3.9 negative sequence reactance the quotient of the reactive fundamental component of negative sequence armature voltage, due to the sinusoidal negative sequence armature current at rat
General
Instrumentation requirements
Measuring instruments and their accessories, including measuring transformers, shunts, and bridges, must have an accuracy class of at least 0.5 as per IEC 60051, unless specified otherwise For the determination of direct current (d.c.) resistances, the required accuracy class is a minimum of 0.2.
The accuracy class for the oscillographic measuring and other recording equipment should be chosen with due regard to the rating of the machine to be tested
The rotation speed can be measured using a stroboscopic method, tachometers (either mechanical or electrical), or a frequency meter, whether the machine operates synchronously with another machine or independently.
Excitation system requirements
In synchronous machines equipped with brushless exciters, the excitation winding connects to the exciter armature winding through a rotating converter, typically a diode rectifier, eliminating the need for slip-rings Consequently, certain tests that involve measuring excitation current, supplying the field winding from an external source, or short-circuiting it may require special arrangements, such as installing temporary slip-rings on the shaft.
Test conditions
Synchronous machine tests must be performed on a fully assembled machine with all automatic regulation devices turned off, unless the test procedure specifies otherwise Additionally, devices that do not affect the parameter values are not required to be installed.
Unless otherwise stated, the tests shall be conducted at the rated speed of rotation
NOTE Test methods with the rotor at standstill may give results different from those received on a rotating machine, for example when damper winding quantities are dependent upon centrifugal forces
Winding temperatures are measured when
– the quantities to be determined by the test depend on temperature, or
– safety considerations require monitoring the temperature during tests
To ensure safety during testing, it is advisable to initiate tests only after the machine has been operated at no-load with standard cooling or has rested sufficiently to achieve a low starting temperature Additionally, temperatures should be closely monitored or pre-determined to allow for the test to be halted before reaching excessive levels.
During the test, the machine winding connection, as a rule, should be as for normal working
The determination of all quantities is made with star connection of the armature winding
When the armature winding is delta connected, the values obtained must align with those of an equivalent star-connected winding, unless specified otherwise by special connections like open delta.
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Per unit base quantities
All equations are presented in either SI units or per unit based on specified fundamental values, typically including rated voltage (\$U_N\$) and rated apparent power (\$S_N\$), along with the derived basic current.
In calculations, it is advisable to use physical values initially, converting them to per unit values later, with time expressed in seconds For characteristic calculations and diagram representations, the excitation current corresponding to the rated voltage on the no-load curve should be considered the fundamental value of the excitation current.
When the diagrams and characteristics are drawn, the currents and voltages may be designated in physical values
If a machine has several rated values, those taken for the basic values shall be stated
Unless otherwise stated, the above-mentioned system is accepted in this standard Small letters designate the quantities in per unit values, and capital letters designate physical quantities
In this standard for calculating synchronous reactances, the positive sequence armature resistance is generally regarded as negligible However, if the positive sequence armature resistance exceeds 0.2 of the measured reactance, the formulas should be treated as approximate.
Conventions and assumptions
This standard defines various quantities and their experimental determination methods based on the widely accepted two-axis theory of synchronous machines It approximates all circuits, including those additional to the field-winding and stationary circuits, using two equivalent circuits: one along the direct axis and the other along the quadrature axis The armature resistance is either neglected or considered only approximately.
As a consequence of this approximate machine representation, three reactances
This standard addresses transient phenomena by considering three reactances—synchronous, transient, and sub-transient—along the direct axis, along with two time constants: transient and sub-transient Additionally, it includes two reactances—synchronous and sub-transient—along the quadrature axis, as well as the armature short-circuit time constant.
The time constants are derived from the assumption of an exponential decrease in specific components such as currents and voltages In cases where the measured component does not exhibit a pure exponential decline, such as in solid rotor machines, the time constant should be understood as the duration needed for the component to reduce to approximately 36.8% (1/e) of its initial value.
Exponential decay curves corresponding to these time constants shall be considered as equivalent curves replacing the actual measured ones
NOTE 1 Frequently the conventional representation by means of three reactances and two time-constants is not satisfactory to describe the machine sufficiently, and higher order parameters should be added to the model This
Turbo type machines can have their models modified by parameters such as X and \( d^{\prime\prime\prime} \tau d \) The process for determining these parameters is detailed in this document, specifically in Annex B.
NOTE 2 This document provides methods to determine the quadrature axis transient parameters q q qo
X , , ′ ′ ′τ τ (see 6.15), though they are frequently not considered in conventional calculations when X q ′= X q is assumed.
