Power factor in three phase system

  In our previous topic, we already know and had knowledge in getting power factor correction. Now in three phase system power factor is also applicable in correcting power consumer that is using this system.

using this example, you can easily get how to solve power factor correction.

Two balanced loads are connected to a 240-kV rms 60-Hz line, as

shown in Figure. Load 1 draws 30 kW at a power factor of 0.6

lagging, while load 2 draws 45 kVAR at a power factor of 0.8 lagging.

Assuming the abc sequence, determine: (a) the complex, real, and reactive

powers absorbed by the combined load, (b) the line currents, and

(c) the kVAR rating of the three capacitors -connected in parallel with

the load that will raise the power factor to 0.9 lagging and the capacitance

of each capacitor.

Power in Balanced system

SUMMARY of WYE and Delta connections formula

DELTA-WYE Connection

example,


A balanced Y-connected load with a phase impedance of is 40 + j 25 ohmssupplied by a balanced, positive sequence -connected source with a linevoltage of 210 V. Calculate the phase currents. Use 
Vab as reference.

Balanced DELTA-DELTA connection

WYE - DELTA connection

WYE-WYE connection

    EXAMPLE:

A Y-connected balanced three-phase generator with an impedance of 0.4+j 0.3 ohms per phase is connected to a Y-connected balanced load with an impedance of 24- + j19 ohms per phase. The line joining the generator and the load has an impedance of 0.6 + j0.7 ohms per phase. Assuming a positive sequence for the source voltages and that Van = 120 ∠ 30 °  V, find : (a) the line voltages, (b) the line currents.

Balanced Three-Phase Voltages

Power Measurement

                   Every house has its own bill provided by their electric utility company. And every month, we are paying for it. But, are you not wonder why there is no such a list of appliances in the electric bill? Like… 1. Electric iron 2. air conditioner and etc.?  Well, probably none and it will never happen because they are categorize by …… and they are charge in a different rate for each kilo-watt hour (kWh) used. A kilo-watt hour (kWh) is 1000 watts of energy used in a one hour period.  A 1000 watt appliance that is turned on for 1 hour equals 1 kilo-watt hour. Well, that’s probably our oven toaster or electric iron. They are just LIKE A BOSS!!

              But so much for that, consumers are operating many appliances, and it gets measured by the electric meter. But the problem is some consumers do not know how electric bill comes up with that amount of charge per month.

For those who are not fun with mathematics, but wanted to know how exactly electric bills are calculated. a li'l mathematics can be apply.

We called it ohm’s Law:

                      Voltage (V) = current (I) x Resistance (R)   

                      Power (P) = current (I) x voltage (V)

                     Voltage (V)        unit is Voltage/ V

                     Current (I)          unit is Ampere/ A

                    Resistance (R)   unit is Ohms/ Ω

                    Power (P)            unit is Watts/ W

Sometimes you notice at the back portion of your appliances, you will see some of the listed above.  Lucky you if you will saw the wattage of it but if it is not, you will force yourself to do calculations. Sometimes voltage and current rating are given. So, you will just multiply the two as shown above to get the power rating.

A consumer consumes 1000 watts load per hour daily for one month. Calculate The Total Energy bill of the consumer if per unit rate is 9 in $ [Take 1 month = 30 Days]

Solution

1unit = 1kWh. 

So Total kWh = 1000 x 24 x 30 = 720000 watts/hour

we Want to convert it into Units, Where is 1unit = 1kWh.
So total Consumed units. 720000/1000...... (k=kilo=1000)
Total Units = 720.
Cost of per unit is 9.
So total Cost or bill= 720 x 9 = 6480 $

(1000 watts for 1 hour = 1kWh = 1 unit of Energy) So if the rate of unit is 5 Dollars, then you will pay 5 Dollars as a bill for your bulb.

Effective RMS Values

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I’ve learned that RMS, or Root Mean Square, is the measurement used for any time varying signal's effective value. As they said it is not an "Average" voltage.  Its mathematical relationship to peak voltage varies depending on the type of waveform. By definition, RMS Value, also called the effective or heating value of AC, is equivalent to a DC voltage that would provide the same amount of heat produced in a resistor.

Apparent Power and Power Factor

Complex power

     Complex power       

                                    factor has been studied and  formalized for a very 

                                   long time just to fined the total effect of Parallel loads. 

                                    It is very important in power analysis because it 

                                    contains all the  information pertaining to the 

                                     power absorbed by a given load. 

S = 1/2 VI*   or    S= Vrms Irms

 and

S= Vrms Irms  ∠θv - θi

                                         But complex power maybe expressed in terms of the load impedance Z so we may write

                                       
Example 

                                          complex power contains all the relevant 
                                          power  information in a given load.

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I’ve learned that complex power is very conceptual and essential to understand.

I’ve learned that Complex numbers can help us in acquiring all loads. And these are, resistor absorbs the real power and dissipates in the form of heat and light. Inductor absorbs the reactive power and dissipates in the form of magnetic field. Capacitor absorbs the reactive power and dissipates in the form of electric or electrostatic filed. Using complex power we can easily determine if it is inductive, capacitive or it is resistive loads. For expressing the complex power we have to first consider a single phase network whose voltage and current can be represented in complex form.