Power Triangle

          In AC circuits, current and voltage are normally out of phase and, as a result, not all the powerproduced by the generator can be used to accomplish work.   By the same token, power cannotbe calculated in AC circuits in the same manner as in DC circuits.   

The power triangle,  equates  AC  power  to  DC  power  by  showing  the  relationship  between  generatoroutput (apparent power - S) in volt-amperes (VA), usable power (true power - P) in watts, andwasted or stored power (reactive power - Q) in volt-amperes-reactive (VAR).   The phase angle(q) represents the inefficiency of the AC circuit and corresponds to the total reactive impedance(Z) to the current flow in the circuit.

The power triangle represents comparable values that can be used directly to find the efficiencylevel  of  generated  power  to  usable  power,  which  is  expressed  as  the  power  factor  (discussedlater).    Apparent  power,  reactive  power,  and  true  power  can  be  calculated  by  using  the  DC equivalent (RMS value) of the AC voltage and current components along with the power factor.

APPARENT POWER

Apparent  Power  (S)  is  the  power  delivered  to  an  electrical  circuit. Equation  is  a mathematical representation of apparent power.   The measurement of apparent power is in volt-amperes (VA).S = I2Z = ITwhereS   = apparent power (VA)I    = RMS current (A)E   = RMS voltage (V)Z   = impedance (W)

TRUE POWER

True power (P) is the power consumed by the resistive loads in an electrical circuit.  The measurement of true power is in watts.P = I2R = EI cosq, whereP   = true power (watts)I    = RMS current (A)E  = RMS voltage (V)R  = resistance (W) q= angle between E and I sine waves.

REACTIVE POWER

Reactive  power  (Q)  is  the  power  consumed  in  an  AC  circuit  because  of  the  expansion  and collapse of magnetic (inductive) and electrostatic (capacitive) fields.  Reactive power is expressed in volt-amperes-reactive (VAR). 

POWER FACTOR

Power factor (pf) is the ratio between true power and apparent power.  True power is the power consumed  by  an  AC  circuit,  and  reactive  power  is  the  power  that  is  stored  in  an  AC  circuit. Cos theta is called the power factor (pf) of an AC circuit.   It is the ratio of true power to apparent power, where q is the phase angle between the applied voltage and current sine waves and also between P and S on a power triangle shown on the figure above.

By: Kirk Macaraeg 

Tesla Coil

While I was finished watching one episode of an anime series scheduled on this day I switched the program to the ‘’Discovery Channel‘’ and in that documentary I saw how they explained the concepts of a Tesla Coil and how it can create a large high voltage spark that look like it was dancing in the air.

The explained that basically a tesla coil is and electrical device based on a type of resonant transformer circuit invented by a man named Nikola Tesla around the year 1891.  Later that day  went to an internet business centers and researched in http://en.wikipedia.org/wiki/Tesla_coil  to know more about Tesla coils and found out that Tesla coils is said to produce high voltage, low current, high frequency alternating current electricity. Tesla coils also produce higher current than the other source of high voltage discharges, electrostatic machines. The Tesla coil circuits were used commercially in spark gap radio transmitters for wireless telegraphy until the year 1920s also in pseudo medical equipment such as electrotherapy and violet ray devices. Today their main use is for entertainment and educational displays. 

In the concept of how a Tesla coil can produce a high voltage, low current, high frequency alternating current electricity from a 220-V  60-HZ power source.

The concept is that an AC source goes through a High voltage Step-up transformer where the output is increased, then it goes through multiple high voltage tank capacitor and a spark-gap and The Tesla coil primary winding connected in series.

  In each circuit experiment, the AC supply transformer charges the tank capacitor until its voltage is sufficient to break down the spark gap. The gap suddenly fires, allowing the charged tank capacitor to discharge into the primary winding. Once the gap fires, the electrical behavior of either circuit is identical. 

However, in the typical circuit the spark gap's short circuiting action prevents high frequency oscillations from 'backing up' into the supply transformer. This in turn allows the supply to move up to the primary and secondary winding until it reaches the top where it is discharged as a high voltage spark.

Here is an image shown below:

By:Leonardo Regino 

Power Factor

Power factor is the ratio of the real power (W) or average power and the apparent power (VA) and it is symbolized by PF.

In the sinusoidal case, the power factor is simply cos (theta - phi), where (theta-phi)is the angle by which the voltage leads the current. It can also be computed by cos (theta L), where (theta L) is the angle of the total impedance of the circuit.

For a purely resistive load, the voltage and current are in phase, (theta - phi) is zero and the PF is unity (1). In other words, the apparent power and the average power are equal. Unity PF, however, may also be achieved for loads that contain both inductance and capacitance if the element values and the operating frequency are carefully selected to provide an input impedance having a zero phase angle. A purely reactive load, will cause a phase angle difference between the voltage and current of either plus or minus 90o, and the PF is therefore zero.

Power factor can also be lagging or leading. Leading and lagging refers to the phase of the current with respect to the voltage. Thus, an inductive load will have a lagging PF and a capacitive load a leading PF.


By: Jonald Sarmiento

Apparent Power

Historically, the introduction of the concepts of apparent power and power factor can be traced to the electric power industry, where large amounts of electric energy must be transferred from one point to another; the efficiency with which this transfer is affected is related directly to the cost of the electric energy, which is eventually paid by the consumer. Customers who provide loads which result in a relatively poor transmission efficiency must pay a greater price for each kilowatthour (kWh) of electric energy they actually receive and use. In a similar way, customers who require a costlier investment in transmission and distribution equipment by the power company will also pay more for each kilowatthour unless the company is benevolent and enjoys losing money.

Assume that the sinusoidal voltage V= V_m cos (⍵t + theta) is applied to a network and the resultant sinusoidal current is I = I_m cos (⍵t + phi). The phase angle by which the voltage leads the current is therefore (theta-phi). The average power delivered to the network, assuming a passive sign convention at its input terminals, may be expressed either in terms of the maximum values: P = (1/2)V_mI_m cos (theta-phi). If our applied voltage and current responses had been dc quantities, the average power delivered to the network would have been given simply by the product of the voltage and the current.

Applying this dc technique to the sinusoidal problem, we should obtain a value for the absorbed power which is “apparently” given by the familiar product V_effI­_eff. However, this product of the effective values of the voltage and current is not the average power; we define it as apparent power. Dimensionally, apparent power must be measured in the same units as real power, since cos (theta-phi) is dimensionless; but in order to avoid confusion, the term voltamperes (VA) is applied to the apparent power. Since (theta-phi) cannot have a magnitude greater than unity, it is evident that the magnitude of the real power can never be greater than the magnitude of the apparent power.

Apparent power is not a concept which is limited to sinusoidal forcing functions and responses. It may be determined for any current and voltage waveshapes by simply taking the product of the effective values of the current and voltage.

By: Jonald Sarmiento

Real/Average Power

Real or average power:  "P" can be defined in two ways: as the real part of the complex power or as the simple average of the instantaneous power. The  second definition is more general because with it we can define the instantaneous power for any signal waveform, not just for sinusoids. Average Power is a continuously varying ne with time, the average must be obtained by integration. Averaging over one period T of the sinusoidal function will give the average power.

It is given explicitly in the following expression.

Since the “rms” voltage and current are given by:

The average power can now be expressed as:

In reality, average power is more convenient to measure. In fact, the wattmeter, the instrument for measuring power, responds to the average power. It is known as the average over time of a modulated signal. The average power (often simply called "power" when the context makes it clear) is the average amount of work done or energy transferred per unit time.


By: Kirk Macaraeg