Consideration of magnetic saturation
Synchronous machine quantities vary with saturation of the magnetic circuits In practical calculations, both saturated and unsaturated values are used
In this standard, the "saturated value" of reactances and resistances is defined as the rated (armature) voltage, while the "unsaturated value" is defined as the rated (armature) current, except for synchronous reactances, which have their unsaturated values taken as the low voltage values and saturated values as the rated voltage under load The saturated values of these quantities are influenced by the mode of operation.
The rated armature voltage reflects the magnetic state of the machine during a sudden short-circuit of the armature winding, occurring from a no-load rated voltage operation while the machine is running at its rated speed.
The rated armature current value refers to the condition where the fundamental alternating current (a.c.) component of the armature current matches the rated current.
No-load saturation and sustained three-phase short-circuit tests are essential for determining the unsaturated values of \$X_d\$ These tests, along with no-load and phase-shifting assessments, allow for the evaluation of both unsaturated and saturated \$X_d\$ values However, the saturated quantities obtained from these tests are not specific to the machine's operational mode and should only be used for comparative analysis across different machines subjected to the same testing conditions.
The negative excitation and low slip tests are used for unsaturated values The phase shifting test permits the unsaturated and saturated values of X q to be determined
The method of sudden three-phase short-circuit is preferred It permits saturated and unsaturated values of X / d to be determined
If the calculation method is used, the values of τ / do and τ / d obtained from the field current decay tests at rated speed (see 6.24 and 6.25) are preferred
A brushless machine can undergo sudden three-phase short-circuit tests and field current decay tests at rated speed, provided it is excited by its own or a separate exciter through temporary slip-rings on the rotor If the machine is excited from its own separately excited exciter, the voltage recovery test can be conducted without the need for slip-rings.
In a brushless machine, the value of \$X/d\$ is calculated using test values of the time constants \$\tau/do\$ and \$\tau/d\$ These values are obtained from field current decay tests conducted at standstill, with the armature winding open-circuited for \$\tau/do\$ and with two phases of the armature winding short-circuited for \$\tau/d\$.
The sudden three-phase short-circuit method is preferred It permits saturated and unsaturated values of X″d to be determined
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Applied-voltage methods are effectively interchangeable for determining the unsaturated values of \$X''_d\$ and \$X''_q\$, but they are generally impractical for saturated values due to the high current demands and the risk of overheating in the windings and solid components.
To determine X′d during a sudden short-circuit test, τ′d should also be assessed from the same test In other scenarios, the preferred method is to use the field current decay approach at rated speed while the armature winding is short-circuited.
When the time constant \$\tau_a\$ is less than one fundamental period, it is calculated based on the reduction of the aperiodic (d.c.) component of the armature winding current Conversely, if \$\tau_a\$ is greater than one period, the preferred measurement method involves assessing the decrease of the periodic component in the excitation winding current.
NOTE For synchronous compensators, the rated active power (output) is replaced by the rated apparent power
All the above-mentioned methods are practically equivalent The application of one or another method depends on the design and the apparent power of the machine under test.
Direct measurements of excitation current at rated load
I fN is the excitation winding current when the machine operates at rated values of voltage, current, power-factor and speed
Graphical methods are employed to assess the zero-power factor loading of the tested machine To accurately determine the rated excitation current through direct measurement under rated conditions, the machine must be excited using its own automatic regulation system This is crucial, as the excitation current can vary significantly when the machine is excited from its automatic system compared to when it is separately excited, particularly in machines equipped with static excitation systems.
NOTE In brushless machines direct measurement of the excitation current may be performed using temporary slip-rings.
Direct-current winding resistance measurements
A stable d.c supply, such as a battery or generator, can be utilized to measure d.c resistance using either the voltmeter and ammeter method, which is recommended, or the bridge method.
The resistance shall be measured directly at the winding terminals with the rotor at rest
The single bridge method is not permissible for measuring resistances less than 1 Ω
Armature winding resistance should be measured individually for each phase If direct measurement of phase resistance is not possible, it is necessary to measure the resistance between each pair of line terminals of the armature winding.
In measuring the d.c resistance of the armature or of the excitation winding by
The bridge method requires a minimum of three readings, each involving a disturbance to the bridge balance It is essential to measure the resistance at the slip-rings or winding terminals to exclude the resistance of the brushes and their contacts from the results.
– the voltmeter and ammeter method, it is recommended to take three to five readings at various steady values of the current
During d.c resistance measurements, it is essential to ensure that the winding temperature rise does not exceed 1 K, assuming adiabatic heating To calculate the adiabatic heating, use the appropriate formula.
