Power System Protection - NPTELnptel.ac.in/courses/Webcourse-contents/IIT Bombay/Power System... · Power System Protection S.A.Soman Review of Per unit Calculation and Modeling of

Power SystemProtection

S.A.Soman

Review of PerunitCalculationand Modelingof Apparatus

ModelingAspects ofStaticApparatusModelling ofTransmission Line

Modeling of MutuallyCoupled Lines

Modeling ofTransformer

Modeling ofSynchronousMachineSequence Modelingof InductionMachines

Modeling of ElectricalUtility Systems

Load Modeling

Modeling of SeriesCapacitors

SequenceNetworkAdmittanceMatrixFormulation

Short CircuitAnalysisUsingSequenceComponentsCalculation of ShortCircuit MVA

Power System Protection

S.A.Soman

Department of Electrical EngineeringIIT Bombay

Sequence Modeling of Power Apparatus


S.A.Soman







Load Modeling





1 Review of Per unit Calculation and Modeling ofApparatus

2 Modeling Aspects of Static ApparatusModelling of Transmission LineModeling of Mutually Coupled LinesModeling of Transformer

3 Modeling of Synchronous MachineSequence Modeling of Induction MachinesModeling of Electrical Utility Systems

Load ModelingModeling of Series Capacitors

4 Sequence Network Admittance Matrix Formulation

5 Short Circuit Analysis Using Sequence ComponentsCalculation of Short Circuit MVA


S.A.Soman







Load Modeling




Objectives

ObjectivesPer unit calculation and its advantages.Modeling aspects of static apparatus like transmissionline and transformers.Modeling of rotating machine like synchronousmachines and induction machinesFormation of sequence admittance matrices.Evaluation of Thevenin’s equivalent.


S.A.Soman







Load Modeling




Review of Per unit Calculation and Modeling ofApparatus

Per Unit Quantity =Actual QuantityBase Quantity

Base Current(Amp) =Base(KVA)× 1000√

3 Base Volts

Base Impedence(Ohm) =Base(Volt)√

3 Base Current

ZP.U =Actual Impedance(Ohm)× Base(MVA in 3 phase)

(Base(Line Voltage in kV))2


S.A.Soman







Load Modeling




Advantages of P.U computation

1 Manufactures usually provide equipment data withname plate rating as base.

2 Range for acceptable % or p.u. values can be easilyfixed.

3 Especially useful in networks with multiple voltagelevels interconnected through transformers.

4 P.U impedance of transformer is independent of the kVbase.

5 Standard base conversion (scaling with MVA Base)formulae are available.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Modelling of Transmission Line


S.A.Soman







Load Modeling




Modelling of Transmission Line contd..

∆Va

∆Vb

∆Vc

=

Zs Zm Zm

Zm Zs Zm

Zm Zm Zs

IaIbIc

Applying sequence transformation, we get∆V1 = Z1I1, ∆V2 = Z2I2 and ∆V3 = Z3I3where Z1 = Z2 = Zs − Zm and Z0 = Zs + 2Zm

Thus, for a transposed transmission line, the positiveand negative sequence impedances are equal. Acommonly used approximation for Z0 is to assume it tobe three times Z1.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Modeling of Mutually Coupled Lines

Ampere‘s law∮

~H.~dl = inet .

i+net = i+a (t) + i+b (t) + i+c (t) = 0

i−net = i−a (t) + i−b (t) + i−c (t) = 0

i+net = I0Conlusion: Mutual coupling exhibits only in zero sequencenetworks.


S.A.Soman







Load Modeling




Mathematical Explaination

∆va1

∆vb1

∆vc1

=

Zs Zm Zm

Zm Zs Zm

Zm Zm Zs

Ia1

Ib1

Ic1

+jα

1 1 11 1 11 1 1

Ia2

Ib2

Ic2

Applying sequence transformation we will get

∆v01

∆v11

∆v11

=

Zs + 2Zm

Zs−Zm

Zs − Zm

I01

I21

I21

+j

3α 0 00 0 00 0 0

I02

I12

I22


S.A.Soman







Load Modeling




Modeling of Ground

+ve sequence circuit, lground = 0, resistance/impenaceof ground or neutral wire plays no role. Hence groundfor +ve sequence circuit is equipotential surface.

Same Conclusion can be drawn for -ve sequencecurrent.

For zero sequence current, ground potential or drop inthe neutral conductor is not zero. It (arrests) the voltageprofile.

Usually, this drop orequivalent impedance is lumpedwith apparatus impedance to creates a equipotentialground plane.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Modeling of Core Type Transformer

Modeling of +ve and -ve sequence impedance isstaright forward - (Equation) net leakage impedance inp.uZero sequence modeling

~φa + ~φb + ~φc = 0 [by KCL]Hence φ0 = 0Practically, zero sequence flux leaks through tankcreats heating. Tank is not (saturates)Not used in unbalanced system (e.g. distribution)X0 –negligible!


S.A.Soman







Load Modeling




Modeling of Shell Type Transformer

+ve and -ve sequence impedance = leakageimpedanceZero sequence impedance

Low reluctance to zero sequence fluxHigh impedance


S.A.Soman







Load Modeling




Modeling of Bank of 1 φ transformer

+ve seq impedance = -ve seq imp = zero sequenceimpedanceRole of circuit interconnections on + - and zero seqcircuits of transformers+, -ve sequence cirduits, staright forward,zero sequence circuit

In delta winding zero sequence currents are exists

in star-ungrounded with I0 = 0 i.e. leads to o.c


S.A.Soman







Load Modeling




Modeling of Transformer contd..


S.A.Soman







Load Modeling






S.A.Soman







Load Modeling






S.A.Soman







Load Modeling




Modeling of Synchronous Machine

The subtransient reactance X′′

d determines the currentduring the first cycle after fault occurs.

