Lesson 36 ac three phase power
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Lesson 36 AC Three Phase Power. Learning Objectives. Compute the real, reactive and apparent power in three phase systems Calculate currents and voltages in more challenging three phase circuit arrangements. Apply the principles of Power Factor Correction to a three phase load. Review.

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Lesson 36 ac three phase power

Lesson 36 AC Three Phase Power


Learning objectives
Learning Objectives

  • Compute the real, reactive and apparent power in three phase systems

  • Calculate currents and voltages in more challenging three phase circuit arrangements.

  • Apply the principles of Power Factor Correction to a three phase load.


Ac power summary

Review

AC Power Summary


Power triangle

Review

Power Triangle

  • The power triangle graphically shows the relationship between real (P), reactive (Q) and apparent power (S).


Active Power to Wye (Y) Load

Y-load

Single phase of Y-load


Active Power (P) to Wye (Y) Load

  • Because we are considering a balanced system, the power per phase (P) is identical and the total active power (PT) is simply PT = 3 P.

  • Using line voltage () and line current (IL=I):


Example problem 1a
Example Problem 1a

EAN = 277-30 V . Compute PΦ, PT.


S

Q = V I sin 



P

Reactive Power (Q) to Wye (Y) Load

  • The reactivepower per phase (Q) is given


Reactive Power (Q) to Wye (Y) Load

  • Because we are considering a balanced system, the power per phase (Q) is identical and the total reactive power (QT) is simply QT = 3 Q.

  • Using line voltage (VL ) and line current (IL):


Example problem 1b
Example Problem 1b

EAN = 277-30 V . Compute QΦ, QT.


Apparent Power (S) to Wye (Y) Load

  • The apparentpower per phase (S) is given

S = VI

Q



P


Power Factor (FP)

  • The power factor (FP) is given

S

Q



P


Example problem 1c
Example Problem 1c

EAN = 277-30 V . Compute SΦ, ST, and FP.


Power to a Delta () Load

 -load

Single phase of -load


Active Power (P) to Delta () Load

  • Total active power (PT) is simply PT = 3 P.

  • Using line voltage (VL=V) and line current ( ):

  • Which was the EXACT same equation as for Y loads


Reactive and apparent power to Delta (Δ) Load

  • The equations for calculating total reactive and apparent power are also identical to the Wye load versions:


Example problem 2a
Example Problem 2a

EAN=120-30 V.

Determine per phase and total power (active, reactive, and apparent). Determine total powers (active, reactive, and apparent) by multiplying the per-phase powers by 3.


Example problem 2b
Example Problem 2b

EAN=120-30 V.

Determine total powers (active, reactive, and apparent) by using these formulas:


Power in advanced 3 phase
Power in Advanced 3 phase

You must pay attention to the problem statement!

Does it ask for total or per-phase power?

What kind of power? S, P, or Q?

Where is the power?

Generator

Line Impedances

Load

Pline=?

Qline =?

Sload =? Pload =?

Qload =?

Sgen=?

Pgen=?

Qgen=?


Power factor
Power Factor

Power factor (FP) tells us what portion of the apparent power (S) is actually realpower (P).

FP = P / S = cos 

Power factor angle

 = cos-1(P / S)=cos-1(FP)

For a pure resistance,  = 0º

For a pure inductance,  = 90º

For a pure capacitance,  = -90º

Review

NOTE:  is the phase angle of ZT, not the current or voltage.


Power factor correction
Power Factor Correction

In order to cancel the reactive component of power, we must add reactance of the opposite type. This is called power factor correction.

Review


Three phase power correction
Three Phase Power Correction

Capacitors will be connected in parallel with each load phase


Power factor correction solution steps
Power Factor Correction Solution Steps

Calculate the reactive power (Q) of ONE PHASE of the load

Insert a component in parallel of the load that will cancel out that reactive power e.g. If the load has QΦ=512 VAR, insert a capacitor with QΦ=-512 VAR.

Calculate the reactance (X) that will give this value of Q Normally the Q=V2/X formula will work

Calculate the component value (F or H) required to provide that reactance.


Example problem 3
Example Problem 3

EAB=4800 V. Frequency 60 Hz.

Determine value of capacitor which must be placed across each phase of the motor to correct to a unity power factor.


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