The basics of metro train running are same as the running of main line trains. The metro trains need quick acceleration and the interstation distances are small. Also the new metro trains are provided with 3- phase induction motors and the gear ratio used for the metro trains are very high.

The metro trains are for the use of the city dwellers. The commuters should take as little time to reach their place of work and return home in the least possible time. The commuters do not carry heavy luggage with them like the long distance travelers. The toilet facilities are provided only on the platform. The doors of the metro trains are closed while it is running. These are some of the features of metro trains.

ACCELERATION
As can be seen from Fig 1, out of the total torque, part is utilized to overcome the load torque and balance is available for accelerating the motor. If the surplus torque is more, the motor accelerates quickly. The motor attains a balancing speed at A when the load torque and the motor torque are equal. Since at point A, no surplus torque is available, the motor will run with a speed corresponding to slip S1.

For the vvvf drive, the points on family of torque slip curves are joined to get a form given as A B and C in the Fig 2 given below.

In Fig 3, A B is a constant torque region and BC is a constant power region. Though for the vvvf drive motor, it is a common practice to show the curve AB & BC as given below, it should be kept in mind, that the vvvf drive motor is an induction motor and behaves like a normal induction motor.

In Fig 3, when a chosen frequency corresponds with synchronous speed for point R, the, motor will develop a torque corresponding to point Q. If the frequency is increased further, the speed will increase till it reaches point T. The speed corresponding to point B is the base speed and the corresponding frequency is the base frequency. The motor will operate most efficiently at the point B and the motor is designed to work at this point. BC region is like a weak field region of dc series motor. The speed in this region is above the normal speed and the torque is reduced and follows a curve BC.

It will be clear from the figure that after point B, the accelerating or surplus torque gets progressively reduced. The rate of acceleration therefore reduces.

The speed with dc motor will increase along line oA and remain stable from point A to B after B it gets reduced due to braking till it reaches point C. This is the speed time curve with dc motor.

The acceleration and retardation are tan a and tan ß respectively. This graph gets slightly modified in vvvf control (Fig 5).

The oA corresponds to the accelerations in constant torque region, followed by AB in constant power region. The rest of the curve is same as in Fig 4. But normally instead of using two accelerations, average acceleration is used and a Fig 4 is used for the calculations of various parameters in practice even for vvvf drive.

The use of high power motor is preferred by many people for achieving the quick acceleration. But, the use of optimum size of the motor should be made to ensure minimum loss of power.
Copper loss is thus proportional to the square of the voltage applied. Use of high acceleration will mean use of high P2 or high V in V/ƒ ratio.

Aiming to achieve high speed in quick time will result into high loss of energy. We therefore need to see whether achieving high acceleration is necessary to obtain the minimum possible interstation running time.

Consider the two speed time curves given in Fig 6.

It is possible to construct the triangle and the trapezium of the same area, which would be the interstation distance. If the maximum speed Vm is high, the altitude of the triangle will be high. The base of the triangle will be therefore less. In the second case, the base is more and the height of the trapezium is less. Thus, with an acceptable running time between the stations, the, altitude of the trapezium can be reduced, thereby reducing the energy loss.

Consider a practical case of one of the metro lines. The maximum speed is 80 kmph, the acceleration is 0.78 m/sec2 and the braking is 1 m/sec2. The interstation distances are approximately 1 km. The smallest interstation distance is 596m and the maximum is 1,432m.

The speed time curve for these two locations is given in Fig 7

Thus it will be seen that it will not be possible to attain a speed of 80 kmph. The traction motor does not touch the knee point but stops short of it. The traction motor runs efficiently at fb & vb, the base frequency and base voltage. At the lower speeds, the motor will operate at high slips and hence, will result into greater loss. It is therefore, desirable to have motor of proper rating to ensure minimum loss. If a bigger size of the motor is selected, apart from the motor running inefficiently, the size of the transformer in the motor coach will be more and also the size of the traction transformer in the substation will be more. This too will result into more loss. The metro systems, if motor size is not properly selected, it will result into loss of energy and will ultimately lead to leakage of revenue.

USE OF HIGH GEAR RATIO
The high gear ratio will result into higher acceleration as the torque will increase at the cost of the speed. This is advantageous at start but the balancing speed is achieved at higher value of voltage in the V/ƒ ratio. Since the copper loss will go up with higher voltage, the use of optimum gear ratio will minimize the loss of energy.

Conclusion: There is a tendency to use bigger size of traction motors for quick acceleration. Similarly to increase the starting torque, higher gear ratios are employed. There is a limit to which higher sizes can help. The use of bigger size of the motor results into higher capital and running costs of metro trains. Therefore, the traction motor and a gear ratio of correct size should be chosen for the metro applications.

(S.P. Khade is Director-Technical, Mumbai Metropolitan Region Development Authority)