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Underexcitation Protection based on Admittance Measurement Excellent Adaptation on Generator Capability Curves

Dr. Hans-Joachim Herrmann Siemens AG, PTD EA13 Nuremberg, GermanyDiego Gao Siemens Power Automation Ltd.(SPA), TS Nanjing, P.R.China

This contribution focuses on under-excitation protection and introduces the admittance measuringtechnique. The theoretical background is covered extensively to facilitate a clear description of the factorsassociated with under-excitation. Apart from deriving the stability limits the transformation of the capabilitydiagram to the admittance is described and consequently the admittance and impedance measuringtechniques are compared. After introducing the Admittance measuring technique and typical protectioncharacteristics some practical applications are described. These are primarily focused on the differentmethods for deriving the setting values. The simplicity of converting impedance setting values of existingrelays to admittance settings is also illustrated.

Keywords: Generator protection, numerical protection, under-excitation, static stability, impedancemeasurement, admittance measurement

1. Introduction

Under-excitation or a total loss of excitation can result from a short circuit or open circuit in the excitationcircuit, a mal-operation of the automatic voltage regulator, incorrect control of generators and transformers,or in the event of a generator connected to a system with capacitive load. In this context under-excitationmeans that the excitation of the synchronous machine is less than required for stable operation at aparticular power level. This excitation limit determines the steady state stability characteristic of thegenerator. If the excitation is not sufficient to provide the power demanded of the generator, then thisstability limit is exceeded. The machine will slip and thereby obtain the required excitation from theconnected three phase system.

Depending on the construction of the generator, nature of the excitation circuit, system conditions, amountof supplied power as well as the influence of voltage and power regulators (AGC), rotor acceleration, local

overheating in rotor and stator, over-voltages on the rotor, mechanical impact on the foundation and powerswings in the three phase system may result. To prevent, or at least limit the duration of these harmfuleffects an under-excitation protection is required to detect the cause (the under-excitation), and to initiate arapid tripping of the machine.

The protection function may be implemented in different ways. The impedance measurement [1, 2], is awidely applied measurement principle. Amongst other reasons this technique was chosen due to thewidespread and proven use of impedance measuring elements in electro-mechanical relays. Approximately35 years ago, Siemens however adopted a different route [3, 4]. A solution, which on the one hand may bedirectly derived from the capability diagram of the generator and on the other hand is immune tofluctuations of the generator voltage was found. This requires a transformation of the generator diagram tothe admittance plane and the processing of admittance measured values.

2. The Capability Diagram of Generators

To aid the following dissertation, the definition of the fundamental electrical quantities is provided hereunder:

- Sign convention: exported power (P, Q >0) is positive- Apparent power: symbol S and has the dimension VA (kVA, MVA)- Active power: symbol P and the dimension W (kW, MW)- Reactive power: symbol Q and the dimension Var (kVar, MVar)- When per unit (p.u.) values are used, the generator nominal values such as the nominal

apparent power S BNB, nominal voltage V BNB, and nominal current I BNB are used for the conversion.

According to the Cartesian co-ordinate system definition (x-axis = real component and y-axis = imaginarycomponent), the first quadrant defines the operating range (P > 0 and Q > 0) of the generator. In the eventof under-excitation, operation is in the 4

P

thP quadrant (P > 0 and Q < 0). Graphic representation of the under-

excitation protection takes place in the 4Pth

P quadrant. To avoid neck strain, the diagram is often rotated tothe left and mirrored in text books (refer to figure1). The author adopts this form of representation.


