# Optimized Algorithms For Effective Driving Of Tap Changer Controlled Electric Locomotives In Indian Railways : A Case Study

AbstractIn this work we propose a strategy for driving a tap changer controlled electric locomotive, specifically WAP4, which will result in the highest possible output performance while remaining within the tolerance limits of the voltage and current in the traction motors.

Indian Railways’ electric locomotive fleet [1] is today dominated by tap changer controlled, or ‘conventional’ machines. In the passenger area, the indigenously designed and manufactured WAP4 is the mainstay of electric traction with over seven hundred units in active service. Fast and high priority trains such as Rajdhani and Duronto Express, as well as tightly scheduled 22-24 coach Superfast trains are regularly hauled by WAP4s. With a continuous output of 5000 horsepower (HP) and a maximum well above that, and a peak tractive effort (TE) upwards of 300 kN, WAP4 is more than adequate for any train haulage task in Indian Railways (IR) at the present time.

However it has been observed that the performance of WAP4 varies enormously depending on the technique of the loco pilot (LP) driving it. This happens because the LP must take the notches and shunts at just the right speeds so that the maximum acceleration may be obtained without the motor voltage and current straying beyond their tolerance values. This is a problem in optimization and is by no means trivial; in the absence of a standardized driving algorithm, the LP is reliant on his_{1} skill and experience to devise a strategy of his own. This often causes him to drive in a very conservative manner, which results in gross under utilization of the capabilities of the loco. This fluctuating performance often makes WAP4 undesirable for a prestigious and fast train, where rapid acceleration from halts, caution orders and adverse signals is essential for a punctual run.

In the present Article we propose a standardized driving algorithm, which can eliminate this variability and enable all WAP4s to perform at their full potential. Numerous important trains across IR are still being allotted WAP4 as regular links, and the systematic adoption of a universal strategy will aid considerably in improving their punctuality performance. Moreover, it will also allow fresh allocation and/or reallocation of three phase locomotives on the basis of energy savings alone rather than section clearance considerations.

### Qualitative considerations

The variety of traction motor used in WAP4 [2] is HS15250, which is a dc series motor [3-4]. In addition, a resistor is introduced in parallel to the field element to achieve flux weakening. The schematic circuit diagram of the dc series motor with diverted field is shown in Fig. 1. Here, we define the resistance of the stator parallel resistor as *R*_{1}, that of the stator serial windings as *R*_{2a} and that of the rotor windings as *R*_{2b}. The applied voltage is *V* and the angular velocity of the rotor about its axis is *ω*. The current flowing through the motor as a whole is *i* and the part through the stator alone is *i*_{2}.

It can be shown that

and the torque of the motor is given by

where *C*_{1}, *k*_{2} and *K* are constants for a given motor, *R** _{tot}* is the total resistance of its circuit and

*Rr*denotes the ratio

*R*

_{2a}/

*R*

_{1}.

In Fig. 2 we show the schematic traction circuit of WAP4, exhibiting one motor connected across the rectifier. The motor is the same as in Fig. 1. The multiple motors of the locomotive are all connected in parallel, so that each motor is independent of the other. (In IR jargon, this is known as 6P configuration.) It should be noted that the shunting lever in the pilot cab applies the shunt to all the motors and not just one of them.

The traction motors can be controlled by varying the voltage and the shunt resistor. Voltage control is by selecting the notch setting between 0 and 32; for constant OHE voltage, *V* is proportional to the notch number *N*. The shunt has five possible settings from 0 to 4; the resistance *R*_{1} decreases and hence *Rr* increases progressively with increase in the setting value *S*. The motor voltage limit is 750 V (in a few derated specimens it is 725 V or 700 V). The continuous current rating is 900 A and the ten-minutes current rating is 1100 A. In newer and/or better-maintained locos, a short-term current of 1300 A is also allowed for a maximum duration of two minutes. The tolerance limits are generally enforced by a relay or equivalent circuitry, which causes the notches to automatically regress if the limits are exceeded. However, since there is always the possibility of malfunction of this circuitry, LPs are generally recommended to consciously stay within the tolerance limits instead of relying fully on the electronics.

