EE6002
POWER SYSTEM TRANSIENTS
LT P C
3003
OBJECTIVES:
To study the generation of switching transients and their control using circuit –
theoretical concept. To study the mechanism of lighting strokes and the production of lighting surges. To study the propagation, reflection and refraction of travelling tr avelling waves. To study the impact of voltage transients caused by faults, circuit breaker action, load rejection on integrated power system.
UNIT I INTRODUCTION AND SURVEY 9 Review and importance of the study of transients - causes for transients. RL circuit transient with sine wave ecitation - double fre!uency transients – basic transforms of the RL" circuit transients. #ifferent types of power system transients - effect of transients on power systems – role of the study of transients in system planning. UNIT II SWITCHING TRANSIENTS 9 $ver voltages due to switching transients - resistance switching and the e!uivalent circuit for interrupting the resistor current - load switching and e!uivalent circuit - waveforms for ransient ransient voltage voltage across the load and the switch - normal normal and abnormal switching switching transients. "urrent suppression - current chopping - effective e!uivalent circuit. "apacitance switching effe effect ct of sour source ce regu regula lati tion on - capa capaci cita tanc ncee swit switch chin ing g with with a rest restri rike ke,, with with mult multip iple le restrikes.llustration for multiple restriking transients - ferro resonance. UNIT III LIGHTNING TRANSIENTS 9 Review of the theories theories in the formation formation of clouds clouds and charge formation formation - rate of charging charging of thunder clouds – mechanism of lightning discharges and characteristics of lightning strokes – model for lightning stroke – factors contributing to good line design - protection using ground wires - tower footing resistance - %nteraction between lightning and power system. UNIT IV TRAVELING WAVES ON TRANSMISSION LINE COMPUTATION OF TRANSIENTS 9 "omputation of transients - transient response of systems with series and shunt lumped parameters and distributed lines. Traveling wave concept - step response - &ewely's lattice la ttice diagram - standing waves and natural fre!uencies - reflection and refraction of travelling waves. UNIT V TRANSIENTS IN INTEGRATED POWER SYSTEM The short line and kilometric fault - distribution of voltages in a power system – Line dropping and load rejection - voltage transients on closing and reclosing lines – over voltage induced by faults -switching surges on integrated system (ualitative application of )*T+ for transient computation. TOTAL TOTAL : 45 PERIODS PE RIODS
OUTCOMES: bility to understand and analye power system operation, stability, control and • protection. TET BOO!S: . llan /reenwood, 0)lectrical Transients in +ower 1ystems', 2iley %nter 1cience, 3ew 4ork, 5nd)dition, 66. 5. +ritindra "howdhari, 7)lectromagnetic transients in +ower 1ystem8, 9ohn 2iley and 1ons %nc., 1econd )dition, 5::6. ;. ".1. %ndulkar, #.+.
.oltage )ngineering', Tata *c/raw =ill, ?ifth )dition, 5:;. 5. R.#. &egamudre, 0)tra =igh >oltage " Transmission )ngineering', 2iley )astern Limited, 6@A. ;. 4.=ase, =andbook of +ower 1ystem )ngineering,8 2iley %ndia, 5:5. B. 9.L.
UNIT I" INTRODUCTION AND SURVEY
CONTENTS
Review and importance of the study of transients causes for transients RL circuit transient with sine wave ecitation double fre!uency transients basic transforms of the RL" circuit transients #ifferent types of power system transients effect of transients on power systems role of the study of transients in system planning
REVIEW AND IMPORTANCE OF THE STUDY OF TRANSIENTS
ELECTRICAL TRANSIENTS :
n electrical transient is a temporary ecess of voltage and Cor current in a electrical circuit when a fault occurs on a system or a switch opens or closes.