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Steady-statestability limit

Steady-statestabilitylimit

under-excited

under-excited

over-excitedover-excited

+ P(W)

+ P(W)

+ Q(Var)

+ Q(Var)

Definition Used in technical papers

Operatingrange

Operatingrange

Figure 1: Alternative representation of the capability diagram

The static stability limit is derived from the equations for the active and reactive power of the machine [5, 6].Equation (1) and equation (2) are the general defining equations and may be used directly for the salientpole generator, which has different direct axis and quadrature axis reactance. Due to the difference in x BdB

and xB

qB

a reluctance response circle with the diameter ( xx

x-x

Vqd

qd2

) results. This circle indicates the steady

state power that the generator can produce with zero excitation (E = 0).

sin2xx

x-x

2

Vsin

x

VEP

qd

qd

2

d

+= (1)

)sinx

x-x(1

x

Vcos

x

VEQ 2

q

qd

d

2

d

+= (2)

with: E rotor voltage (e.m.f.) p.u.V terminal voltage of the generator p.u.x

BdB synchronous direct axis reactance p.u.x

B

qB

synchronous quadrature axis reactance p.u.

rotor angle

In the case of turbo generators the equations (1), (2) are simplified as the direct axis (x BdB) and quadrature

axis (xBqB) reactance are approximately the same. The theoretical stability limit is = 90. Accordingly the

limit value in the derived representation is given by the direct axis reactance x BdB. For the salient polegenerator, this limit is dependent on the reactances x

BdB and xBqB, as well as excitation and the terminal voltage.The theoretical limit on the Q-axis is determined by the quadrature axis reactance xBqB. The permitted rotor

angle is less than 90. These limits are graphically visualised in figure 2 and 3 by means of the voltageand current vectors, as well as the capability diagram for both machine types.

V

E

I

I xd

Voltage vectors

Q [p.u.]

P [p.u.]1

P =1theorecticalstabilitylimit

Eexc/xd2

Capability diagram

maximum

turbine limit

rotorlimit

stator limit

Vx

d

2

Figure 2: Vector and capability diagram of the turbo generator with xBdB = x BqB

(EBexcB : rotor voltage; I : stator current)


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Q [p.u.]

P [p.u.]1

P =1

theorecticalstabilitylimit

Eexc/xd2

Capability diagram

maximumturbine limit

rotorlimit

stator limit

Vx

d

2

Vxq

2

Voltage vectors

VE

I

I xd

I xq

xd - xqxq

V

Figure 3: Vector and capability diagram of the salient pole generator (xBdB xBqB)

From these diagrams it is apparent that the operating range of the generator is limited:

In the over-excitedrange:by the power supplied by the turbine and the excitation (rotor values)

and

in the under-excited range:by the power supplied by the turbine, the stator limits or the stability limit.

For operation on an interconnected system, the actual (practical) stability limits apply. These take intoconsideration the superseding reactances (e.g. unit transformer) which are always present, and a securitymargin. The actual admissible value for stability is therefor smaller than the theoretical value. Themanufacturer of the generator specifies the limits that must be adhered to with the capability diagram. As infigure 1, various representations and scales of the axes can be found. These may have dimensions (MW,MVar) or be dimensionless (p.u.). The latter representation is preferred. If the values in a dimensioned

characteristic are divided by the nominal apparent power, the result is the p.u. representation.The following figures 4 and 5 provide an example of a turbo generator and salient pole generator capabilitydiagram.

Figure 4: Capability diagram of a turbo Figure 5: capability diagram of a salientgenerator pole generator

In the case of the turbo generator the practical stability curve is inclined to the right due to the supersedingreactances, when compared to the theoretical curve. On the other hand, in the case of the salient polegenerator, the theoretical stability characteristic is shifted to the right as a whole. The base point with thereactive power axis is approximately at the centre of the reluctance power circle [5].


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The representation in the capability diagram is applicable with nominal voltage and current (V BNB, IBNB).Constant voltage may however not always be assumed. The following computation example illustrates theinfluence on the stability limits by variation of the voltage. The theoretical stability limit of the turbogenerator (refer to figure 2) is used to illustrate the influence of a 10% change in the voltage [7].