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= Δ θ K/s where j is the current density during test, in amperes per mm 2 ; c is a constant, equal to 200 for copper and 86 for aluminium
If the winding heating is unknown, the current should be not more than 0,1 of the rated winding current and should be supplied for not longer than 1 min
For accurate measurements, it is crucial that the readings from the instruments are stable at the moment of measurement, ensuring that any transient fluctuations in both the instruments and the circuits being assessed have dissipated.
The winding temperature during the measurements should be determined by means of built-in or embedded temperature detectors where fitted
Thermometers and thermocouples used for contact measuring the winding temperature should have been in place for not less than 15 min and should be protected from any outside influence
The identification numbers of the instruments should be recorded, in order to use the same instruments when performing the heat test.
No-load saturation test
Test procedure
The no-load saturation test can be performed in three ways: a) by operating the test machine as a generator using a prime mover, b) by running the machine as a motor without any shaft load from a symmetrical three-phase voltage source, or c) during the machine's retardation phase.
During the no-load test, it is essential to adjust the excitation in gradual steps from high to low voltage, utilizing evenly distributed points Ideally, this should start from the voltage level corresponding to the excitation at rated load, but it must not drop below 1.3 times the rated voltage of the machine being tested, continuing down to 0.2 times its rated voltage, unless the residual voltage exceeds this value.
Measure the residual voltage of the generator when the excitation current is decreased to zero
It is preferred to conduct test a) with a d.c calibrated prime-mover, as it also permits the no- load losses to be determined during the test
When using test b), it is also necessary to measure armature current At each voltage step, readings shall be recorded for minimum armature current that corresponds to unity power- factor
When conducting test c), the deceleration rate must not exceed 0.04 of the rated speed per second If the machine's deceleration exceeds 0.02 of the rated speed per second, a separate excitation source is necessary for stable testing Prior to disconnection from the line, the machine should be excited to at least 1.3 times the rated voltage The excitation is then gradually reduced in steps, with speed (frequency) readings taken at each step.
The retardation test will be conducted multiple times to ensure all necessary steps are completed, utilizing a constant excitation current This procedure is intended for internal use at the specified locations of MECON Limited in Ranchi and Bangalore, as supplied by the Book Supply Bureau.
– for test b), minimum armature current that corresponds to unity power-factor;
No-load saturation characteristic determination
To plot the armature open-circuit winding voltage at the terminals against the excitation current at rated speed, refer to Figure 8 If the no-load characteristic intersects the axis above the origin due to high residual voltage, a correction is necessary This involves projecting the straight portion of the no-load curve, known as the air-gap line, to its intersection with the abscissa axis The length on the abscissa cut by this projected curve indicates the correction value to be added to all measured excitation current values.
When the test frequency differs from the rated value, all the measured voltage values shall be referred to the rated frequency.
Sustained three-phase short-circuit test
Test procedure
The sustained three-phase short-circuit test can be performed in three ways: by operating the test machine as a generator using a prime mover, by applying a retardation to the test machine, or by running the test machine as a motor.
To ensure accurate testing, the short-circuit should be positioned near the machine terminals, with the excitation current applied only after the short-circuit is closed It is important to take one of the readings at a current level that is close to the rated armature current.
It is preferred to conduct test a) with a d.c calibrated prime-mover, as it also permits the short-circuit losses to be determined during the test
Record simultaneously excitation current and armature line current
NOTE 1 The speed of rotation (or frequency) may differ from the rated value but should not fall below 0,2 of rated value
When conducting test b), the deceleration rate must not surpass 0.10 of the rated speed per second If the machine's deceleration exceeds 0.04 of the rated speed per second, an external excitation source is necessary.
In test c), the machine functions as a synchronous motor at a fixed voltage, ideally around one-third of the normal voltage, while ensuring stable operation at the lowest possible value The armature current is adjusted by controlling the field current, varying it in approximately six steps between 125% and 25% of the rated current, including one or two measurements at very low current levels.
NOTE 2 The maximum test current value, traditionally set at 125 %, should be obtained from the manufacturer as stator cooling may not permit operation in excess of 100 % rated current without damage
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For each point taken in descending order (for more uniform stator coil temperatures), record armature current, armature voltage and field current.
Three-phase sustained short-circuit characteristic
The relationship between the armature short-circuited winding current and the excitation current is drawn from the data of the three-phase sustained short-circuit test (6.5.1)
Plot the armature line current measured at the terminals (ordinate) versus the excitation current (abscissa) at rated speed (frequency) as shown in Figure 8.