When the speed is low, the shunt must be kept at zero value to maximise torque. Practically, taking a few notches at low speed immediately results in *i* reaching its tolerance value. Maximum *i* on zero shunt however correspond to maximum torque, which in turn means maximum TE and acceleration. As the train speed increases, *i* will come down rapidly as per (2b), and the question arises as to whether the LP should take a notch or a shunt to counteract this decrease. This issue is resolved by writing (2) in the form

Since higher shunt settings mean higher values of *Rr*, for a constant *i*, the torque is greater for the lower position of the shunt. Hence, whenever possible, the LP should try to attain the tolerance current value at the lowest possible shunt.

Thus, after first hitting tolerance current at low speed, low notch and zero shunt, the LP should wait for the train to accelerate and the current to decrease to such a level that the next notch may be taken without going over the limit. At this point, he should increment the notch level by one, and then again wait before yet another notch can be taken. In this manner, the LP should continue taking notches one after another until either the maximum notch level or the tolerance limit on *V* has been reached. For maximum motor utilization, *i* should jump up all the way to its tolerance value after each notch increment. Using (1b), this implies the successive notches should be incremented at a uniform rate in speed, say one additional notch after every 5 km/hr speed gain.

When the limiting notch has been reached on zero shunt, the shunts come into play. After reaching the last notch, the LP must wait for the current to decrease to a level such that the first shunt may be taken without crossing the limit. If at this point, the torque on first shunt exceeds that on zero shunt, then he should take the first shunt (this condition is found to be satisfied in WAP4). In a like manner, the second shunt should follow the first shunt, the third follow the second and so on. In some locomotives it is observed that *V* decreases after taking of shunts. This is not the expected behaviour as per the ideal characteristics, and it happens because of the non-idealities (finite resistance) in the rectifier as a voltage source. This decrease in *V* worsens the motor performance for no reason, hence it should be immediately compensated by taking extra notches as required. During the entire shunting phase, *V* should be kept as close to its tolerance value as is possible.

Although acceleration is the primary component, which affects the overall timings of a WAP4-driven passenger run, another factor which also plays a role is the tightness with which MPS_{2} is maintained by the LP. The key to achieving constancy of speed is to find the

balancing point i.e. the notch and shunt setting at which the TE of the loco will just equal the train resistance at MPS. For most passenger trains, the balancing power is significantly less than the full power of the loco. The balancing notch and shunt settings are typically determined by hit and trial. If the precise balancing voltage corresponds to a fractional notch, a time-partition between two adjacent notches will be required to balance the train. This will cause oscillations of the speed but since the power on both the higher and lower notch settings is very close to the ideal, these oscillations should be very small and very slow. Even after the balancing point is found once, that does not mean that the train speed will remain constant for all time. Terrain features like gradients and curves, and OHE voltage fluctuations cause the train speed to deviate from the set value. The time scale of these deviations is generally quite large however and the LP should be able to react as soon as a 1-2 km/hr error is encountered. The strength of the reaction should be dependent on the rate at which the train speed is changing – a slow change can be offset by increasing or decreasing a single notch while a rapid change should be attacked with more notches and/or shunts as required. It should be noted that fluctuations due to change in OHE voltage alone can be eliminated by adjusting the notch level so that the voltmeter reading *V* remains constant at all times.

With this we complete the general description of the optimized driving algorithm for any tap changer loco. Our prescriptions constitute an elaboration of the general comments made in [5], and are easier to implement by the loco pilots. In the next Section we obtain numerical values of its various parameters and hence derive the specific triplets (*N*,*S*,*v*) which will enable the LP to get maximum performance out of it.

### Quantitative approach

For a strategy, which can be implemented by a LP on the run, we must talk not in terms of abstract concepts but in terms of hard, concrete numbers. These numbers can be specified only if we know the numerical values of the various motor constants. Some of these constants can be obtained from specification sheets and brochures; some however are not mentioned in the literature. Even for the specified parameters, there can be considerable gap between theory and practice since values change during actual usage. Accordingly, we have first evaluated all the motor parameters by careful interpolation from dozens of data sets obtained from actual runs of WAP4s with passenger trains. Then we have decided on the final values by corroborating these figures with the specifications in manuals. The references used here are [6-8].

