Selección de variables. Justificación

Ans: Methods of laying underground cables

Underground cables are generally required in urban areas where there is a high density of population. The highest load density and the most restrictive limitationson feeder layout occur simultaneously in the central cores of major cities. Load densities are usually in the range of 60 to 100 MW per square mile.

Some problems associated with underground cable systems are as follows:

urban area are densely populated with/pedestrian walk ways, as well as water, sewer, storm drain, phone and other utility systems in addition to electrical. So there is limited room. The electrical utility must stake its claim to the routes and space allocated to it with its own duct banks.

Secondly, duct banks are needed to protect underground cable from the constant dig- ins of other utilities, stress form settling, and heat and moisture in this environment. Thirdly, digging into the street in an urban area for new additions or repairs is very expensive. Traffic control and other requirements add to cost and also digging around all the other utilities. Thus electric utilities have no choice but to use duct banks and cable vaults to create their own “cable tunnel system“ under the streets in dense urban areas.

Finally branching of underground cable providing for “T” or “X” connections of paths, while possible, is not as simple or as inexpensive as in overhead lines.

Summarizing, the underground urban area systems have the following characteristics • Layout is restricted to street grid

• Loads are large and invariably three phase • Fixed cost is very high

• The cost of capacity shortfall is extremely high Q.16 Write short notes on any TWO of the following :-

(i) Switched reluctance motors. (ii) Parallel operation of transformers.

(iii) Selsyns. (7 x 2 = 14)

Ans:

(i) Switched reluctance motors: A synchronous motor with salient poles but no field winding is known as the reluctance motor. It is used for low power, constant speed applications where special arrangements for d.c. excitation would be cumbersome. The principle of this motor is that the stator produces a rotating field in space and the rotor is noncylindrical such that the reluctance of the magnetic path offered by the rotor to the rotating field is a function of the space angle. Here the rotor has the tendency to align itself in the minimum reluctance position with respect to the synchronously rotating flux of the forward field. The motor is made self starting by the induction principle by providing short-circuited copper bars in the projecting parts of the rotor.

In the single phase reluctance motor the rotating field can be produced by one of the phase-splitting methods. The salient pole structure is given to the rotor by removing some of the teeth of an induction motor rotor as shown in Fig M2. The remaining teeth carry short-circuited copper bars to provide the starting induction torque. After starting, the rotor reaches near synchronous speed by induction action and is pulled into synchronism during the positive half-cycle of the sinusoidally varying synchronous torque.

This would only be possible if the rotor has low inertia and the load conditions are light. The torque speed characteristic of a typical reluctance motor with induction start is given in Fig M3. Here the starting torque is highly dependent upon the rotor position because of the projecting nature of the rotor. This phenomenon is known as “cogging”. For satisfactory synchronous motor performance the frame size to be used must be much larger than that for normal single- phase induction motor. This accounts for the high value of starting torque shown in Fig M3.

(ii) Parallel operation of transformers: when the load exceeds the capacity of an existing transformer, it may be economical to install another one in parallel rather than replacing it with a single larger unit. Also for reliability two smaller units in parallel are preferred. The cost of maintaining a spare is also less with two units in parallel.

For satisfactory parallel operation of transformers the following conditions have to be fulfilled:

(i) They must be connected with proper polarities; this is to ensure that the net voltage around the local loop is zero. A wrong polarity connection results in a dead short circuit.

(ii) 3 phase transformers must have zero relative phase displacement on the secondary sides and must be connected with proper phase sequence. Only the transformers of the same group can be paralleled. For example Y/Y and Y/∆ transformers cannot be paralleled as their secondary voltages will have a phase difference of 300

(iii)The transformers must have the same voltage ratio to avoid no-load circulating current, when the transformers are in parallel on both primary and secondary sides. (iv) There should exist only a limited disparity in the per unit impedances (on their own bases) of the transformers. The currents carried by the two transformers are proportional to their ratings if their p.u. impedances on their own ratings are equal.

