POWER FACTOR CORRECTION

POWER FACTOR CORRECTION

         Power factor correction is a measure of how effectively the current is being converted into useful work output. Recall that the power triangle shows the relationship between real power (P), reactive power (Q) and apparent power (S). In single phase circuits, we apply power factor correction and it is also being applied in three-phase circuits.  According to conservation of ac power, power is neither be created nor destroyed. It is just converted from one form to another.

           In big power plants, industrial systems and etc, they were used to meet and maintain the standard power factor. It is in the sense that if their power factor is less than to the limit or standard, they will be penalized. A load with a low power factor draws more current than a load with a high power factor. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.

         The ideal power factor reaches unity which is equal to 1. This can only be happen if phase angles of voltage and current are in phase and apparent power is equal to real power (S=P). Inductive loads cause the current to lag the voltage. The wave forms of voltage and current are then out of phase. The more out of phase they become, the lower the power factor. This induction is caused by equipment such as lighting loaded electric motors, transformers, welding sets and etc.

SAMPLE PROBLEM:

SOLUTION:

LEARNINGS:

           I’ve learned and realized that it is quite difficult to solve power in three-phase systems especially you don’t know whether the connection is delta or wye but by remembering that a three phase power is simply three times the single phase power, any three phase problem can be simplified.  When calculating the current use the phase voltage which is related to the line voltage by the square root of three.  Using these rules it is possible to work out any three phase problem without the need to remember and/or resort to formulas. Especially, memorizing all the formulas is useless without knowing when, where and how will you apply these formulas and without analyzing the given circuit.

tHree pHaSe pOweR MeAsUrEmeNt

INTRODUCTION:

           There are various ways of solutions and mathematical calculations that you can use to get the three-phase power calculation to make sure that your wiring distributes your load evenly maintaining a balanced system.  These ways of calculations are useful for many purposes such as when you have single phase equipment and three-phase equipment running on the same power lines (transmission lines).

 

PRACTICAL APPLICATION:

           Mostly, wye connection is used for long distance transmission of electric power. It is because the line voltage is much greater than the delta connection but line current is smaller. On the other hand, delta connection is used when single-phase circuits are desired from a three-phase source. Since our household lighting and appliances use single-phase power, this transformation or conversion of three-phase to single-phase is required in residential housing.

The animation of three-phase current flow above is taken from this link:

http://en.wikipedia.org/wiki/Three-phase_electric_power

   














NOTE:

           The total apparent power is NOT just the total of each apparent power phase but the square root of the square of the sum of total real power and reactive power.

The sample problem represented below is taken from the book FUNDAMENTALS OF ELECTRIC CIRCUITS (Fourth Edition) Chapter 12 #29 p528.

LEARNINGS:

            I've learned that it is advantage to have three-phase power systems than single-phase because in terms of power distribution, it uses lesser amount of wire. The power distributed to the source is not the same with the power distributed to the load since source power is greater than the load power.  This is what we called the power loss which converted to other form of energy.

THREE-PHASE CIRCUITS

THREE-PHASE CIRCUITS

CONTENTS:

-Introduction

-Balanced Three-Phase Voltages

-Definition of terms

-Balanced Wye-Wye Connection

- Balanced Wye-Delta Connection

- Balanced Delta-Delta Connection

- Balanced Delta-Wye Connection

-Examples and Applications

-Practice Sample Problems

-Learnings

INTRODUCTION:

From our past lessons, we always dealt with single-phase circuits. A single-phase ac power system is consists of a generator connected to a pair of wires to a load. These pair of wires is what we called transmission line. Polyphase are circuits or systems which the ac sources operate at the same frequency but different phases. A two-phase system is produced by a generator consisting of two coils placed perpendicular to each other so that thee voltage generated by one lags the other by 90⁰ while a three-phase system is produced by a generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120⁰.

See the difference of the said three systems above by means of figures:

                  Single-phase two wire system
           

                                                                                                 Two-phase three wire system

            Three-phase four wire system

In our household, we single-phase three wire system because the terminal voltages have the same magnitude and the same phase. Also, whether it is single-phase, two-phase or three-phase system, we can’t put load as many as we can. We must also consider the power supplied by the source if it is enough to accommodate certain number of loads. Example of this is a power amplifier we’ve made; we have 70V and 8A a total of 560W power. Our power amplifier is 100W so; I can say that there must only 10 100-W power amplifier that must be put in the circuit.

BALANCED THREE-PHASE VOLTAGES

Three-phase voltage is often produced by a three-phase ac generator. Balanced phase voltages are equal in magnitude but different in phase angle because they are out of phase with each other by 120⁰. A three-phase system is equivalent o three single-phase circuits. A voltage sources can be connected either wye-connected or delta-connected. Loads can also be connected either wye or delta connectio

                  DELTA CONNECTION

                                                               WYE CONNECTION

There are also two types of phase sequence, one is positive or abc sequence in which V_an leads V_bn which in turn leads V_cn. The other one is negative or acb sequence in which V_an leads V_cn which in turn leads V_bn. This phase sequence is the time order in which the voltages pass through their respective maximum values.