The relevant parameters are *k*_{2}*K*, *Rr* and *R** _{tot}*. Since

*Rr*is different for each shunt, we will have to determine its values corresponding to all the shunts. We will label these values with the subscript

*S*i.e.

*Rr*on 2

^{nd}shunt will be denoted as

*Rr*

_{2}.

*R*

*also changes with the shuntvalue as per the rule*

_{tot}Thus by knowing *R*_{2a} and *R*_{2b} and using the determined values of *Rr* at each shunt, we will be able to get the corresponding *R** _{tot}*. The parameter

*C*

_{1}of (2) is an overall normalization constant for the torque and will not affect the strategies in any way.

The units used by us are: *V* in kV, *i* in kA and *ω* in km/hr. By the last one we mean that the numerical value of *ω* in our units will be equal to the numerical value of *v* in km/hr. The conversion to rpm obtains by using the gear ratio and the wheel diameter; for WAP4, the motor rotation rate in rpm is about 12.5 times the train speed in km/hr. The references yield that *Rr*_{0}=0.05. Fixing this, we have interpolated the actual data to obtain the best-fit values *k*_{2 }*K*=0.0062 and* R*_{tot}_{0}=0.26. The ratio in which this gets split between* R*_{2a} and* R*_{2b} is again found from brochures [6] and [7] : the best values are *R*_{2a}=0.09 and *R*_{2b}=0.17. Since the resistances can vary by as much as 10 percent [6], there is no point in specifying the values to greater precision. A combination of the rules taught in driving schools and interpolation from our data sets yields *Rr* for the four shunts as follows : *Rr*_{1}=0.15, *Rr*_{2}=0.26, *Rr*_{3}=0.42, *Rr*_{4}=0.70.

With all the motor parameters determined, we can now express the general strategies of the previous Section in quantitative terms. In Tables 1 and 2 we indicate the speeds at which the various notch and shunt transitions should be taken to maintain maximum motor current at *i*=1.1 kA and* i*=1.25 kA respectively. These of course correspond to the two most common current limits tolerated by WAP4s; since 1.3 kA is a maximum limit we have taken 50 A less as a safety factor. Since the maximum permissible notch level as well as the notching pattern varies with changing OHE voltage, we indicate the strategies for three different voltage levels, corresponding to *V*=0.75 being attained at *N*=24, *N*=27 and *N*=30 respectively. The shunting transitions have been calculated assuming that the voltage remains 0.75 throughout – compensating notches need to be taken by the LP if necessary and have not been shown.

These Tables however have certain prominent limitations. The first is that only three levels of OHE voltage have been considered but in reality the OHE can be at any level between these three. What is the LP supposed to do in that case ? Second is the fact that the motor parameters can vary significantly. As we have already mentioned, the resistance allows for 10 percent variation on either side of the mean. The parameter *k*_{2}*K* is also going to show apparent variation from loco to loco on account of differences in wheel size. For a loco with almost new wheels, 100 km/hr might be equivalent to 1230 rpm, while for a loco with heavily worn wheels it might correspond to 1310 rpm. Since the actual motor variables depend upon its rpm and not on the train speed, *k*_{2}*K* will have to be varied to accurately cover for these two cases. Then are we going to construct a separate table for each of hundreds of combinations of *R** _{tot}* and

*k*

_{2}

*K*?

One way of resolving the above dilemmas would be to propose algorithms based on ammeter readings, which are absolute. But that would not be practical to implement. The resolution is achieved by noting that though the absolute speeds of the various transitions can vary widely with change in parameters, the difference in speed between successive transitions changes only by a small value. Thus, the first column of Table 1 features notch increments at 5 km/hr intervals; for a different set of parameters this interval might change to 5.2 or 5.3 km/hr, which is quite a small change. The shunting intervals too are quite robust to small variation in parameters. And the trend in the notching intervals as OHE voltage varies is also readily apparent – as the line voltage decreases, the interval becomes lower and lower. Periodically

the LP will have to check the ammeter to verify that things are all right but on the whole he can just proceed with notching and shunting at the prescribed intervals. For additional convenience on run, we may round off the shunting intervals to the appropriate multiple of 5 km/hr – that is easier for LPs to remember and execute and causes minimal decrease of loco performance.

