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.