Calculation of PWt

The item PW_t 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 full load, 89%
    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 full load, 88.5%
    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.

Home Economics of Use of Electrical Apparatus Calculation of PWt


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Calculation of PWt Author: E.E. Kimberly The item PW_t 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 full load, 89% 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 full load, 88.5% 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.
Home Economics of Use of Electrical Apparatus Calculation of PWt