Motor no-load test
The test is conducted as in 6.4.1 b), i.e with the machine under test operating as a motor, with no-load on the shaft, but with zero excitation-winding current
To obtain the unsaturated value of the reactance X d , the value of the terminal voltage of the machine should not exceed 50 % to 70 % of the rated value
Phase shifting test
The test is performed using one of two methods: either by operating the test machine with a standard synchronous motor and connecting its armature winding to a low-voltage supply of the same frequency via a phase shifter, or by using a synchronous motor equipped with excitation windings in both the direct and quadrature axes, with the armature winding of the driven machine linked to a symmetrical low-voltage supply of the same frequency as the synchronous motor.
The current in the test machine varies depending on the position of the pole axis between a minimum value corresponding to X d and a maximum value corresponding to X q
To measure the maximum and minimum values of armature current and the corresponding terminal voltage of a synchronous motor, one can either operate the phase shifter (method a) or vary the excitation in both axes (method b).
During measurements, it is essential to keep the excitation winding open-circuited To prevent potential damage when measurements are not being conducted, the excitation winding should be short-circuited or connected through a discharge resistance.
When using method a), the phase shifter shall be able to shift the armature applied voltage by not less than 180 electrical degrees
In method b), the driving motor's power is influenced by the voltage applied to the armature winding of the tested machine, which generates torque as it transitions between positions.
To determine unsaturated values of reactances X d and X q , the value of the applied voltage should not exceed 0,5 p.u of the rated value
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Over-excitation test at zero power-factor
The over-excitation test at zero power-factor is performed with the machine functioning either as a generator or a motor In generator mode, the active power must be zero, while in motor mode, the shaft load should also be zero.
The excitation current is measured during the test, ensuring that the voltage and armature current values differ by no more than ± 0.15 per unit from the rated values, while operating at zero power-factor with over-excitation.
The over-excitation test at zero power-factor and rated values of voltage and armature current is preferred.
Negative excitation test
The test is performed with the machine running without load alongside the grid The excitation current is gradually decreased to zero, reversed in polarity, and then increased until the machine slips by one pole pitch.
NOTE This test is not suitable for permanent magnet machines, as it requires readings with either excitation winding open-circuited or at zero excitation current
Record: voltage, armature current and excitation current up to the moment when the machine begins to slip.
On-load test measuring the load angle
The test is performed with the machine running in conjunction with the grid, ensuring that the loading of the machine is at least 0.5 of the rated active load at the specified power factor.
Record: armature current and voltage, active power or directly measured cos φ, field current and load angle
NOTE Load angle δ is the internal angle between the vectors of terminal voltage and e.m.f., the latter indicating the q-direction.
Low slip test
During the low slip test, a subnormal symmetrical three-phase voltage ranging from 0.01 U_N to 0.2 U_N is applied to the armature terminals of the machine being tested, ensuring that the machine does not engage The excitation winding must be open-circuited, and the rotor should be driven by a prime mover at a slip of less than 0.01, or significantly lower for solid rotor machines, to minimize the impact of induced currents in the damper circuits during synchronous operation on the measurements.
To prevent potential damage during the switching on and off of the supply, the excitation winding must be short-circuited or connected through a discharge resistance Measurements of armature current, voltage, slip-ring voltage, and slip should be taken using indicating instruments or recorded with an oscilloscope If the residual voltage prior to testing exceeds 0.3 times the supply test voltage, it is necessary to demagnetize the rotor This can be achieved by connecting the field winding to a low-frequency source with a current approximately 0.5 times the no-load rated voltage excitation current of the machine being tested, while gradually reducing both the amplitude and frequency if feasible.
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NOTE This test is not suitable for permanent magnet machines, as it requires readings with either excitation winding open-circuited or at zero excitation current.
Sudden three-phase short-circuit test
The test is performed at rated speed by applying a short-circuit to the armature winding while operating at the specified voltage under no-load conditions Typically, the machine's excitation is provided by its own separately-excited exciter.
If the internal exciter of a machine is unavailable, a separate exciter can be utilized, and for brushless machines, temporary slip rings may be necessary The rated current of the external exciter must be at least double the no-load field current of the machine being tested, and its armature resistance should not exceed that of the main machine exciter It is essential that this exciter is separately excited.
Simultaneously short-circuit all three phases, ensuring that the phase contacts close within 15 electrical degrees of each other This limit can be exceeded during testing when the armature d.c component is not significant To measure the short-circuit current, utilize non-inductive shunts, air-cored transformers, or appropriate current transformers It is important to use current transformers specifically for a.c current components, selecting them so that the initial value of the sub-transient component of the short-circuit current aligns with the straight portion of the transformer characteristic.
