AC Circuits 2

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-AC Circuits Part 2 Polyphase System J '

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MUL TIVECTOR Review and Training Center. Rm. 867, Ground Floor, Isabel Bldg. F. Cayco corner Espafia Sts. Sampaloc, Manila Tel. No. 7317423

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MUL TIVECTOR

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~EVIEW

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AC Circuits Part 2 Three Phase Circuits/ Systems

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Balanced 3$ Circuits/ Systems:

I.

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Wye (Star) Connected System

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~-X------~·~>~~--------------~--~ Relationships :

2.

Delta (Mesh) Connected System:

Relationships:

where: V~-phase voltage I~ -phase current v,.- line.voltagc I~_- line current

Power in Balanced 3$ Circuits/Systems

..

(Whether Wyc or. Delta connected) Pr

=

'>[3 Y1 11 (p.f.) = 3V~I~(p:f.)

=

3 1/R~ watts

Or= 13 Y1 It(r.f.) ~ 3 V4>14> (r.f.) = 3 I4> 2X4> vars Sr ·=

YJ

V~_I 1

=

3Y4>14> = 3I/Z4> = ~P/ + Or 2 va

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Impedance Trian~)c:

Power Triangle:.

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Sr

.JPr 2 + o/ va

=

From the above triangles: · p.f. •c

COS ()I ..

r,.

KW . R,

s,~

KV t\

z,

r.f. =sino,=. Or , KVAR =_& Sr KVA Z~ tan 0 1 ""

Or -_ KVAR __ - --

-

Pr

~ R~

KW

where:

r,- total real power drawn by the balanced 3cp load Or- total reactive power drawn by the balanced 3cp load S1 - total apparent power drawn by the balanc.cd 3 load 01 - power. factor angle of the ba'anccd 3cj> load

Phase Sequence-- the order in which the generated voltages in the phase windings of an alternator reach or attain their peak or maximum values. a.

Positive Phase Sequence ABC~

BCA

~CAB

AB- BC- (:A~ BC- CA- t\B AN- BN- CN

~

BN -

CN- AN

~CA--AB-BC

~

CN --AN- BN

Examples of Vector Representations

Vc =/Vel L-240"

V11

=

/Yn/ '

Vn -·/Vn/ .L-120"

Vc = IVc/.c-.120"

Sequence ABC

Sequence BCA

L-240"

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Sequence CAB

MUL TIVECTOR REVIEW AND TRAINING CENTER b. ·Negative Phase Sequence ACB ,_

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CBA

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BAC

AB · CA ~-· BC ~ C!\- BC -1\B ~ i3C- AB-C!\ AN

CN

BN-tCN-BN-AN~BN--1\N-CN

Examples 0f Vecto)· Representations Vn = JVnJ L:-240"

JVnl /0''

Vn SeqtJCnce ACB

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JVnl L-120"

Sequence CBA

Sequence BAC

If the phase sequence is not given. assume a positive phase sequence. Three pha~c'·(3$) alternators arc designed to operate with positive phase sequence voltages.

Power Measurements in three Phase (3$) Systems. I.

2.

One-wattmeter Method- used to measure the total real power in a balanced three-phase system with a single wattmeter. Methods ~mployed: a. Potential.., lead shift Method b. Artificial- neutral Method c. T Method d. Current-transformer Method Two-wattmeter Method -·usually used.tomeasure the real power being drawn by a tfu·e~-phase (3$). 3-wire ry~rn. . Current Coil 1 II.

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Balanced. 3$ Source

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Balanced 3$ Load

Potential Coifz Current Coil 2 ,!,

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Q 1 =·f3· (W 1 - \V 1 ),

9r""

V(\Vl-\VI),

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where:

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if W 1 > \V 2

·if\~/

YJ(W,-Wz) W I -1·\V 2 .

0 power factor of the balanced 3~ load P 1 total real ot' true power drawn by the balanced 3$ load