With all these modifications in place, the final sheet describing our algorithm is given on the next page. The format of this page is such that it can directly be printed and given to an LP or loco inspector for use on the run. Some additional tips for good driving have been included in points 1 and 4.

### Algorithm for acceleration of WAP4 locomotive

Note : Speeds written in the following format assumed to be in km/hr : **123**

*For 1100 A in traction motor :*

- At start of acceleration run, keep shunt set to 0. Use a small current to bring the couplers to tension and then take notches quickly until ammeter reading becomes 1100 A.

- From this point on keep taking one additional notch at equal intervals of speed. This interval is
**5**if OHE voltage is high,**4**if OHE voltage is low. Just before taking each notch, your ammeter should read about 1050 A.

- Stop taking notches when voltmeter reads 750 V. This should happen at speed around
**75**. Note the exact speed at which you have taken the last notch.

- Starting from the speed noted above, take the four shunts at speed intervals of
**10**,**10**,**10**and**25**Just before taking 1^{st}, 2^{nd}and 3^{rd}shunt your ammeter should read 1000 A or lower. Just before taking 4^{th}shunt your ammeter should read 950 A or lower. However, a shunt transition is best avoided if you are close to the train MPS and the acceleration is still appreciable.

- Take additional notches after successive shunts to compensate voltage drop due to shunting.

*For 1250 A in traction motor :*

- At start of acceleration run, keep shunt set to 0. Use a small current to bring the couplers to tension and then take notches quickly until ammeter reading becomes 1250 A.
- From this point on keep taking one additional notch at equal intervals of speed. This interval is
**5**if OHE voltage is high,**3.5**if OHE voltage is low. Just before taking each notch, your ammeter should read 1200 A or lower.

- Stop taking notches when voltmeter reads 750 V. This should happen at speed around
**60**. Note the exact speed at which you have taken the last notch.

- Starting from the speed noted above, take the four shunts at speed intervals of
**10**,**10**,**10**and**15**Just before taking 1^{st}, 2^{nd}and 3^{rd}shunt your ammeter should read 1150 A or lower. Just before taking 4^{th}shunt your ammeter should read 1100 A or lower. However, a shunt transition is best avoided if you are close to the train MPS and the acceleration is still appreciable. - Take additional notches after successive shunts to compensate voltage drop due to shunting.

It should be noted that the strategies presented above are in very good agreement with the techniques already being used by the best LPs when achieving a quick acceleration run.

### Concluding remarks

We devote one last paragraph to the following issue : it is well known that the intuition and experience of a good loco pilot play a pivotal role in determining the performance of the train; does our scientific algorithm make these qualities redundant ? The answer to this is an emphatic no. Our strategies are meant to supplement and not supplant a dexterous LP’s instincts. As we have already mentioned, the motor parameters can vary from loco to loco and a single strategy cannot account for a thousand parameter combinations. We can prescribe intervals ranging between 3.5 and 4.5 km/hr but the best value in any given situation will have to be determined live, in the cab. The better the LP, the better will he find this interval and the closer will he remain to the motor’s permitted current. The same considerations hold for maintenance of MPS – we may mention typical balancing positions for certain loads but again the specific point has to be worked out by the LP on the run. That said, our algorithms will go a long way in improving the performance of LPs on a daily basis. A less skilful LP will just have to follow the more conservative paths through our strategy sheets, such as taking the maximum intervals when a range has been specified. Still, the difference between his performance and the optimal performance will be quite small, unlike what happens now. Even skilled LPs have to accumulate a lot of experience before their instincts can take them close to the optimal strategy; our algorithm will enable them to clock good figures from their first day at the controls. Moreover, an LP driving by instinct is bound to show variation from one run to the next; this variation can be greatly reduced if the overall strategy is learnt like a formula and mechanically executed on run. Finally, a definite algorithm has enormous pedagogical advantages over instinctive methods; in driving schools, it can easily be imparted to the LPs during initial and/or refresher training.