 

            POSITIVE SEQUENCE

                                                                                             NEGATIVE SEQUENCE

NOTE:

A balanced load is one in which the phase impedances are equal in magnitude and in phase. Wye connected load has impedances connected in neutral node while delta connected has impedances connected around a loop.

DEFINITION OF IMPORTANT TERMS:

Line current - current flowing from the generator to the load in each

transmission line

line voltage - the voltage between in each pair of lines

phase current – current flowing through each phase

phase voltage – voltage of each phase

BALANCED WYE-WYE CONNECTION

A balanced Wye-Wye system is a three-phase system with a balanced connected source and a balance connected load. We can solve for its line current by getting a single-phase loop from the circuit and applying KVL.

SUMMARY: 

BALANCED WYE-DELTA CONNECTION

A balance wye-delta system consists of a balanced wye-connected source and a balanced delta-connected load. This connection is perhaps the most practical three-phase system. We can also solve for its phase currents by getting a loop from the circuit then apply KVL. Line currents are obtained from the phase currents that were solved by applying KCL at node A,B, and C.

For alternative or another way of analyzing and solving wye-delya connection, we may transform the delta –connected load to wye-connected load by using delta-wye formula:

BALANCED DELTA-DELTA CONNECTION

A balanced delta-delta system is one in which both the balanced source and balanced load are delta-connected. For easy analyzing the delta-delta connected circuit, transform both the source and the load to their wye equivalent.

SUMMARY: 

BALANCED DELTA-WYE CONNECTION

A balanced delta-wye system consists of a balanced delta-connected source and a balanced wye-connected load. There are also the line voltages as well as the phase voltages. We can generate an equation through getting a loop from the circuit and this may help us solved for the line currents. Like in other connections, we may also transform delta-connected source to wye-connected source.

SUMMARY: 

SAMPLE PRACTICE PROBLEM:

Answers: 12< -60⁰ A, 12< -180⁰ A, 20< 60⁰ A,

20.78< -90⁰ A, 20.78< 150⁰ A, 20.78< 30⁰ A

LEARNINGS:

After the partial discussion of three-phase system, I’ve learned that in a wye-connected balanced source, line currents and phase currents are equal while in a delta-connected balanced source, line voltage and phase voltage is equal. For solving, its easy to solve the required parameters if the system is a wye-wye connection because it has a single-phase equivalent circuit that is easy to analyze. Also, I’ve found out that the electric power is generated and distributed in three-phase at the standard operating frequency.

Power Measurement and Energy Consumption Cost

POWER MEASUREMENT

 Power is symbolize as (P). It is defined as the amount of energy consumed per unit time. The unit of power is known as the Watt (W). The average power that is absorbed by the load is measured by a wattmeter. Loads consume electric power, converting it to other forms such as mechanical work, heat, light, etc. Examples of loads are electrical appliances, such as light bulbs, electric motors, and electric heaters. When we are using AC, power is determined not only by the r.m.s. values of the voltage and current, but also by the phase angle which will determine the power factor.

As I said, wattmeter is the device used to measure electrical power. This consists of current coil and the voltage coil. A current coil with very low impedance is connected in series with the load. This low impedance or ideally zero results to a very high current and zero voltage. The voltage coil has a very high impedance is connected in parallel. This high impedance or ideally infinite has a high voltage and a zero current. In a wattmeter, the current coil helps in measuring current and the potential coil is used for measuring voltage. A wattmeter does a complex job. Aside for measuring the power flowing through an electrical circuit, it also simultaneously measures the voltage and current values and multiplies them to give power in watts.

ELECTRICITY CONSUMPTION COST

Every appliance we have in our house has its own corresponding power. This power really matters on how much we pay in our electric bills that is why it is important to know how much power present in our appliance. Since we are paying for the electric energy over a period of time, we have to consider how long we use our appliances in our house.

TYPICAL WATTAGES OF VARIOUS APPLIANCES

·        Aquarium = 50–1210 Watts

·        Clothes washer = 350–500

·        Clothes dryer = 1800–5000

·        Fans

 Ceiling = 65–175
Window = 55–250
Furnace = 750
Whole house = 240–750

·        Hair dryer = 1200–1875

·        Heater (portable) = 750–1500

·        Clothes iron = 1000–1800

·        Microwave oven = 750–1100

·        Personal computer
CPU - awake / asleep = 120 / 30 or less
Monitor - awake / asleep = 150 / 30 or less
Laptop = 50

·        Radio (stereo) = 70–400

·        Refrigerator (frost-free, 16 cubic feet) = 725

·        Televisions (color)

·        19" = 65–110

·        27" = 113

·        36" = 133

·        53" - 61" Projection = 170

·        Flat screen = 120

·        Toaster = 800–1400

·        VCR/DVD = 17–21 / 20–25

·        Vacuum cleaner = 1000–1440

                                                                  How is energy use of Home Appliances calculated?