Fig N1 shows two transformers paralleled on both sides with proper polarities but on no load. The primary voltages V1 and V2 are equal. If the voltage ratios of the two

transformers are not identical, the secondary voltages E1 and E2 though in phase will not be equal in magnitude. The difference (E1-E2) will appear across the switch S. When the secondaries are paralleled by closing the switch, a circulating current appears even though the secondries are not supplying any load. The circulating current will depend upon the total leakage impedance of the two transformers and also the difference in their voltage ratios. Only a small difference in the voltage ratios will be tolerated.

Division of load between transformers in parallel. Equal voltage ratios When the transformers have equal ratios E1=E2 in Fig N1, the equivalent current of the two transformers would then be as shown in Fig N2 on the assumption that the exciting current can be neglected in comparison to the load current.

It follows from the sinusoidal steady-state circuit analysis that ) 1 ( _ __________ __________ 2 1 2 1 IL Z Z Z I + = and _____________________₍₂₎ 2 1 1 2 IL Z Z Z I + = also

I

+

I

=

I

Taking V_Las the reference phasor and defining complex power as V *I , the multiplication of V_L on both sides of equations (1) and (2) give

L S Z Z Z S 2 1 2 1 + = L S Z Z Z S 2 1 1 2 + = where S₁=VL*I₁ 2 2 V * I S = L L L L

V

I

S

=

*

The above equations S1, S2 and SL are phasor relationships giving loadings in the magnitude and phase angle.

(iii) Selsyns: Selsyns or synchros are control system components which are used for transmission of small torques or motions electrically. They can be categorize into three kinds:

(a) for transmission of small torques electrically, as sinchro-transmitter-receiver pair (Fig P2)

(b) for indicating the difference in positions, as generator – transformer combination (Fig P3)

(c) as differential selsyns(Fig P4)

In the synchro-transmitter-receiver pair (Fig P2) which is a single phase selsyn, the stator has three windings like the polyphase induction motor. The rotor is similar to the rotor of a small alternator and of one winding. Fig P1 shows the cross –section of a single phase selsyn.

Although it shows three stator windings, it is still a single –phase device. Any a.c. current in the rotor will produce at “stand–still” three stator voltages which are in time phase. Two of these devices in the circuit of Fig P2 provides a system for transmission of motion.

It is assumed that the generator and motor are similar units and that for the initial conditions the voltages produced on the stator of the generator by the generator rotor are equal in magnitude and 1800 out of phase with those produced by the motor rotor in the motor stator. Under these conditions the stator currents will be zero and no torque will be present in either machine.

If the rotor of the generator is turned through an angle θ while the position of the rotor of the motor is left unchanged, a circulating current Ia will result in the stators. The current acting on the air gap flux will tend to restore the generator to its original position. The current will produce a torque in the motor which wil tend to cause the rotor of the motor to assume an angle corresponding to that occupied by the rotor of

the generator. If the rotor of the motor is free to turn, it will follow the angular position of the generator rotor. The rotor of the motor therefore is an indicator of the position of the generator rotor or any device connected mechanically to it.

Selsyns as position indicators: If the circuit to the rotor of the motor is opened (Fig P3) a voltage will be produced in the rotor winding, the magnitude of which is a function of the angular position of the rotor of the motor w.r.t. that of the generator rotor. When the motor rotor is at a position of 90 electrical degrees from the position occupied and the rotor is electrically connected and free, the magnitude of the rotor voltage will be zero. Then any movement of the generator rotor will produce a voltage in the motor rotor which is a function of the angular position of the generator rotor (or other equipment coupled to it). This circuit has found use in many servomechanism systems. For this application the motor unit serves just as a control transformer.

A third useful application of the selsyn system is that of the differential selsyn shown in Fig P4; this is constructed like a wound rotor induction motor having a 1:1 ratio of turns. When the rotors of the motor and generator of Fig P3 are in a given position, the differential selsyn will adjust the position of the rotor to its stator such that minimum current flows in its windings. With the rotor of the motor locked in a particular position, a change in the position of the generator rotor will cause a corresponding change in the position of the rotor of the differential selsyn. In this way the circuit of Fig P4 performs the same function as that shown in Fig P3.