1. DC Electric Circuits
In order to identify an electrical system in DC, a measurement of the electrical current, I, flowing through the bipoles and their electric voltage, V, across the terminals has to be formed.
These measurements can be arranged by means of a DC ammeter and voltmeter. The electric power, P, related to such a bipole, can be defined as the product of the voltage and current applied to: P =V × I . The power generated by an active bipole can
2. Single-Phase AC Electric Circuits
The electric power in a single-phase AC circuit can be defined as:
p(t) = v(t)i(t)
where p, v, i are instantaneous power, voltage, and current, respectively.the instantaneous power is
p = v.i = 2 V I cos wt . cos (wt - φ)
The average power is
where V and I are the effective (R.M.S.) values of the voltage and current.
Voltage & Current Relationship in 3-Phase Circuit
3. Three Phase Power Measurement using Two Watt-meter
Figure below shows the Two Watt-meter connection may be used to determine the power in a three-phase three-wire circuit (for unbalanced condition).Star connection:
Power indicated by W1 :
P1 = VAB IA cosΦ
Power indicated by W2 :
P2 = VCB IC cosΦ
Power indicated by W2 :
P2 = VCB IC cosΦ
ΦCB-C is the phase difference between VCB and IC. VCB = VCN - VBN (Potential drop across W2).
Sum of the powers measured by the two wattmeters W1 and W2 would equal:
PT = P1 + P2
4. Three Phase Power Measurement – Analysis in the Balanced Case
Phase difference between VAB and VAN is 30°.
If the load is assumed to be inductive, the current is lagging behind their respective phase voltage by Φ, the phase difference between IA and VAB is = (30°+ Φ).
For a balanced supply and three-phase load:
Power indicated by Watt-meter W1:
P1 = VabIa cosΦab-a = VL.IL.cos(Φ+30o)
where VL is the magnitude of the line voltage and IL that of the line current.
Power indicated by wattmeter W2:
P2 = VcbIc cosΦcb-c = VL.IL.cos(Φ - 30o)
The sum of the two Wattmeter readings:
P1 + P2 = VL.IL.cos(Φ +30o) + VL.IL.cos(Φ-30o) = VL.IL.[cos(Φ+30o) + cos(Φ-30o)]
= VL IL cosΦ
5. To Solve for Power Factor from the above analysis Consider P1 = W1 & P2 = W2
by using above formula we can easily calculate the condition of Power Factor.
An AC system of Active power (P), Reactive power (Q), and Apparent power (S) plays a major role in electric power technology.
The terms of Active power, Reactive power, and Apparent power are applied to steady-state alternating current circuits in which the voltages and currents are non-sinusoidal.
Today it is characteristic in most parts of the applications that the current and voltage are Non-Sinusoidal.
1. Definition of Power Factor
In the earlier definition the power factor is the classical definition, for pure sine wave current and voltage
2. Zero Cross Detection
3. Definition for non-sinusoidal current and sinusoidal voltage of power factor is
Energy, heat, work and power are four concepts that are often confused. If force is exerted on an object and moves it over a distance, work is done, heat is released (under anything other than unrealistically ideal conditions) and energy is transformed. Energy, heat and work are three facets of the same concept. Energy is the capacity to do (and often the result of doing) work.
1. Energy meter or watt hour meter is classified in accordance with several factors such as
3. Electronic Energy Meters
It is an advanced metering technology involving placing intelligent meters to read, process and feedback the data to customers. It measures energy consumption, remotely switches the supply to customers and remotely controls the maximum electricity consumption. Smart metering system uses the advanced metering infrastructure system technology for better performance.
5. Formula to calculate the amount of Energy consumed by a Load
The calculation is as follows:
[number of hours’ use] x [number of days’ use] x ([capacity of appliance expressed in watt] / 1,000) = number of kWh
The capacity should be divided by 1,000 to convert the number of watts into the number of kilowatts. This finally gives us the number of kWh (kilowatt-hours).