If the excitation is equal to 0 the rotor voltage E=0. The maximum reactive power that can be imported is Q= -VP

2P/xBdB , and reaches the following values:

dd

2

d

2

dd

2

d

2

x

1.21

x

1,1

x

VQ:1.1V:At

x0.81

x0,9

xVQ:0.9V:At

====

====

Compared to the value at nominal voltage, the stability limit is shifted to the right during under-voltageconditions and further limits the amount of reactive power that may be imported. The influence isproportional to the square of the voltage. The over-voltage conditions are not critical as the stability limit isshifted to the left in this case.

The foregoing explanations apply to slow variations of system conditions. During sudden changes of load orsystem conditions, transient quantities apply, and a transient response will occur. Therefor a dynamic

stability limit also exists. To reach a simplified approximation, the transient values (x BdB, xBqB and E) areapplied to equation (1) and (2) [5]. In figure 6 the basic result is shown. For this purpose it was assumedthat the steady state and transient quadrature axis reactance is the same. From the diagram it is apparentthat the machine may even remain stable in the dynamic condition with a rotor angle >90. An analogywith the turbo generator can also be found. In this case the dynamic stability limit is determined by thetransient direct axis reactance. In practice the limit is also greater than 90 and is in the range between110 and 120.

Q [p.u.]

P [p.u.]1

P =1

theorecticalsteady-statestabilitylimit

Eexc/xd2

maximumturbine limit

rotorlimit

stator limit

Vxd

2

Vxq

2

Vx'd

2

theorecticaldynamicstabilitylimit

Figure 6: Dynamic stability limit (salient pole generator)

In figure 7 the statements regarding the limits during under-excitation are summarised. They are:

- The practical (steady state) stability limit is to the right of the theoretical value and is given bythe capability diagram of the generator. It applies at nominal voltage.

- If the generator is operated with a voltage V < V BNB, the limit is shifted to the right.

- To consider dynamic conditions, a dynamic stability limit is introduced. If it is exceeded, themachine must be disconnected from the system immediately, as a pole slip will most likely takeplace.


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practicalstabilitylimit

overexcited

+ P(W)

+ Q(Var)

underexcited

Stabilitylimit atV < VN

theorecticalsteady-statestabilitylimit

maximum oftheorecticaldynamicstabilitylimit

Vx'd

2

Vxd

2

Figure 7: Summary of the statements regarding stability limits

The loss of synchronism by a salient pole is illustrated in figure 8 [3]. In the diagram the increase of therotor angle following loss of excitation can be seen. Due to the constant turbine power, the real power does

not change, the imported reactive power increases and the steady state stability limit is exceeded. As aresult of the slip an additional flux appears in the excitation circuit or an additional induced rotor voltageappears which attempts to maintain the armature reaction of the machine at a constant level. This isapparent from figure 8 where in the range between 90 and 180 the excitation current increasessignificantly again. Only shortly before 180 is the rotor accelerated towards the stator pole. This large

acceleration causes large slip and thus increased influence by the damper windings. When = 180 theflux change and therefore the (no longer measurable) rotor voltage becomes equal to zero. As this takesplace in an inductive circuit, the zero crossing of the excitation current and the measured rotor voltage isdelayed. The rotor is now decelerated until it almost reaches synchronous speed as the synchronising

torque shortly after = 180 becomes very large. The result of this is a strong torque impulse that is alsonoticeable as a significant real power impulse (refer to Figure 8a). The mechanical power driving the

machine is however too large to allow a recovery and the machine will continue slipping. Between = 180and 360 and also between n 180 and (n+1) 180 this sequence is repeated. Some deviations apply

during the transient state before the steady state slip condition is reached. The reactive power minimumfollowing the first torque impulse therefore has a different value compared to the following swing cycles.The swing and transient conditions are particularly severe in the salient pole machine due to the differencein direct axis and quadrature axis reactance. The slip changes dramatically during one cycle.

a) b)

Figure 8: Out of step condition on a 30-MVA-salient pole generator (caused by rapid loss ofexcitation) with P= 0,8, ie =1,3 ie0 [3]

[a) course of power flow; b) excitation signals (ie =excitation current, ie0= zero load nominalexcitation current, ve = excitation voltage, ve0 = zero load excitation nominal voltage]


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3. Admittance measuring principle

As mentioned in the introduction, the transformation of the capability diagram into the admittance plane hasthe distinct advantage that when using the p.u. representation, a direct reference to the generator capabilitydiagram is provided, that is independent of the actual generator voltage.