NOTE 2 For machines with rated frequencies less than 60 Hz, d.c shunts may be used
Recording must persist for at least 3τ′ d after a short circuit, and steady state values should be captured by restarting the oscillogram once stable conditions are achieved If prior tests on similar machines indicate an exponential decay of the current value, shorter oscillographic records may be acceptable.
The air-cored transformer is connected to the oscilloscope through an integrating amplifier
When it is required to determine the maximum aperiodic and periodic values of short-circuit current components only, an integrating galvanometer may be used
The total resistance of measuring instruments and their leads in the secondary circuit of current transformers must not exceed the rated values specified for that particular type of transformer.
To determine the quantities related to the unsaturated state of the machine, tests are conducted at various armature voltages ranging from 0.1 to 0.4 of the rated value The results from each test are plotted against the initial values of alternating current (a.c.) transient or sub-transient armature currents This relationship allows for the extraction of the necessary quantities at the rated armature current value.
To achieve values that reflect the saturated state of the machine, the test is conducted with the rated voltage applied to the machine's terminals prior to short-circuiting the armature winding.
When the sudden short-circuit test cannot be performed at rated armature voltage, it is recommended that the tests should be conducted at several armature voltages (e.g 30 %,
The rated armature voltage is determined by conducting tests at 50% and 70% of the rated voltage, with the resulting quantities plotted against the open-circuit voltage By applying the extrapolation method, the approximate rated armature voltage can be accurately identified before short-circuiting occurs.
Record immediately before the short-circuiting:
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Record oscillograms of the armature current in each phase and excitation current during the short-circuiting period Data from oscillograms are analysed according to 7.1.2.
Voltage recovery test
Operate the test machine at its rated speed, ensuring the armature winding is short-circuited by a circuit breaker Set the excitation current to a value that aligns with the linear section of the no-load saturation curve, typically not exceeding 0.7 of the rated open-circuit armature voltage.
In the event of a sustained short-circuit, it is essential to disconnect all three phases almost simultaneously, ensuring that the currents are interrupted within angles of θ ≤ 0.5·τ’’d (where τ’’d is measured in electrical degrees) and no later than 180 electrical degrees Additionally, oscillographic records are necessary, capturing the initial high-speed segment of one line-to-line voltage recovery and one armature current.
This test can be conducted on a brushless machine if it has temporary slip-rings for excitation from a separate exciter, or if the machine can be excited by its own separately excited exciter.
Record immediately before disconnecting short-circuit:
Record oscillograms of the armature current in each phase and excitation current after switching off the short-circuit
Data from oscillograms are analysed according to 7.1.3.
Suddenly applied short-circuit test following disconnection from line
A three-phase short-circuit test can be performed during the machine's deceleration, as long as the rate of deceleration does not exceed 0.05 of the rated speed per second.
Before disconnecting from the line, the no-load machine is excited to a current value that achieves a unity power factor or a lower current value The excitation current and voltage are then measured and documented.
The machine must be short-circuited immediately after disconnection, ideally within 1 second The general requirements for the equipment, measuring devices, excitation, and quantity determination align with those specified in section 6.12.
In salient pole machines, the current can be increased to the rated value as long as the machine's vibration remains within permissible limits Conversely, for non-salient pole machines, the armature current is typically restricted to 50% of the rated value.
Direct current decay test in the armature winding at standstill test
The d.c decay test in the armature winding is conducted while the system is at a standstill, where a DC voltage is applied to the armature winding through a resistance This involves connecting two terminals while keeping the third open, or connecting two phases in parallel with the third in series Upon closing contactor K, the winding is short-circuited, leading to a decay in the current within the armature winding, and the entire current decay process is meticulously recorded.
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Figure 1 – Schematic for d.c decay test at standstill
The resistance of contactor K must be significantly lower than that of the armature winding resistance Additionally, the resistance in series with the voltage source should be selected to ensure that closing the contactor does not cause a substantial change in the source current, ideally limiting the variation to just a few percent.
The test involves positioning the rotor along both the direct and quadrature axes after initially magnetizing the machine's magnetic system by applying a direct current to the armature winding, leading to saturation Subsequently, a gradual demagnetization process is executed until reaching the test current value, followed by short-circuiting or disconnection after closing contactor K.
To effectively record the decay current, it is essential to obtain curves with varying time bases in a ratio of approximately 10:1:0.1 This approach allows for a detailed analysis of a) the initial portion of the decay, b) both the initial and middle portions of the curve, and c) the entire decay curve.