### Acknowledgement

I would like to express my heartfelt thanks to Shri Bhawnath Jha, loco pilot (Rajdhani) of ALD Division, NCR for painstakingly collecting dozens of run time data sets, which I have used in this Article. Without his contribution, the calculations presented here would have been impossible and I remain forever grateful to him.

### Footnotes

_{1} In view of the overwhelming preponderance of males in the profession of LP, we use the masculine forms to denote both male and female LPs.

_{2} In this Article the abbreviation MPS refers to maximum permissible speed only. We do *not* follow the convention found in some documents e.g. [5] of using ‘MPS’ to denote the shunting lever.

### References

[1] http://elocos.railnet.gov.in/Loco_bank/shedwise.aspx

[2] http://www.irfca.org/faq/faq-loco2e.html#wap-4

[3] http://www.railelectrica.com/traction-motor/dc-series-motor-as-traction-motor/

[4] A E Fitzgerald, C Kingsley and S D Umans, “*Electric Machinery*,” Sixth Ed. Mc Graw Hill New York, USA (2008)

[5] Electrical Engineering Directorate, Indian Railways, “Tips for better enginemanship for loco pilots.” http://www.indianrailways.gov.in/railwayboard/uploads/directorate/ele_engg/Circulars/TIPS _041011(1).pdf

[6] RDSO, “Pamphlet on Traction Motor HS 15250A,” Gwalior, MP (2010). http://www.rdso.indianrailways.gov.in/works/uploads/File/Pamphlet%20on%20Traction%20Motor%20HS-15250A-eng.pdf

[7] http://trainweb.org/railworld/Electric_Locos/wap4.htm

[8] http://www.cgglobal.com/frontend/ProductDetail.aspx?id=j7Cu6ITnQ60=

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Sir,

Thank you very much for posting this article on this website. In this comment I would just like to add here the results for the maximum acceleration of certain standard loads, which I have obtained through simulation of the driving strategy combined with train weights from official documents and train resistance formula from this website itself. For LHB coaches, the drag formula is F = m(0.699+0.0215v+0.0000835v^2) where m is the train mass in tonnes, v is the speed in km/hr and F is in kgf. This gives the following acceleration time and distance to accelerate from 30 km/hr to 129 km/hr :

Loco with 1100 A capacity :

15 coach (740t excluding loco) : 2m 50s, 4.1km

18 coach (880t) : 3m 25s, 5.0km

21 coach (1020t) : 4m 00s, 5.9 km

Loco with 1300 A capacity :

15 coach : 2m 25s, 3.6km

18 coach : 2m 55s, 4.3km

21 coach : 3m 30s, 5.2km

For 24 coach, 1320t ICF load the figures from 30 km/hr to 109 km/hr are 4m 00s, 5.0km and 3m 25s, 4.3km with 1100 A and 1300 A loco respectively.

In many cases however I have observed that acceleration of Rajdhani with LHB rake is taking significantly longer time than the above prescription even though near-optimal strategy is being followed by LP. The power required to balance the load is also significantly higher than that predicted by the drag formula above. Since most of the deviation occurs at the high speed range, I decided to modify the coefficient of the quadratic term. The value 0.000345 (instead of 0.0000835) provided a good fit to the data. With this drag formula, the re-calculated acceleration times and distances are :

Loco with 1100 A capacity :

15 coach : 3m 20s, 5.0 km

18 coach : 4m 20s, 6.8 km

21 coach : 5m 35s, 9.0 km

Loco with 1300 A capacity :

15 coach : 2m 50s, 4.3 km

18 coach : 3m 35s, 5.6 km

21 coach : 4m 35s, 7.3 km

These are in good agreement with the actual observations. Finally, since authenticity and integrity of research is an important issue in today’s world, I have made public the experimental records which were used to obtain the algorithm. These can be found at my homepage, home.iitk.ac.in/~shayak subfolder Motors and Traction, filenames WAP4 Data 2 Set 1 & Set 2. Set 1 deals with 16 coaches, 790 tonnes and Set 2 has 15 coaches, 740 tonnes load.

Shayak