Lesson 33: 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.

AC Power Summary P = VI [W] P = I2R =V2/R P = 0 [W] Q = 0 [VAR] Real Power P = VI [W] P = I2R =V2/R P = 0 [W] Reactive Power Q = 0 [VAR] Q = I2XL =V2/XL Q= I2XC =V2/XC Resistance Reactance R [Ω] XL = L XC = 1/C

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

Active Power (P) to Wye (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):

Reactive Power (Q) to Wye (Y) Load The reactive power per phase (Q) is given by: Q = V I sin  P S 

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):

Apparent Power (S) to Wye (Y) Load The apparent power per phase (S) is given by: S = V I Q  P

Power Factor (FP) The power factor (FP) is given by: S Q  P

Example Problem 1 For the Y-Y system shown, EAN = 277-30 V . Find PΦ, PT, QΦ, QT, SΦ, ST, and FP. 10Ω 277-30 V 15Ω system is capacitive (-VAR)

Example Problem 1 cont. For the Y-Y system shown, EAN = 277-30 V . Find PΦ, PT, QΦ, QT, SΦ, ST, and FP. 10Ω 277-30 V 15Ω Remember that current is our indicator here and since the system is capacitive (-VAR) we can say it’s leading.

Power to a Delta () 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 2 EAN=120-30 V. a) Determine per phase and total power (active, reactive, and apparent). 2080 V 12Ω Iab 6Ω system is inductive (+VAR) b B

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 =? Sgen =? Pgen =? Qgen =? Sload =? Pload =? Qload =? 17

 = cos-1(P / S)=cos-1(FP) Power Factor Power factor (FP) tells us what portion of the apparent power (S) is actually real power (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 NOTE:  is the phase angle of ZT, not current or voltage.

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.

Three Phase Power Correction Capacitors will be connected in parallel with each load phase.

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. Note the (-) sign here! Always use the opposite value of calculated Qφ

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. The Qφ is what will be used for Qc in determining the value of the capacitor to used 149𝜇𝐹

QUESTIONS?