NOTE The test may also be carried out once, using equipment with three oscilloscope channels
During the test with the rotor positioned along the d-axis and the excitation winding short-circuited, the current in the winding is recorded using an oscilloscope, ensuring that there is no effective additional resistance in the excitation winding circuit.
During the testing process, the rotor is positioned in the q-axis, where the excitation winding is left open-circuited, and the induced voltage is measured using an oscilloscope This procedure is similarly applied when the rotor is aligned along the d-axis, maintaining the excitation winding in an open-circuited state.
After the test, the d.c resistance of the excitation winding circuit and the excitation winding itself are measured
Data from oscillograms are analysed according to 7.1.4.
Suddenly applied excitation test with armature winding open-circuited
The suddenly applied excitation test with armature winding open-circuited is performed on a machine running at rated speed with the excitation winding initially open-circuited Excitation
The machine is licensed to MECON Limited for internal use at the Ranchi and Bangalore locations, supplied by the Book Supply Bureau It is recommended that the machine's power is sourced from its own separately excited exciter.
If the built-in exciter is unavailable, a separate exciter can be utilized, provided its rated current is at least double the no-load excitation current of the machine being tested, and its armature resistance does not exceed that of the main machine's exciter Additionally, this separate exciter must be separately excited.
The exciter voltage is adjusted to a level within the linear range of the no-load saturation curve, typically not exceeding 0.7 times the rated open-circuit armature voltage The excitation winding of the tested machine is then abruptly connected to the exciter, while the armature voltage, excitation current, and exciter voltage are recorded for analysis.
The test is considered satisfactory if the exciter voltage remains substantially constant during the test
Data from oscillograms are analysed according to 7.1.5.
Applied voltage test with the rotor in direct and quadrature axis positions
AC voltage, at rated frequency, is applied to any two line terminals of the armature winding
The excitation winding is short-circuited with means to measure its current The duration of the voltage application should be limited to avoid serious overheating
NOTE In brushless machines, the excitation winding should be disconnected from the rotating rectifier and short- circuited
The rotor is gradually rotated to identify the angular positions that correspond to the maximum and nearly zero values of the excitation winding current, with the first position indicating the direct-axis and the second the quadrature-axis While the rotor remains stationary in these positions, measurements of supply voltage, armature-winding current, and power input are taken The excitation winding current is essential for determining the rotor's position, so high precision in measuring instruments is not required.
The test results may reflect the saturation of the damper winding leakage paths, influenced by the armature current When measured at rated current, these quantities are compared to the unsaturated values of the damper winding paths.
As a rule, the saturated values cannot be determined from this test because of the large current required and possible overheating of the windings and solid parts
When tests cannot be conducted at the rated armature current, it is essential to determine the quantities related to the unsaturated state of the machine through multiple tests using varying armature currents, specifically ranging from 0.2 to 0.7 times the nominal current (I_N).
The quantities are plotted against the armature current, and the required values are found by extrapolation
For machines with closed or semi-closed armature slots and closed damper winding slots, the supply voltage shall be not lower than 0,2 of the rated value.
Applied voltage test with the rotor in arbitrary position
To conduct the test, a.c voltage is applied in turn to each pair of the armature winding line terminals of the stationary machine under test
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The excitation winding shall be short-circuited and its current measured It is necessary that the rotor position remains the same for all three applications of test voltage
NOTE In brushless machines, the excitation winding should be disconnected from the rectifier and short-circuited
If necessary, the rotor should be braked The duration of the voltage application should be limited so as to avoid serious overheating of solid parts
The applied voltage, current and power input to the armature, and the excitation winding current are measured when applying a.c supply voltage to each pair of the terminals
Requirements for obtaining quantities referred to the unsaturated or saturated state of the machine are similar to those in 6.17.
Single phase voltage test applied to the three phases
To perform the test, a single-phase voltage is applied to the terminals of the three phases, which can be connected either in series or parallel, while the machine operates at or near its rated speed The configuration must ensure that the current flows in each phase in the same direction as defined by the zero sequence, and the excitation winding is short-circuited.
Record voltage U, current I and active power P.
Line-to-line sustained short-circuit test
To perform the line-to-line sustained short-circuit test, two line terminals are short-circuited, and the machine is operated at its rated speed using a prime mover.
Figure 2 – Circuit diagram for line-to-line short-circuit test
The short-circuit current I k2 , excitation current and the voltage between the open line terminals and one of the short-circuited terminals are measured U k2
To increase the accuracy of the measurements in the presence of voltage or current harmonics, it is recommended to measure active power P and reactive power Q
The measurements are taken at several values of the short-circuit current
To prevent significant overheating of solid components, the duration of a line-to-line sustained short-circuit with current exceeding 0.3 I_N should be restricted to the time necessary for instrument readings.
