Electrical Engineering is a free introductory textbook to the basics of electrical engineering. See the editorial for more information....

# Calculation of PWt

Author: E.E. Kimberly

The item PWt is the total present worth of the service desired over the period of n years. Hence,

Example 23-1. - A motor is to be bought to drive an air compressor. The motor will run continuously 8 hours every day. The load is intermittent and of uncertain duration, but is 50 hp for an average of 6 hours per day and 10 hp for 2 hours per day. Power is available at 440 volts, 3 phase, 60 cycles.

```Salesman No. 1 offers the following synchronous motor:
3 phase, 60 cycles, 440 volts, 50 hp, 1.0 power factor,
40 deg C temperature rise, 1200 rpm
Life expectancy, 20 years Price complete with exciter and automatic starter and
base plate........................................\$1400
Cost of installation...................................100

Total cost (Cc).......................................\$1500

Efficiency at 1/2 full load, 35%
Cost of maintenance, \$25 per year

Salesman No. 2 offers the following wound-rotor induction motor:

3 phase, 60 cycles, 440 volts, 50 hp
40 deg C temperature rise, 1150 rpm
Life expectancy, 20 years
Price complete with base plate and automatic starter.....\$1068
Cost of installation......................................100

Total cost (Cc)..........................................\$1168

Efficiency at 1/2 full load, 34.0%
Power factor at full load, 88.5%
Power factor at 1/2 full load, 52.0%
Cost of maintenance, \$20 per year

The cost of energy is \$0,025 per kw-hr
The cost of taxes and insurance is 9 per cent of the purchase price The interest rate is 6%
It is required to determine the choice of motor on the assumption that service will be discontinued after 40        years.
```

Solution. - The present worth PWt of proposal No. 1 will be found first, as follows:

The annual cost of operation is the sum of the separate costs enumerated as follows:

The cost of taxes and insurance is

The total annual operating cost is then Therefore,

The present worth of proposal No. 2 will now be found as follows:

The annual cost of operation is the sum of the separate costs enumerated as follows:

The cost of taxes and insurance is

The total operating cost is then

Therefore,

The difference between

the costs of the two proposals is Based on the present worth of' the first proposal, the second one is better by 1.28%.

The power-factor correction possibilities of the synchronous motor (see Chapters 19 and 25) have not been credited to it. Furthermore, if the load should decrease by 40 or more per cent, the decreased power factor of the induction motor would bring a penalty through the power-factor penalty clause, if any, in the power contract, whereas the power factor of the synchronous motor could be held above the penalty point.

If the number of hours of use should increase above that given, the slightly superior efficiency of the synchronous motor would cause the foregoing calculations to favor that machine even more.

Last Update: 2010-10-06