The transformation is explained by the following equation:

The equations (3) and (4) describe the fundamental definition of the complex power and the complexadmittance.

QjPSIVS * +== (3)

BjGYV

IY +== (4)

with: Y admittanceG conductance (real component of the admittance)B Susceptance (reactive component of the admittance)

The relationship for the transformation can be derived by multiplying in equation (4) with the conjugatedcomplex voltage.

V

Qj

V

P

V

QjP

V

S

VV

VIY

2222

*

*

*

=

==

= (5)

Comparing the coefficient in equation (4) and (5) it results in the definition of the admittance values.

V

QB

V

PG

22== (6)

The values from the axis in the generator capability diagram must simply be divided by the square of thevoltage. If subsequently the sign of the reactive component is inverted, the transformation is complete.When V = V

BNB = 1, the per unit numerical values in the capability diagram are identical with those in theadmittance diagram (refer to figure 9). From the per unit capability diagram it is therefor possible to directlyderive the setting values of the under-excitation protection.

prakticalstabilitylimit

overexcited

+ P(p.u.)

+ Q(p.u.)

underexcited

Stabilitylimit atV < VN

Vxd

2

overexcited

+ G(p.u.)

+ B(p.u.)

underexcited

1xd

stability limitindependentof thevoltage

P, Q- Plane G, B- Plane Figure 9: Capability diagram of the generator and admittance diagram

The protection measuring algorithms are based on the equations (3) and (6). The vector signals are derivedfrom the sampled instantaneous values in the 3 phase to ground voltages and the 3 phase currents. Thepositive sequence components are calculated from these vectors. According to the definition in equation (3),the positive sequence voltage and current components are employed to calculate the active and reactivepower. Division by the positive sequence voltage V1 according to equation (6), results in the transformationfrom the power plane into the admittance plane.

Figure 7 can be used to extract the characteristics required by the protection functions. The given staticstability limit must be monitored. Generally 2 lines are sufficient for this purpose. A further threshold valuewhich depends on the dynamic stability limit applies. From the area of extreme under-excitation (on left of

char. 3), it is highly unlikely that the machine will recover to the stable operating range. Therefor fasttripping is required in this case. This is different if the static stability limit is exceeded (char. 1 and 2 in figure10). In this case, if the excitation voltage is still sufficiently large, a recovery by the machine to the stableoperating range is not inconceivable. The monitoring of the excitation voltage (V

BexcB


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as an additional criterion. This criterion controls the tripping time of char. 1 and 2. In this manner, overfunctions as result of transient transgression of the static stability limit due to dynamic impulses that arefollowed by a recovery to statically stable conditions, are prevented.

To set these characteristics, the setting parameters that consist of the intersection with the B-axis as basepoint of the line, and the inclination, are applied. The angle of inclination may be derived from the generatorcapability diagram (refer also to section 5). The setting should be such that it is close to the given stabilitycharacteristic. The excitation circuit controller characteristic supersedes this.

prakticalstabilitylimit

over

excited

+ G(p.u.)

underexcited

1xd,21x

d,1

123

char. 1char. 2char. 3

+ B(p.u.)

