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Consider the following CFG G:S SS | T T aTb | abDescribe

Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser ISBN: 9781133187790 221

Solution for problem 2.46 Chapter 2

Introduction to the Theory of Computation | 3rd Edition

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Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser

Introduction to the Theory of Computation | 3rd Edition

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Problem 2.46

Consider the following CFG G:S SS | T T aTb | abDescribe L(G) and show that G is ambiguous. Give an unambiguous grammar H where L(H) = L(G) and sketch a proof that H is unambiguous.

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EEE 576 Spring 2016 Power System Dynamics Protective Relay in Details 1 System Relaying in Stability Studies Relays detect the existence of the abnormal conditions by monitoring specific system quantities. Transient stability analysis deals with the ability of the system to maintain synchronism when subjected to a severe disturbance. Satisfactory performance of certain types of relays is important in ensuring system stability. 2 An important aspect of transient stability analysis is the evaluation of the performance of relays during the transient period- specifically, relays used to protect transmission lines and generators. 3 Transmission Line Protection Choice of line protection based on following factors: • Type of circuit – single line, parallel line, multiterminal, magnitude of fault current infeeds • Function of line, its effect on system reliability, speed at which fault has to be cleared. • Coordination and matching requirements 4 3 Basic Line Protection Schemes • Overcurrent • Distance relaying • Pilot relaying Overcurrent – Mainly used in subtransmission systems and radial distribution systems. Faults on these systems do not affect stability. Distance relaying – This relay responds to the ratio of measured voltage to measured current – effective impedance < setting. 5 Impedance is a measure of distance along the transmission line. Relay has excellent discrimination and selectivity. Types of distance relays • Impedance relays • Reactance relays • MHO relay • Modified MHO and impedance relays. 6 7 Distance relaying is most widely used form of relaying for transmission lines Zone 1 – Protects 80% of line Zone 2 – Reaches beyond line ≈120% Zone 3 – Provides back-up protection for line C-D and set to reach beyond C-D 8 Pilot-Relaying Schemes Uses principle of differential relaying based on communication channels (pilots). Relays determine if fault is internal or external. For internal faults C.B.s at all terminals of the protected line trip. For an external fault 9 Relaying Quantities During Swings E and E are Let us examine A B voltage, current, voltages behind apparent IMP at transient this Bus reactance E A  E 0 B I  E C E ZAI A Z T 10 Impedance seenby relayat Bus C E E Z I  Z C C  A A I I  E A Z I A EA  Z T Z A EA  E B If E  E 1.0pu A B Z Z C Z  A T 101 101  Z  Z A T 101 101   1cos   Z A Z T 1  j  11  2  2sin   ZT  Z T     Z A  j cot   2   2 2  With E AE LocuB of Z  St.liCe This perpendicularlybisectstotal systemimpedance between Aand B. 12 When E  A B The apparentimpedancelociare circles.With their centerslocatedon theimpedance line AB. 13 Electricalcentersarenot fixed points,since theinternal EMFand theimpedanceseen by themachinesvary. The voltageat theelectricalcenterdrops tozeroas increasesto180and thenincreasesin magas increases furtheruntilit reaches360.When reaches180, the generatorwill haveslipped a pole. 14 If the system is unstable following the disturbance the angle δ increases gradually until it reaches 180°, when a pole is slipped.At this time voltages and apparent impedance near the electrical center oscillate rapidly. We have considered the idealized case. Actual loci of apparent impedance are more complex. These loci are readily determined by transient stability programs. 15 Shows impedance loci for constant voltage ratio 16 Shows impedance loci for constant angle separation 17 Distance Relay Performance During Swings During swing conditions the performance of relays can be determined by calculating the impedance measured by the relays during the step-by-step simulation. ~ ~ Z  E p  Ep p I y E  E~  pq pq p q The apparentimpedance is then plotted on the R-X diagram along with the relaycharacteristic. 18 During swing conditions we would like to: 1) Prevent tripping during stable swings while allowing tripping for unstable transients. 2) Prevent tripping during unstable transients and force separation at another point. 19 20 The out-of-step relay should not be operated for stable swings. They must detect unstable swings. Normal load conditions should not be picked up. The movement of the apparent impedance locus under out-of-step conditions is slow when compared to its movement during a fault. 21 The transientswing conditioncan bedetectedby using two relayshaving verticalor circularcharacteristic on an R-X plane.If the timerequired tocross the twocharacteristics(00S2,00S1)exceeds a specifiedvalue.The out-of -stepfunction isinitiated. 22 In an out-of-step blocking scheme zone 2 and perhaps zone 1 relays are prevented from initiating tripping of the line monitored, and transfer trips signals are sent to open circuits at a remote location in order to cause system separation at a more preferable location. 23 Out-of-Step Tripping of Generators When the electrical center is out in the transmission system, line protection performs out-of-step protection. When the electrical center is within the generator or step-up transformer, a special relay must be provided at the generator. 24 If circletoolarge MHO element monitors therealy willtrip Z APPooking into the forstableswings. systemfrom the HV Bus. Relay trips generator If  Coolarge when Z enters offest APP tripping canoccur MHO characteristic.TypicallyC when Z enters circle whenseparation APP isset to120. 180 andputs enormousstress on circuit breaker. 25 Blinder Scheme The generator is tripped when ZAPPis within MHO characteristic and crossesboth blindersand the time of crossing exceedsa set threshold. Two impedance elements 26 Modeling of common types of relays in stability programs. Load Shedding Relay This relay either sheds or restores load on operation. The load restoring capability is valid only if the load was shed by under frequency load shedding. 27 This type of relay can perform different actions based on the quantity monitored and the relay control action performed. Under Frequency Load Shedding Relay trips if the frequency of the Bus remains continuously below a set value for a period specified by the time delay V nV  jnr ni V n1 V n1r  jV n1i V V V V f  ni n1r nr n1i n 2 2 V n t 28 Under V oltage Load Shedding Relay trips if the voltage magnitude of the relay Bus remains continuously below the set value for a period specified by the time delay. Voltage Difference Load Shedding Relay trips if the voltage magnitude of the relay Bus remains continuously below the difference between initial Bus voltage magnitude and voltage deviation set value for a period specified by the time delay 29 Frequency Based Load Restoring a) Relay trips instantaneously if the frequency at the relay Bus goes above the set value b) Relay trips if the frequency at the relay Bus remains continuously above the set value for a period specified by the time delay. To model this relay the relay data can be entered for a specified Bus or for all Buses in an area or zone – where all relays have the same setting. 30 This kind of relay could have the following quantities specified • Relay set point • % of load to be shed or restored • Time delay • Breaker operation time 31 32 33 34 Under Frequency Load Shedding Relay Relay sheds load on a specified Bus if frequency of this Bus falls below the set value for a time governed by the inverse minimum time characteristic. The time lever specified by user. 35 36 Generator Under Frequency Relay Relay operates if generator frequency falls below a specified value. Typically two frequency set points can be specified, one with a time delay and another for an instantaneous trip. Impedance/Distance Relay This relayoperateswhen Z seenby the APP relayfallswithin a specifiedcirclein the R  X plane. 37 38 39 40

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Chapter 2, Problem 2.46 is Solved
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Textbook: Introduction to the Theory of Computation
Edition: 3
Author: Michael Sipser
ISBN: 9781133187790

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Consider the following CFG G:S SS | T T aTb | abDescribe