Electric Power Calculations (Basics):-

**Electric power definition: **P is the electric power in watt (W).

**Electric power calculation: **Electric power is the rate of energy consumption in an electrical circuit. The electric power is measured in units of watts.

The electric power P is equal to the energy consumption E divided by the consumption time t:

Example: P = E / t = 120J / 20s = 6W;

where,

E is the energy consumption in joule (J),

t is the time in seconds (s),

**Power of DC circuits: **Electrical power is the “rate” at which energy is being consumed in a circuit.

The electrical power within an electrical circuit is only present when both the voltage and current are present, that is no open-circuit or closed-circuit conditions.

P = V · I;

or

P = I[2] * R;

or,

P = V[2] / R;

where,

V is the voltage in volts (V),

I is the current in amps (A),

R is the resistance in ohms (Ω),

**Power of AC circuits: **Electrical power follows the constant change of the current wave and has two components, an instant resisitive value and a reactive value.

P = Vrms*Irms = Irms[2]R,

Vrms and Irms are the direct resistive values components and they give the same heating effect as an equivalent DC power,

Vpk = Vrms × √2,

Vrms = Vpk * 0.7071,

Pavg = Vrms[2] / R,

Irms = Pavg / Vrms,

where:

Vpk = Peak Voltage value,

Vrms, Irms are Voltage respective Current Root-Mean-Squared values,

Pavg is the average power value,

**Power Factor: **The power factor is equal to the real or true power P in watts (W) divided by the apparent power |S| in volt-ampere (VA):

The electrical power consumed by a resistance, (R) is called the true or real power and is simply obtained by multiplying the rms voltage with the rms current. The power stored by a reactance, (X) is called the reactive power and is obtained by multiplying the voltage, current, and the sine of the phase angle between them.

The symbol for phase angle is θ (Theta) and which represents the inefficiency of the AC circuit with regards to the total reactive impedance (Z) that opposes the flow of current in the circuit.

PF = P(W) / |S(VA)|;

PF - power factor,

P - real power in watts (W),

|S| - apparent power - the magnitude of the complex power in volt⋅amps (VA),

For sinusuidal current, the power factor PF is equal to the absolute value of the cosine of the apparent power phase angle φ (which is also is impedance phase angle),

PF = |cos φ|,

φ is the apprent power phase angle,

Number of Units = kilowatt-hour (kWh)

Total electricity cost per month = (Number of Units) * (kWh average price),

The kWh average price is based on utility provider contract value.

Example:

SO Cal. Edison Electric rates as 2018 are:

Tier 1: 0-356 kWh || $0.17/kWh,

Tier 2: 357-1424 kWh || $0.25/kWh,

Tier 3: 1425+ kWh || $0.33/kWh,

A household consuming 2500 units per month will pay:

Tier 1: $60.52 for first 356 units,

Tier 2: $266.75 for the next 1067 units,

Tier 3: $354.75 for the last 1075 units,

It comes to a totl of $681.75 for 2500 units of electric energy consumed in a month time.

At $8181.00 per year, it becomes an incentive to go for solar panel based power generation.