Settings:

1xd,1

1xd,2

1xd,3

=1xd

= 0.9 1xd,1

= 2xd,1

1 approx. 802 = 903 approx. 110

exciterlimit

char. 1:

char. 2:

char. 3:

1xd,3

Figure 10: Characteristic of the admittance protection (turbo generator) [8](At salient pole generators char.1 is approximately 1/x

BdB +1/2(1/x BqB -1/xBdB) and char.2 is

approximately 1/xBdB with 2 = 100)

The protection response resulting from the characteristics in figure 10 is:

a) characteristic 1, 2 exceeded, excitation voltage monitoring (Vexc


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Conversely, the characteristics in accordance with IEEE [1] can be converted to the per unit generatorcapability diagram. The following rule must be observed here: circles which do not pass through the origin,will again give circles when inverted. Figure 12 shows the transformation. It is apparent that in comparisonto the admittance principle (refer to figure 10) this provides a much rougher approximation of the stabilitycharacteristic. This measuring principle cannot detect if the stability limit provided by the generatormanufacturer is continuously exceeded by a small amount. The control system (under-excitation limitor) orthe operating personnel must be relied upon to detect such failures. Alternatively, additional monitoring (e.g.additional impedance circle) must be provided. Following is a real example occured at Ertan HPP inSichuan, P.R.China: The excitation CB tripped ever accidentally and unexpectedly due to the unknownreasons. Unfortunately the Loss of Filed protection with impedance measuring principle didnt give out a tripcommand and finally have to disconnect the generator manually. After the fault analysis, the engineersfound the terminal impedance located outside of the impedance circle or stayed not long enough inside.The Loss of Field protection couldnt pick up to lead to a trip command.

The greater margin is however of advantage during dynamic situations (transient transgression of thestability characteristic). Such incidences do not result in pick up, or only result in transient pick up, by theprotection. Additionally, the significant points, as well as the rules for the transformation are indicated infigure 12.

+ X(p.u.)

+ R(p.u.)

xd

R, X- Plane

1

0.5 x'd

Over-

excited

+ P

(p.u.)

+ Q(p.u.)

Under-excited

2x'd 1

xd

22 + x'd

1

22 xd + x'd

P, Q- Plane

Figure 12: Transformation of the IEEE impedance characteristic to the capability diagram

In figure 13 a summarised comparison of the admittance and impedance measuring principle is shown for aturbo generator. The typical setting recommendations were considered for this purpose (refer to figures 10and 12). For example, in the case of under-excitation, the admittance measurement can, as a result of itsmore accurate match to the static stability characteristic, provide an early alarm. This may be seen from theindicated trajectory in the event of under-excitation. Furthermore figure 13 shows that the two measuringtechniques are largely similar. The significant differences may be found in the thresholds.,

Admittance Plane

2

0

2

4

Admittancetrajectory incase of underexcitation(P = const.V decreasing)


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Figure 13: Comparison of the impedance and admittance measurement loci in per unit capabilitydiagram (x

BdB = 1.81; x BdB = 0.27)

5. Application

In this section, the following question is addressed: how are the setting values derived?

The question is essentially answered in sections 2 to 4. Depending on the available information, thedifferent methods for obtaining the setting parameters are employed:

a) If the generator capability diagram is available, the setting parameters may be derived directly there from(per unit representation required). Settings for characteristic 3 are derived according to figure 10.

b) If the direct axis reactance of the generator is known, the setting values may be directly obtained fromthe recommendations given in figure 10. For the slopes, the indicated angles must be used. Thisrecommendation is in accordance with the IEEE recommendation. [1].

c) If the protection is replaced in the course of a protection refurbishment, the previously used impedancesettings can naturally be converted to admittance settings. Assuming secondary setting values, thefollowing equation provides the conversion to secondary per unit admittance values.