Transient surges are defined as momentary bursts of energy that are induced upon power, data, or communication lines. They are characteried by etremely high voltages that can drive tremendous amounts of current into an electrical circuit for a few millionths, up to a few thousandths of a second. 1urge activity is often assumed to be an outside engendered anomaly. Lightning induced electrical energy bursts, for eample, typically come to mind as the primary source of surge activity. =owever, while lightning induced surges represent are the most formidable transient related e!uipment menace, most surges are originate from internal sources within a facility. %nternal transient generators range from copiers to coffee makers, from vacuum cleaners to variable speed drives, and from fluorescent light ballasts to furnace igniters. 1tudies have verified that approimately @:D of transient activity at a given facility is internally generated. "opiers and laser printers, for eample, are notorious transient generators – as are heating and air conditioning systems. ny time an inductive load, whether it is a vacuum cleaner or a heavy duty variable speed drive, is either powered on or off – it generates a low magnitude surge impulse that propagates back through the electrical distribution. 2hile internally generated transient activity can weaken e!uipment over time, the threat posed from lightning activity is particularly disconcerting due to its capability of delivering vast amounts of energy into unsuspecting electronic e!uipment loads.
CAUSES OF POWER SYSTEM TRANSIENTS There are different causes for power system transients. ?or eample, lightning strokes to the wires in the power system or to ground and component switching
either
of network
components or end user e!uipment can produce transients. 3ature of power system transients are very much event dependent.
1hort duration events can be classified into three classesE
. )vents that can be identified by their fundamental fre!uency magnitude. >oltage magnitude in such events goes through significant changes for long periods. The changes are well apart and observable with respect to time. This enables magnitude estimators to identify and resolving events having significant changes. These are observed mainly in fault induced events, transformer saturation, induction motor starting, etc. >oltage dips with duration typically between F:ms and several seconds and interruptions with duration from several
seconds up to many hours are associated with such transient events.
5. )vents having significant changes in the fundamental fre!uency magnitude but of short duration. %n such events, it is very difficult to etract voltage magnitude of transients. These are normally observed in fuse-cleared faults and self-etinguishing faults.
;. )vents of very short duration GtransientsH for which the fundamental fre!uency magnitude does not offer important information. ?or this class, the higher fre!uency components of the signal must be considered for a thorough characteriation and classification.
&ased on waveform shape, power system transients, can be classified into
.$scillatory transients 5.%mpulsive transients ;.*ultiple transients
#$ IMPULSIVE TRANSIENTS
n impulsive transient is defined as a sudden change in the steady state condition of voltage, current or both, that is unidirectional in polarity either positive or negative. nalysis of impulsive transients is done by their rise and decay times. %mpulsive transients are damped !uickly by the resistive circuit elements and do not propagate far from their source. Thus their effects are localied.
%mpulsive transients are common during lightning. Lightning stroke may appear directly or by indirect induction. 2hen a lightning stroke hits a transmission line Gdirect strokeH an impulsive over voltage is induced. They have high magnitude. Lightning over voltage can also be induced by nearby strokes to the ground or between clouds. These over-voltages are of lower magnitude than those produced by direct strokes. 3ormally impulsive transient shows a sudden rise followed by an eponential decay. &ut in some cases, lightning transient shows a sudden rise followed by a sudden drop and an oscillation with relatively small amplitude.
2$ OSCILLATORY TRANSIENTS
$scillatory transient is alternating in nature. %t shows a damped oscillation with a fre!uency ranging from a few hundred herts up to several *ega herts. $scillatory transients can be mathematically derived by the homogenous solution to linear differential e!uations. s the electric power system can approimately be described by a set of linear differential e!uations, oscillatory transients are the 7natural transients8 in electric power system. ?or this reason, oscillatory transients dominate over impulsive transients. ?or eample, oscillatory transient can be caused by the energiing of a capacitor bank where, fre!uency of oscillation is mainly determined by the capacitance of the capacitor bank and the short circuit inductance of the circuit feeding the capacitor bank Gcapacitor energiingH. nother common cause of oscillatory transient is event of energiing of transmission line.
