Selection of Transformer to Supply a Cyclic Load 2

[VTer]

Hi All,

I saw a reference that "When the load cycle is sufficiently short so that the temperature of the transformer does not change appreciably during the
cycle, the minimum transformer size is the rms value of the load."

The equation that is provided is S=sqrt((S1^2*t1+S2^2*t2)/t(cycle))

For example: S1=100kVA for 2 min, S2=50kVA for 2min total cycle time is 4 min.

Using the above equation the resultant min transformer size is 79kVA.

My question is, why the need to perform RMS of the load which is already a resultant value of RMS current and voltage? Why not just take the average value which in this case would be 75kVA?


"Throughout space there is energy. Is this energy static or kinetic! If static our hopes are in vain; if kinetic ù and this we know it is, for certain ù then it is a mere question of time when men will succeed in attaching their machinery to the very wheelwork of nature". û Nikola Tesla

 

[waross]

To put this in perspective, the OP was asking about a 26.6% overload.
The question was to do with the formula for a load that cycled between 50 KVA and 100 KVA and a complete cycle time of 4 minutes, on a calculated minimum transformer size of 79 KVA.
The OP asked why he couldn't use the average for a calculated transformer size of 75 KVA.
His question was explained to his understanding and satisfaction in the first reply.


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[crshears]

Fair point, Bill, but so many other interesting things have come up in this thread that I would have missed out on had it not continued...

For example, the mention of rail track transformers brings to mind a discussion I once had with a very knowledgeable subway train driver with the Toronto Transit Commission: based on what I was told, even if an operator there selects full ahead from the control cab, the automatic train controls are set up to step the traction motors on load sequentially such that shock load is never applied to their supply transformers or rectifiers. This driver told me that the reason a person could feel sequential "jerks" in the motion of the train as it accelerated from rest was because of this stepping action. Further to this, I was also told that since the traction motors were all series motors, they would not sustain damage if something went wrong with the stepping action and just one set of motors ended up doing all the work of accelerating the train.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

 

[waross]

That has more to do with DC motor starting than with transformer effects.
The current drawn by a motor is proportional to the difference between the applied voltage and the back EMF.
This current is limited by the motor impedance.
In an AC motor the greater part of the impedance when at rest is the inductive reactance.
The impedance limits the DOL starting current to about 6 times full load current.
In a DC motor the current is limited by the resistance of the armature circuit.
The starting current of a DC motor started DOL will be unacceptably high.
There are exceptions for fractional HP motors and special cases such as engine starting but the majority of DC motors of any size above about 1/2 HP must use reduced current starting.
DC drives may use some method to limit the effective applied voltage.
Old school, series resistors were used to limit starting current.
Traction motors used transpositions. Various series parallel combinations as the motors accelerated.
Starting from rest, even with all the motors in series, would still give the transformers a current hit.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[prc]

crshears, track side transformers in traction substations and loco transformers inside the engine room are different items. Track side transformers are single phase units stepping down power from 33- 400 kV ( between phases) to 25 kV (normal) single phase between rail and overhead line.Trackside units get pulsating load due to the varying traffic density in the lines. Loco transformers are inside engine room taking power at 25 kV by pantograph and stepdown to lower voltages (< 1Kv) to feed converters(thyristors) In 1950s there used to be an OLTC on primary side of loco transformer.Driver used to operate this tap-changer for controlling speed by adjusting the secondary voltage. DC output used to feed DC traction motors. From 1990 onwards 3 phase induction motors are used as traction motors. In this arrangement,OLTC is no more used. Transformer secondary output feed IGBTs. DC is again inverted to 3 phase AC to feed induction motors.

 

[crshears]

It appears I knew not whereof I spoke; please forgive me.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

 

[7anoter4]

In my opinion,the o.p. is refering to:
IEEE Std C57.96-1999 IEEE Guide for Loading Dry-Type Distribution and Power Transformers
4.5 Short-time loading and life expectancy determined by measured temperatures
The relative life expectancy in percent, P, for an initial equivalent constant load followed by an equivalent constant peak load may be determined as follows, using measured temperatures:
a,b,c,e,
f) The relative life expectancy resulting from such a load cycle repeated every t1 + t2 hours during the
operation of transformers is
Pr = (t1 + t2)/[(t1/P1) + (t2/P2)]
So if P1=100 kVA t1=2/60 hrs and P2=50 kVA for 2/60 hrs
Pr=(2+2)/(2/100+2/50)=66.67% relative life expectancy