In about 0.1sec, reactance increases to transientreactance X

′

d .

In about 0.5sec to 2sec reactance increases to Xd , thesynchronous reactance; this is the value thatdetermines the current flow after a steady statecondition is reached.


S.A.Soman







Load Modeling




Modeling of Synchronous Machine

During a fault, motor acts as a generator to supply faultcurrent. The rotor carrying the field winding is driven by theinertia of the rotor and load. Stator excitation is reduced dueto drop in voltage. The fault current diminishes as the rotordecelerates. The generator equivalent circuit is used forsynchronous motor. The constant driving voltage and threereactance X

′′

d , X′

d , and Xd are used to establish the currentvalues at three points in time. Synchronous condensers canbe treated in same manner as synchronous motors.


S.A.Soman







Load Modeling




Negative sequence Impedance of SynchronousMachines

For a synchronous machine, positive and negativesequence impedances cannot be equal.

Hence, double frequency emf and currents are inducedin rotor.

Negative sequence impedance is 70-95% ofsubtransient reactance.


S.A.Soman







Load Modeling




Zero Sequence Impedance of SynchronousMachines

Zero Sequence currents cannot create rotating mmf. Infact, with sinusoidally distributed three phase windings,the net flux at any point in the air gap is zero.

Hence, zero sequence impedance is only a small %(0.1-0.7) of the positive sequence impedances

Since synchronous machines only generate positivesequence voltage, the internal voltages used withnegative sequence and zero sequence networks arezero.

If Y point is grounded through impedance Zg , then 3Zg

will have to be added to zero sequence impedance ofgenerator.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Sequence Modeling of Induction Machines

In asynchronous machines, transient state of current isdamped quickly i.e. within 1-2 cycle. During a fault,rotor is driven by inertia of load and rotor itself. There isno dc field excitation on rotor. Rotor winding is shortcircuited. Hence, whatever rotor excitation is present, itis due to the induced fields in the rotor from the rotatingstator mmf. As stator excitation is lost and rotor slowsdown, this field is lost quickly. The current contributionof an induction motor to a terminal fault reduces anddisappears completely after a few cycles.As a consequence, only the sub transient value ofreactance X

′′

d is assigned for positive and negativesequence. This value is almost equal to the lockedrotor reactance. Subsequently, machine behaves as apassive element with impedance of value Z = kV 2

MVAwhere rated LL voltage and 3 phase MVA rating is used.Zero Sequence modeling can be treated in similar linesas synchronous machines because rotor plays nosignificant role.For fault calculations an induction generator can betreated as an induction motor.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Modeling of Electrical Utility Systems

The generator equivalent circuit can be used to represent autility system. Usually, the utility generators are remote fromthe industrial plant. The current contributed to a fault in theremote plant appears to be merely a small increase in loadto the very large central station generators, and this currentcontribution tends to remain constant. Hence, it isrepresented at the plant by single valued equivalentimpedance referred to the point of connection.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Load Modeling

One approximate way of accounting prefault load flowcondition in short circuit analysis associated withtransmission system is to model load as positive sequenceshunt impedance.

V 1

I1 =|V 2

i

(Pi − jQi)

The shunt load impedances are added into diagonal of Y oldbus.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Modeling of Series Capacitors


S.A.Soman







Load Modeling




Sequence Network Admittance MatrixFormulation

Iabc1

Iabc2...

Iabcn

=

Y abc

11 Y abc12 · · · Y abc

1nY abc

21 Y abc22 · · · Y abc

2n...

......

...Y abc

n1 Y abcn2 · · · Y abc

nn

V abc1

V abc2...

V abcn

V abc1

V abc2...

V abcn

=

[T ]

[T ][T ]

[T ]

V 0121

V 0122...

V 012n

I0

busI1bus

I2bus

=

Y 0BUS

Y 1BUS

Y 2BUS

V 0bus

V 1bus

V 2bus


S.A.Soman







Load Modeling




Differences between YBUS Modeling in SCAand LF

Load flow analysis uses only positive sequenceadmittance matrix while short circuit analysis requirespositive, negative and zero sequence admittancematrix.

In load flow analysis, the voltage at generator terminalis assumed to be fixed. Hence, source impedance andinternal generator voltages are not modeled.

In SCA


S.A.Soman







Load Modeling





S.A.Soman







Load Modeling




SCA

Step1: Build Y 1bus, Y 2

busandY 0bus

Step2: To compute Thevenin‘s equivalent impeance atbus ‘i’ inject 1pu current in each network and solve for‘v’ i.e. solve [Y 0

bus][V0] = [ei ] and obtain Z 0

ii[Y 1


ii[Y 2


ii

Step3: Use Standard fault current calculate formulae tosolve for fault currents

Remark: Solution in step-2 can be done by efficientsparse matrix computational technique.


S.A.Soman







Load Modeling












S.A.Soman







Load Modeling




Calculation of Short Circuit MVA

3φ− short circuit MVA = I3φ(in pu)× 3φ− base MVA

S − L − G Short circuit MVA = IS−L−G(in pu)× 3φ−base MVA


S.A.Soman







Load Modeling




Closing Remarks

Fault analysis methods are quasi steady state model ofdynamic system. It uses Limited Data

More accurate models requires EMTP -EMTP requireslarge data

approximate asymmetrical currents due to dc offset infauls analysis are obtained by using approximatemultiplier (... .....)

SCA ysed for relay coordination, breaker () selectionetc.....

Documents

Power System Protection - NPTELnptel.ac.in/courses/Webcourse-contents/IIT Bombay/Power System... · Power System Protection S.A.Soman Review of Per unit Calculation and Modeling of