3$ MULTIPLE TRANSIENTS WITH A SINGLE CAUSE
*ultiple transients are combination of many overlapped transients occurred due to more than one switching action. ?or eample, in three phase system the switching action in the individual phases rarely take place at the same instant. 1uch events produce multiple transients. "urrent chopping and re-strike are other two major causes of multiple transients. "urrent chopping is done when the current during opening of a circuit breaker becomes ero before the natural ero crossing. This results in transients of high over-voltages. Re-strike may occur when a capacitor is de-energied by a slowly moving switch where the voltage over the capacitor increases faster than the voltage-withstand of the gap between the contacts of the switch.
RL CIRCUIT TRANSIENT WITH SINE WAVE ECITATION
A sinusoidal voltage is switched on to a series connection of an inductance and a resistance (Figure 1.1). This is in fact the most simple single-phase representation
of
a
high-voltage
circuit
breaker
closing
into
a
shortcircuited transmission line or a short-circuited underground cable. The voltage source E represents the electromotive forces from the
connected synchronous generators. The inductance L comprises the synchronous inductance of these generators the leakage inductance of the power transformers and the inductance of the bus bars cables and transmission lines. The
resistive losses of the
supply circuit are
represented by the resistance R. !ecause we have linear network elements only the current "owing in the circuit after closing the switch can be seen as the superposition of a transient current and a steady-state current. The transient current component is determined by the inductance and the resistance only and is not in"uenced by the sources in the network (in this case by the voltage source E). #t forms the general solution of the $rstorder homogeneous diferential equation whereas the steady-state current component is the particular solution of the nonhomogeneous diferential equation. #n the latter case the transient oscillations are damped out because their energy is dissipated in the resistive part of the circuit. Applying %irchho&'s
voltage
law
gives
di&erential euation of the circuit in Figure 1.1
us the
nonhomogeneous
switch can close the circuit at any ti me instant and the phase angle can have a value between : and 5 π rad. To find the general solution of the differential e!uation, we have to solve the characteristic e!uation of the homogeneous differential e!uation
Ri I Lλi J :
G.5H
The scalar λ is the eigenvalue of the characteristic euation. *e $nd for λ + , (R/L) and thus the general solution for )!uation G.H is
ihGtH J "eKGRCLHt
G.;H
The particular solution is found by substituting in uation (1.1) a general epression for the current
ipGtH J sinGt I ϕH I &cosGt I ϕH A and B can be determined
This results in the particular solution for the current
G.BH
The complete solution, which is the sum of the general and particular solution, is
&efore the switch closes G?igure .H, the magnetic flu in the inductance L is e!ual to eroM this remains so immediately after the instant of closing, owing to the law of the conservation of flu. Therefore, at t J :, the instant of closing, we can write
This gives us the value for C M hence, the complete epression for the current becomes
The first part of )!uation G.6H contains the term epNK(R/L)t O and damps out. This is called the DC component . The epression between the brackets is a constant and its value is determined by the instant of closing of the circuit. ?or N ϕ K tanK(ωL/R)O J : or an integer times π , the #" component is ero, and the current is immediately in the steady state. %n other words, there is no transient oscillation. 2hen the switch closes the circuit 6:P earlier or later, the transient current will reach a maimum amplitude, as can be seen in ?igure .5. The current in ?igure .5 is called an asymmetrical current . %n the case where no transient oscillation occurs and the current is immediately in
the steady state, we speak of a
symmetrical current . The asymmetrical current can reach a peak value of nearly twice that of the symmetrical current, depending on the time constant L/R of the supply circuit. This implies that, for instance, when a circuit breaker closes on a short-circuited high-voltage
circuit, strong dynamic forces will act on the connected bus bars and lines because of the large current involved. 2hen the time constant of the supply circuit is rather high, which is the case for short-circuit faults close to the generator terminals, the transient and subtransient reactance of the synchronous generator cause an etra-high first peak of the short-circuit current. fter approimately 5: milliseconds, when the influence of the transient and subtransient reactance is not present any longer, the synchronous reactance reduces the root-mean-s!uare value Grms valueH of the short-circuit current. Qnder these circumstances, an alternating current flows without current eros for several periods in the case of a fault in one of the phases because of the large #" component. This current cannot be interrupted because the current ero necessary for current interruption is lacking.
