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elena55 [62]
3 years ago
9

An industrial plant consists of several 60 Hz single-phase motors with low power factor. The plant absorbs 600 kW with a power f

actor of 0.75 lagging from the substation bus. The supply voltage is 12.47 kV. The power factor can be improved by connected a capacitor in parallel with the supply or by using a synchronous motor, which generates reactive power. Analyze both of these cases independently:(a) Find the required kVAR rating of a capacitor connected across the load to raise the power factor to 0.95 lagging.
(b) Assuming a synchronous motor rated at 250 hp, with an 80% efficiency is operated from the same bus at rated conditions and a power factor of 0.85 leading, calculate the resultant supply power factor.
Engineering
1 answer:
Gelneren [198K]3 years ago
8 0

Answer:

(a) Q=332 kvar and C=5.66 uF

(b) pf=0.90 lagging

Explanation:

Given Data:

P=600kW

V=12.47kV

f=60Hz

pf_{old} =0.75

pf_{new} =0.95

(a) Find the required kVAR rating of a capacitor

\alpha _{old}=cos^{-1}(0.75) =41.41°

\alpha _{new}=cos^{-1}(0.95) =18.19°

The required compensation reactive power can be found by

Q=P(tan(\alpha_{old}) - tan(\alpha_{new}))

Q=600(tan(41.41) - tan(18.19))

Q=332 kvar

The corresponding capacitor value can be found by

C=Q/2\pi fV^{2}

C=332/2*\pi *60*12.47^{2}

C=5.66 uF

(b) calculate the resultant supply power factor

First convert the hp into kW

P_{mech} =250*746=186.5 kW

Find the electrical power (real power) of the motor

P_{elec} =P_{mech}/n

where n is the efficiency of the motor

P_{elec} =186.5/0.80=233.125 kW

The current in the motor is

I_{m} =(P/\*V*pf)

The pf of motor is 0.85 Leading

Note that represents the angle in complex notation (polar form)

I_{m} =(233.125/12.47*0.85)

I_{m}=18.694+11.586j A

Now find the Load current

pf of load is 0.75 lagging (notice the minus sign)

I_{load} =(600/12.47*0.75)

I_{load} =48.115-42.433j A

Now the supply current is the current flowing in the load plus the current flowing in the motor

I_{supply} =I_{m} + I_{load}

I_{supply}= (18.694+11.586)+(48.115-42.433)

I_{supply} =66.809-30.847j A

or in polar form

I_{supply} =73.58°

Which means that the supply current lags the supply voltage by 24.78

therefore, the supply power factor is

pf=cos(24.78)=0.90 lagging

Which makes sense because original power factor was 0.75 then we installed synchronous motor which resulted in improved power factor of 0.90

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