ENERGY CONSUMPTION COST

Electrical consumption cost is the amount of electricity consumed by the household appliances. It is measured in kWh.

HOW DOES IT MEASURED

The electric company used a device to measured the amount of electric of each houses in the area. This is called the meter.

Digital meter

Every end of the month, they read the meter and using their device they instantly give the electrical statement.

All appliances have the same electrical consumption (Watt). Look at the picture below:

The refrigerator is the 24/7 on in all appliances and it consumed 727W per hour, think about it.  The television (flat screen) consumed only 133 W/h not like the tube TV consumed almost 330W/h.

HOW TO CALCULATE THE MONTHLY USED OF ELECTRICITY

The formula to compute the monthly electricity consumtion is:

Wattage of appliance x average hrs used in a day x no. of days in a month that it is used x the electrical cost

For example the flat screen TV consumed 133W and  you used it 8 hrs every weekends but on weekdays you used it 3 hrs only. The electrical cost is 7 pesos per KWh  To solved this problem, used the table to know the wattage of this appliance and then compute how many days in weekends and weekdays in a month. Then solved it using the formula.

For weekends

133W x 8hrs = 1064Wh or 1.064KWh

1.064 x 8 days = 8.512KWh in a month

For weekdays

133W x 3hrs = 399 W

399W x 22 days =8.778KWh in a month

Sum it up

8.512 + 8.778 =17.29

17.29 x 7 = 121. 03 pesos

The cost is 121.03 pesos. This is only in your TV not included the refrigerator iron and air conditioner.

TIPS TO LESSEN THE AMOUNT OF COST

1. Unplug the appliance is not in used. like the tv if it is in standby mode it also consumed electricity.

2. Using the washing machine and iron, create a schedule to used it for example once a week.

3. Before going to bed, check all the appliances if it is turn off /unplug and also turn down the thermostat of the refrigerator to lessen the cool.

4. Used only the rice cooker if it is needed, like you are busy for something and you can used this but if not you can used the stove or the coal to cook rice.

5. Used only the CFL to save more energy.

6. In case of brownout, Unplug all the appliance for safety and do not plug it immediately if the electricity came back.

7.  If buying new appliances, look the Energy efficiency first before buying it.

8. Used only the computer or laptop in important things.

MAXIMUM POWER TRANSFER

MAXIMUM AVERAGE POWER TRANSFER

To obtain the  maximum average power transferred from a source to a load, the load impedance should be chosen equal to the conjugate of the Thevenin equivalent impedance representing the reminder of the network. This means that the load impedance must be solved using the thevenin’s theorem

The formulas to solve for ZL:

STEPS IN SOLVING THE ZL AND POWER TRANSFER

1. Solve the load impedance (ZL) using the Thevenin’s theorem. Short the voltage source and open the current source.

2. Solve the Vth where Zl parallel to it, this means that the ZL is not concluded to solve the Vth.

3. The ZL must be in rectangular form . Used only the real part ( Rth +/- jXth)

4. The RL is equal to the conjugate of Zth. (see in formula)

5. Solve the power using the  formula below:

where: Vth=Voc

(Click the image to enlarge)

      The maximum average power transfer is a method to identify the maximum impedance load that is needed in the given ac circuit. This can be solve using thevenin’s theorem.

EFFECTIVE OR RMS VALUE

   The effective or root mean square(RMS) value of a periodic current is the DC value that delivers the same average power to a resistor as the periodic current.

IN SINUSOID

The Root Mean Square (RMS) value of a sinusoidal voltage or current is equal to the maximum value divided by square root of 2.

APPARENT AND COMPLEX POWER

• Real power (P) [Unit: W]
• Reactive power (Q) [Unit: VAR]
• Complex power (S) [Unint :VA]
• Apparent Power (|S|)

Real power  (P) is equal to the Voltage magnitude times Current magnitude time cos(angle of v -angle o i).

P=VrmsIrmscos(Av-Ai)

Reactive power (Q)= to Ssin(angle v-angle i)

Apparent power is the power that is “appears” to flow to the load. (S= |Vrms||Irms|)

Complex power (solve in polar form) = Vrms(Irms)*.    note * is the conjugate or the angle will be in opposite sign.

or S = P + jQ  (if converted in rectangular)

where P is the real power and Q is the reactive power.

power factor(pf) = P/S = cos(angle v-angle i)

Example (Click to enlarge)

USING THE POWER TRIANGLE

The power triangle graphically shows the relationship between real (P), reactive (Q) and apparent power (S).

Example: Find the complex power of the three loads

Solution:

Using the power triangle, it is more easily to solve the given problems and if you know how to used trigonometric functions then the problem is a piece of cake to you. But first things to do in solving the problem is to understand it, what is asked and what method is easily to solve the given problem