TIPS TO CONSERVE ENERGY AND TO SAVE MONEY!!

Unplug electronic appliances and gadgets when not in use.

When buying new appliances, be sure to purchase energy-efficient 

Lessen the hours of using the appliances.

Leave thermostat’s fan switch on “auto”.

Replace light bulbs with CFL’s.

Set the thermostats of the refrigerator at the appropriate temperature.

Clean or replace furnace and air-conditioner filters regularly, following 
manufacturer's instructions.

Have self-discipline.                                                     

                                                                    

LEARNINGS:

I've learned that the more wattage, the more power, or equivalently the more electrical energy is used per unit time. High energy consumption will result to high electricity bill. I realized that we also need to conserve energy to decrease the quantity of energy used and also, we must use appliances in our house efficiently. Appliances that generate heat contributes high power such as flat iron, rice cooker, and etc.

Effective or RMS Value, Apparent Power and Power Factor & Complex Power

RMS Value (Effective Value) 

Root-mean-square (rms) refers to the most common mathematical method of defining the effective voltage or current of an ac wave. In a direct current dc, voltage and current are simple to define, but in an alternating current ac , the definition is more complicated, and can be done in several ways. That is why, root-mean-square (rms) is very applicable in dealing with ac because it is the most common mathematical method of defining the effective voltage or current of an ac wave.

The root-mean-square (rms) value or effective value of an ac waveform is a measure of how effective the waveform is in producing heat in a resistance. That's why rms (or effective) values are useful: they give us a way to compare ac voltages to dc voltages.

Practical Example:

            If you connect a 5 V_rms source across a resistor, it will produce the same amount of heat as you would get if you connected a 5 V dc source across that same resistor. On the other hand, if you connect a 5 V peak source or a 5 V peak-to-peak source across that resistor, it will not produce the same amount of heat as a 5 V dc source.

APPARENT POWER AND POWER FACTOR

Total power in an AC circuit, both dissipated and absorbed or returned is referred to an apparent power. Apparent power is symbolized by the letter S and is measured in the unit of Volt-Amps (VA). In an AC circuit, the product of the rms voltage and the rms current is called apparent power. When the impedance is a pure resistance, the apparent power is the same as the true power. But when reactance exists, the apparent power is greater than the true power. The vector difference between the apparent and true power is called reactive power. The apparent power is the absolute value of the complex power, so it is defined only for sinusoidal excitation. It is a function of a circuit's total impedance (Z). 

Power Factor has an economic impact on consumers of large power (industrial loads)A load with a low power factor that consumes P watts of power draws higher current from a constant voltage source. Higher currents increase line losses and increase the amount of supplied power. Such loads can be charged at a higher rate by power companies. Ideally a pf of 1.0 is desired. Most loads that consume a large amount of power are inductive. Inductive load can be changed by adding capacitors to increase the pf towards unity value, thus optimizing cost.

COMPLEX POWER

In power system analysis the concept of Complex Power is frequently used to calculate the real and reactive power. This is a very simple and important representation of real and reactive power when voltage and current phasors are known. Complex Power is defined as the product of Voltage phasor and conjugate of current phasor. Complex power is applicable only to circuits with sinusoidal excitation because complex effective or peak values exist and are defined only for sinusoidal signals. The unit for complex power is VA. It is composed of a real number which is the average power (P) and an imaginary number which is the reactive power (Q).

                                         

POWER TRIANGLE

             



These three types of power -- real, reactive, and apparent -- relate to one another in trigonometric form. We call this the power triangle:

RESISTIVE LOAD

            

In a purely resistive circuit, all circuit power is dissipated by the resistor(s). Voltage and current are in phase with each other.

 REACTIVE LOAD

  In a purely reactive circuit, no circuit power is dissipated by the load(s). Rather, power is alternately absorbed from and returned to the AC source. Voltage and current are 90^o out of phase with each other.

RESISTIVE/REACTIVE

 In a circuit consisting of resistance and reactance mixed, there will be more power dissipated by the load(s) than returned, but some power will definitely be dissipated and some will merely be absorbed and returned. Voltage and current in such a circuit will be out of phase by a value somewhere between 0^o and 90^o.

LEARNINGS:

    I’ve learned that reactive loads such as inductors and capacitors dissipate zero power and the fact that they drop voltage and draw current gives the deceptive impression that they actually do dissipate power.

   I’ve also learned that Poor power factor in an AC circuit may be corrected, or re established at a value close to 1, by adding a parallel reactance opposite the effect of the load's reactance. If the load's reactance is inductive in nature (which is almost always will be), parallel capacitance is what is needed to correct poor power factor. Low power factor has higher current, otherwise lower. Leading power factor means that current is leading while lagging power factor means lagging current. Mostly, inductive loads consume high current while resistive loads consume less.