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Sudden line-to-line short-circuit
The line-to-line short-circuit test, performed at rated speed, is essential for determining negative phase-sequence reactance and resistance Prior to initiating the short-circuit, the machine must operate with the armature winding open-circuited.
The requirements for the excitation system and choice of measuring instruments shall be in accordance with those stated in 6.12
The terminal voltage of the machine, the excitation current and the rotor temperature are measured immediately before short-circuiting
To calculate negative-sequence reactance, oscillograms of the armature winding voltage at the terminals to be short-circuited, armature current in the same phases, and current in the excitation circuit are recorded The recording and analysis methods for these oscillograms must comply with section 6.12.
To determine X (2) for the machine's unsaturated state under rated current conditions, tests are conducted at various line-to-line voltages, akin to the sudden three-phase short-circuit test outlined in section 6.12 The necessary value is derived from the plotted results.
To achieve X (2) at the machine's saturated state, the voltage across the machine's terminals must match the rated value prior to the line-to-line short-circuiting of the armature (primary) winding.
If the test cannot be conducted at the rated voltage, it can be performed at lower armature voltages, as shown in 6.12, with X (2) calculated for each test These values are then plotted against the open-circuit voltage prior to short-circuiting, allowing for the determination of an approximate value corresponding to the rated voltage through extrapolation.
The short-circuit test must be conducted to ensure that the aperiodic component is nearly at its maximum, meaning the actual short-circuit should take place within 30° of the voltage zero crossing.
Line-to-line and to neutral sustained short-circuit test
To perform the line-to-line and neutral sustained short-circuit test, the armature winding is connected in a star configuration Two line terminals are short-circuited to the neutral, and the machine is operated at its rated speed while being excited.
Figure 3 – Circuit diagram for line-to-line and to neutral sustained short-circuit test
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Measurements are taken of the voltage U 0 from the open terminal to neutral and the current I 0 in the connection from the short-circuited terminals to neutral
To take into account the influence of harmonics, measurements are taken of active and reactive power
The measurements are taken at several values of the neutral current The current values and the duration of the test are limited by rotor overheating or vibration.
Negative-phase sequence test
The test involves applying a reduced symmetrical voltage ranging from 0.02 U_N to 0.2 U_N to the machine, which is driven at its rated speed This setup connects the machine to an external supply with a negative-phase sequence, effectively operating it as an electromagnetic brake with a slip of 2.
The excitation winding shall be short-circuited
If the machine's residual voltage exceeds 30% of the supply voltage, it is essential to demagnetize the rotor prior to testing During the test, measurements of voltage and current across all three phases, as well as the supply power, are taken.
Field current decay test, with the armature winding open-circuited
Test at standstill
7.17.4 DC decay in the armature winding at standstill 6.15 7.17.5 Suddenly applied excitation with open-circuited armature 6.16
Direct-axis sub- transient short-circuit time constant τ′′ d
7.18 Sudden three-phase short-circuit 6.12
Direct-axis sub- transient open-circuit time constant τ″ do
7.19.2 DC decay in the armature winding at standstill 6.15 Preferred
Quadrature-axis transient short-circuit time constant τ′ q
DC decay in the armature winding at standstill
Quadrature-axis transient open-circuit time constant τ′ qo
7.21.1 DC decay in the armature winding at standstill 6.15
Quadrature-axis sub- transient short-circuit time constant τ″ q 7.22.2 DC decay in the armature winding at standstill 6.15 Preferred Quadrature-axis sub- transient open-circuit time constant τ″ qo
7.23.1 DC decay in the armature winding at standstill 6.15
7.24.1 Sudden three-phase short-circuit 6.12 Preferred
Armature short-circuit time constant τ a 7.24.2 Calculation from test values -
Unit acceleration time τ J, stored energy constant H
Excitation current, re: rated armature short- circuit current i fk
Over-excitation at zero power-factor and variable armature (primary) winding voltage Sustained three-phase short-circuit test
7.28.2 Asynchronous operation at reduced voltage 6.33
7.28.3 Applied variable frequency voltage at standstill 6.34 7.28.4 DC decay in the armature winding at standstill 6.15 Preferred Short-circuit ratio K c 7.29 No-load saturation,
Sustained three-phase short-circuit
7.30.2 By diagram from no-load saturation characteristic and known i fN
Initial starting impedance of synchronous motors Z st
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Measuring instruments and their accessories, including measuring transformers, shunts, and bridges, must have an accuracy class of at least 0.5 as per IEC 60051, unless specified otherwise For the measurement of direct current (d.c.) resistances, the required accuracy class is a minimum of 0.2.