DOUBLE FRE%UENCY TRANSIENTS
The circuit-breaker 1 may have L and " parameters on its two sides, as shown in ?igure ;.;. &efore clearance the points a and b are at the same potential. fter the fault is cleared, he, the @? has been etinguished, both the circuits oscillate at their own natural fre!uencies, a composite double fre!uency transient appears across the circuit breaker 1
The fre!uencies are given by
f n1
=
1 2 π √ L1 C 1
and
f n2 =
1 2 π √ L2 C 2
The magnitude and the 2aveform for the total voltage is proportional to the inductances and is given byE
−cos ω t a (¿)+ a ( 1 −cos ω t ) TRV =¿ E ¿ 1
1
1
2
2
E ¿ 2here
a1 =
L1 L1 + L2
∧a = 1
L2 L1+ L2
ω1 =
1
√ L C 1
1
∧ω = 2
1
√ L C 2
2
BASIC TRANSFORMS OF THE RLC CIRCUIT TRANSIENTS&
T'()*+,)- R,*./)*,*
1o far all the calculations we have performed have led to a 1teady 1tate solution to a problem i.e. the final value after everything has settled down. There are in fact two parts to the total response of a system to an input, these areE The 1teady 1tate which lasts indefinitely and The Transient Response, which decays to ero, leaving only the steady state. The steady state values can be determined using circuit laws and comple number theory. The transient is more difficult as it involves differential e!uations.
?or an inductorE
?or the circuitE
but
giving usE second order.
$nce again we can use as a solutionE
This gives us
This can be solved but begins to become complicated especially if the value in the s!uare root is negative and we end up with comple values.
1olving for transient conditions is therefore not easy. To make the solving of these problems easier we use Laplace Transforms. Laplace Transformation. 2hat we are able to do is to take a problem in the time domain GtH and to convert it into the Laplace domain GsH. The conversion is carried out using a simple set of rules
/ules
.%f a function of time is multiplied by a constant then the Laplace transform is multiplied by the same constant. e.g. a step of Av to an electrical system is the same as A times a unit step and therefore has the value ACs. 5.%f an e!uation contains the sum of two separate !uantities that are functions of time then the transform is the sum of the individual transforms. ;.The Laplace transform of a first derivative of a function isE
Transform of where
is the value of the function at tJ:
DIFFERENT TYPES OF POWER SYSTEM TRANSIENTS
&ased upon the origin . $f atmostpheric origin ie., lightning 5. $f switching origin ie., all switching operations, load rejection and faults. &ased upon the mode of generation of transients "lassification can be done based upon the mode of generation of transients. . )lectromagnetic transients /enerated predominantly by the interaction between the electrical fields of capacitance
and
magnetic
fields
of
inductances
in power
systems.
The
electromagnetic phenomena may appear as travelling waves on transmission lines,cables,bus sections and oscillations between inductance and capacitance
EFFECTS OF TRANSIENTS ON POWER SYSTEM
Transients are very much related to the operation and performance of different parts of power system as well as loads and measuring and protective devices also. 3ature and duration of Spower system transients are related to correct operation of circuit breakers, and over voltage due to switching of high voltage lines. =igh magnitudes of voltage transients break insulations of the system. =igh magnitude of current transients can burn out devices and instruments. Transients can cause mal-operation of relays and mal-tripping of circuit breakers. ?re!uent number of direct or indirectly induced oscillatory transients may change the magnetic properties of core materials used in electric machines. ROLE OF THE STUDY OF TRANSIENTS IN SYSTEM PLANNING
$vervoltages from lightning strikes, electrical failures or switching actions, as well as other transient phenomena, may significantly impact system performance and e!uipment condition. Respective modeling, analysis and insulation coordination studies build the foundation for the resilience of e!uipment and systems. SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
