussed by Rankin [B42] in great detail. Rankin designated the ifdbase as the reciprocal system.
Rankin developed this system by indicating that the stator-to-field and field-to-stator p.u. mutual
inductances were equal or reciprocal in value. For a discussion of an alternate (nonreciprocal) Ifdbase, see
Canay [B8]. This nonreciprocal base field current, in amperes, is that required to induce 1.0 p.u. V (or kV),
Ea, on the open-circuit air-gap line.

The relationship between the two field current bases is shown in Equation (9-11).

i fdbase = I fdbase ( X adu ) (9-11)

where

Xadu is the unsaturated p.u. value of the direct-axis magnetizing reactance

The Equation (9-11) relationship is also shown graphically in Figure 32 and Figure 33. This conversion
from the reciprocal system to the nonreciprocal system is also discussed more fully, with numerical
examples, in IEEE Std 1110.

9.2.5 Base frequency

The base frequency is regularly selected as equal to the rated frequency. From this value, the base electrical
angular velocity, ωN, and the base time constant, tN, if needed, are obtained by Equation (9-12).

1
ω N = 2πf N , rad/s or t N = (9-12)
fN

A time constant, in seconds, may be converted to per unit by dividing by tN. However, in accordance with
usual practice, this guide is arranged so that the formulas express time constants in seconds.

Figure 32—P.U. field excitation reciprocal excitation scale, Xadu = 1.82

95
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

Figure 33—P.U. field excitation nonreciprocal excitation scale

96
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

10. Tests for determining parameter values for steady-state conditions

10.1 Purpose

Some of the steady-state tests suggested in this clause are required for analyzing the performance of a
synchronous machine under normal operating conditions. Under such conditions, changes in
megavoltampere output or in terminal voltage conditions are relatively small or slow. In addition, machine
conditions are balanced; that is, all three phases are carrying the same current, and each of the three-phase
voltages are equal and 120° apart in electrical displacement.

Unbalanced but relatively steady conditions are also of interest, even though they can sometimes be
tolerated only for a few seconds or at most a few minutes. Negative or zero sequence reactances or
resistances are used for analyses of these conditions. Such quantities affect the performance of the machine
and, in this sense, could also have been considered in Part I of this guide. However, since some of these
sequence quantities are used in stability studies or in dynamic analyses, they are included in Part II. In any
case, tests for such parameters sometimes need to be performed to ensure compliance with design values.

This clause starts with an investigation of synchronous reactance and concludes with recommended
practices for determining internal electrical (load) angles. For single-phase machines or for polyphase
machines of other than three phases, modifications to some tests may be required, but test procedures can
usually be determined after consultations with designers or manufacturers of such machines.

10.2 Instrumentation

The instrumentation required for most of the tests outlined in this clause is the usual array of current and/or
voltage transformers and the associated ammeter, voltmeter, or wattmeter configurations required in three-
phase measurements. Phase-angle measurements require special instrumentation as described in 10.8.2.

10.2.1 Types of parameters to be determined

The following is a list of quantities, some of which are derived (usually in per unit) from steady-state tests.
Parameters are listed in the order in which the test procedures occur and are described in 10.3 to 10.8 (see
also The IEEE Standards Dictionary [B29]).

X du Unsaturated direct-axis synchronous reactance, as defined by test

X ds Some particular saturated value of Xdu, which depends on synchronous machine terminal voltage
as well as machine megavoltampere rating and power factor
X adu Unsaturated direct-axis synchronous mutual reactance, which is the portion of Xdu assumed to be
subject to saturation. X du = X adu + X l . X l is the synchronous machine stator leakage
reactance.
X ads The saturated portion of X ds , where X ds = X ads + X l
X qu Unsaturated quadrature-axis synchronous reactance
X qs The quadrature-axis synchronous reactance, as defined by tests
X2 Negative-sequence reactance, as defined by tests
R2 Negative-sequence resistance, as defined by tests
X0 Zero-sequence reactance, as defined by tests
R0 Zero-sequence resistance, as defined by tests

97
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.
 IEEE Std 115-2009
IEEE Guide for Test Procedures for Synchronous Machines
Part II—Test Procedures and Parameter Determination for Dynamic Analysis

SCR Short-circuit ratio, as defined by test

δ Internal electrical angle

10.3 Direct-axis synchronous reactance, Xd

For 10.3 and 10.4, the determination of parameters follows immediately after the description of the test
procedures.

For the definitions of direct-axis synchronous reactance and impedance, see The IEEE Standards
Dictionary [B29]. The definitions are not test-related and are based on rated armature current.

For machines of normal design, the magnitude of the direct-axis synchronous reactance is so nearly equal
to that of the direct-axis synchronous impedance that the two may be taken to have the same numerical
value.

The unsaturated direct-axis synchronous impedance can be derived from the results of the open-circuit
saturation test (see 4.2.4) and the short-circuit saturation test (see 4.2.7). This synchronous impedance in
per unit is equal to the ratio of the field current at base armature current, from the short-circuit test, to the
field current at base voltage on the air-gap line (see 4.2.5).

In terms of the quantities identified in Figure 17 (see 5.2.2.1), synchronous reactance can be calculated
using Equation (10-1). In Figure 17, base values are plotted as 1.0 p.u. Figure 17 can also be plotted with
base values in actual amperes or volts.

I FSI
X du = p.u. (10-1)
I FG

where

X du is the unsaturated synchronous reactance

I FSI is the field current corresponding to the base armature current on the short-circuit saturation
curve
I FG is the field current corresponding to base voltage on the air-gap line

Saturated values of synchronous reactance, Xds, depend upon synchronous machine operating conditions.
As noted in Clause 5, Xd is assumed to be composed of Xad, the stator to rotor mutual reactance, plus Xl the
stator leakage reactance.

Thus, in general,

X d = X ad + X l

where

X ad is the saturated portion of X d

As a corollary,

X du = X adu + X l

98
Copyright © 2010 IEEE. All rights reserved.

Authorized licensed use limited to: J.R.D. Tata Memorial Library Indian Institute of Science Bengaluru. Downloaded on October 01,2021 at 15:30:47 UTC from IEEE Xplore. Restrictions apply.