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.