The accuracy class for the oscillographic measuring and other recording equipment should be chosen with due regard to the rating of the machine to be tested
The rotation speed can be measured using a stroboscopic method, tachometers (either mechanical or electrical), or a frequency meter, whether the machine operates synchronously with another machine or independently.
In synchronous machines equipped with brushless exciters, the excitation winding connects to the exciter armature winding through a rotating converter, typically a diode rectifier, eliminating the need for slip-rings Consequently, certain tests that involve measuring excitation current, supplying the field winding from an external source, or short-circuiting it cannot be performed without special modifications, such as installing temporary slip-rings on the shaft.
Synchronous machine tests must be performed on a fully assembled machine with all automatic regulation devices turned off, unless the test procedure specifies otherwise Additionally, devices that do not affect the parameter values are not required to be installed.
Unless otherwise stated, the tests shall be conducted at the rated speed of rotation
NOTE Test methods with the rotor at standstill may give results different from those received on a rotating machine, for example when damper winding quantities are dependent upon centrifugal forces
Winding temperatures are measured when
– the quantities to be determined by the test depend on temperature, or
– safety considerations require monitoring the temperature during tests
To ensure safety during testing, it is advisable to begin tests only after the machine has been operated at no-load with standard cooling or has rested sufficiently to achieve a low starting temperature Additionally, temperatures should be closely monitored or pre-determined to allow for the test to be halted before reaching excessive levels.
During the test, the machine winding connection, as a rule, should be as for normal working
The determination of all quantities is made with star connection of the armature winding
When the armature winding is connected in delta, the values obtained must align with those of an equivalent star-connected winding, unless specific configurations like open delta are indicated.
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All equations are presented in SI units or in per unit based on specified fundamental values, typically including rated voltage (\$U_N\$) and rated apparent power (\$S_N\$), along with the derived basic current.
In calculations, it is advisable to use physical values initially, converting them to per unit values later, with time expressed in seconds For characteristic calculations and diagramming, the excitation current at rated voltage on the no-load curve should be considered the fundamental value of the excitation current.
When the diagrams and characteristics are drawn, the currents and voltages may be designated in physical values
If a machine has several rated values, those taken for the basic values shall be stated
Unless otherwise stated, the above-mentioned system is accepted in this standard Small letters designate the quantities in per unit values, and capital letters designate physical quantities
In this standard for calculating synchronous reactances, the positive sequence armature resistance is generally regarded as negligible However, if the positive sequence armature resistance exceeds 0.2 of the measured reactance, the formulas should be treated as approximate.
This standard defines various quantities and their experimental determination methods based on the widely accepted two-axis theory of synchronous machines It approximates all circuits, aside from the field-winding, using two equivalent circuits: one along the direct axis and the other along the quadrature axis, while either neglecting armature resistance or considering it only approximately.
As a consequence of this approximate machine representation, three reactances
This standard addresses transient phenomena studies by considering three types of reactances: synchronous, transient, and sub-transient, along with two time constants—transient and sub-transient—on the direct axis Additionally, it includes synchronous and sub-transient reactances and one time constant (sub-transient) on the quadrature axis, as well as the armature short-circuit time constant.
The time constants are derived from the assumption of an exponential decrease in specific components such as currents and voltages In cases where the measured component does not exhibit a pure exponential decay, like in solid rotor machines, the time constant should be understood as the duration needed for the component to reduce to approximately 36.8% (1/e) of its initial value.
Exponential decay curves corresponding to these time constants shall be considered as equivalent curves replacing the actual measured ones
NOTE 1 Frequently the conventional representation by means of three reactances and two time-constants is not satisfactory to describe the machine sufficiently, and higher order parameters should be added to the model This
Turbo type machines can have their models modified by parameters such as X and \( d^{\prime\prime\prime} \tau d \) The process for determining these parameters is detailed in this document, specifically in Annex B.
NOTE 2 This document provides methods to determine the quadrature axis transient parameters q q qo
X , , ′ ′ ′τ τ (see 6.15), though they are frequently not considered in conventional calculations when X q ′= X q is assumed
Synchronous machine quantities vary with saturation of the magnetic circuits In practical calculations, both saturated and unsaturated values are used
In this standard, the "saturated value" of reactances and resistances is defined as the rated armature voltage, while the "unsaturated value" is considered the rated armature current However, for synchronous reactances, the unsaturated values are based on low voltage quantities, and the saturated values correspond to the rated voltage of the machine under load It is important to note that the saturated values of these quantities are influenced by the mode of operation.