XI3

V

x

1

Settingold,SecN,

SecN,

secd, =

(7)

with: VBN,SecB secondary nominal voltage (e.g. 120V)IBN,SecB secondary nominal current (e.g. 5A)XBold,SettingB old previous setting in Ohm

In figure 14 a practical example of the parameter conversion is shown. The left hand section of the diagramindicates the previous characteristic and possible setting values of the protection that is to be replaced. Theright hand section shows the setting table of the numerical protection with the converted parameters. Withthe conversion equation (7), the reactances are converted to per unit values. Furthermore, the excitationvoltage monitoring is not used. The three characteristics of Figure 10 are therefore applied separately.Characteristic 1 is used for alarm purposes. With the angle of 80, a good estimate of the stability limit isachieved. The time delay for the alarm was set to 10 s. Characteristic 2 provides the replica of the larger

impedance circle of the previous protection and trips with short time delay. The converted susceptancevalue for characteristic 2 is 0.51 and a time delay of 1 s was selected. To achieve a better match to thecircle, the characteristic is slightly tilted to the left (refer to figure 13), and a setting of 100 was chosen.

With these setting parameters, characteristic 3 corresponds to the inner circle.

+ X(p.u.)

+ R(p.u.)

R, X- Plane

1.87

25.

08

13.8

6

1.1 *Char. 2

VN,Sec. = 120 VIN,Sec. = 5 A

1

V

I3X

Sec.N,

Sec.N,

Sec

1

V

I3X

Sec.N,

Sec.N,

Sec

Figure 14: Conversion example: impedance to admittance values


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6. Summary

The static stability limit is given by the generator capability diagram. This limit is closely matched by theadmittance measurement. It correctly takes into consideration the influence of the generator voltage on thecapability diagram.

The under-excitation of both basic generator types, salient pole and turbo generator, was explained atlength. The fundamentals of the stability limit and the signals that influence it were discussed. Subsequently

the transformation from the capability diagram to the admittance plane, admittance measuring techniqueand implementation of the under-excitation protection function, was looked at. Furthermore the differencesrelative to the impedance measurement and the transformation of the capability diagram to the impedanceplane were dealt with. The section Applications was dedicated to the calculation of the setting values andshowed the different solutions. The scope of testing is reduced to a minimum by employing numericaltechnology.

Literature:

[1] IEEE Guide for AC Generator Protection. IEEE Std. C37.102 1995,

Approved 12 December 1995, ISBN 1-55937-711-9

[2] IEEE Tutorial on the Protection of Synchronous Generators. (1995) IEEE Catalogue Number:95 TP 102

[3] Fischer, A., Zurowski, E: Neuartiger Untererregungsschutz (New type of under-excitationprotection*)Siemens magazine , (1966) paper.8, p. 634 640

[4] Untererregungsschutz (under-excitation protection*) RG66, product pamphlet of Siemens, 1967

[5] Bonfert,K : Betriebsverhalten der Synchronmaschine (synchronous machine operational response*).Berlin, Gttingen, Heidelberg, Springer-Verlag 1962

[6] Wenigk, K.-D.: Kraftwerkselektrotechnik (power station electronics*). vde verlag gmbh, Berlin,Offenbach 1993, ISBN 3-8007-1724-7

[7] Born,E.; Fischer, A.:Elektronischer Untererregungsschutz (electronic under-excitation protection*).Siemens-magazine. (1972) paper.12; p. 912 915

[8] Multifunction Generator, Motor and Transformer Protection Relay 7UM62. (2001) SiemensManual, order No. C53000-G1176-C149-1

[9] - ( Statistics and analysis on the tripping behaviour

of generator-transformer protection system in Ertan HPP )

* these titles only available in German.

Author Resume

Dr. Hans-Joachim Herrmann

Born in 1952 and have 29-years protection experience. He graduated from Technical University of Dresden in 1977.During 1977-1991,worked as Assistant Professor on the Technical University of Zittau. Then join SIEMENS as Member of Product ManagementProtection in the Energy Automation Division. Up to now, there are totally approx. 60 Contributions in Papers and Conferencespublished. He is also the Co-author of a Protection Book (in Russian) and the author of a Book Numerical Protection (in German).

Diego Gao

Born in 1975 and have 8-years protection experience. In 2004, he joined Siemens Power Automation Ltd. (SPA) serving as atechnical support engineer on generator-transformer protection.

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