Three Phase Power Calculations

Front 1

Calculate ST (or PT, QT) total of a Three-Phase balanced load

Back 1

ST = VL×IL×1.732

PT = VL×IL×1.732×Pf

QT = VL×IL×1.732×sin (cos-1)

Front 2

Calculate one-phase of a three-phase unbalanced circuit

Back 2

SP = VP×IP

PP = VP×IP×pf

QP = VP×IP×sin (cos-1)

Front 3

Calculate ST (or PT, QT) for balanced and unbalanced circuits

Back 3

ST = SA+SB+SC

PT = PA+PB+PC

QT = QA+QB+QC

Front 4

Calculate phase values (SP, PP, QP) in a balanced three-phase circuit

Back 4

1. ST = VL×IL×1.732

2. SP= ST

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3

Front 5

Power

Back 5

Is the rate at which energy is converted from one form to another. Also referred to as active or true power.

Front 6

The unit of measurement

Back 6

For apparent power = voltampere (VA)

For power = watt (W)

For reactive power = voltampere reactive (Var)

Front 7

The symbol

Back 7

Apparent power = S

Power = P

Reactive power = Q

Front 8

Reactive Power Energy (Q)

Back 8

Creates both the electromagnetic & electrostatic field in a circuit. Reactive power measures the rate at which energy is returned to the circuit when the field collapses or discharges.

Front 9

Reactive power

Back 9

Is also called (Q) quadrature power

Front 10

Power Factor (pf)

Back 10

Is the ratio between power (P) and apparent power (S)

Front 11

A balanced condition in a Three-Phase circuit is

Back 11

When there is the same magnitude of current in each phase & same power factor in each phase.

Front 12

Calculate reconnection of delta load to wye connection in a resistive circuit (VA=W)

Back 12

1. Power per phase:

PPHASE = IP×VP

PPHASE = W

2. Total power: PT = PP+PP+PP

3. Delta power = W = 3

---- ----

Wye power = W = 1

Front 13

Calculate the power & reactive power for each load

Back 13

Motor load:

PM = hp(horse power)×746 W = W

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Efficiency %

SM = W = VA

----

pf

QM = VA×sin (cos-1) = var

Oven/Resistor load:

PO = W, SO = W, QO = 0W

Front 14

Power Quality Analyzer (PQA)

Back 14

Measures:

Dips

Swells

Fast transients

Harmonics

Pf

Front 15

Single-Phase PQA

Back 15

Measures:

Voltage (volt rms)

Current (amp rms)

Pf

Active power (watt)

Reactive power (var)

Apparent power (VA)

Frequency (Hz)

Front 16

Some Single-Phase PQA

Back 16

Measures:

Harmonic analysis (1st to 24th harmonic)

Dc measurements

Maximum/Minimum values

Front 17

Single-Phase PQA

Back 17

Can be a three-lead or clamp-meter style. They are portable

Front 18

Single-Phase PQA

Back 18

Meter can be used on a three-phase circuit, but only if the load is balanced

Front 19

Single-Phase PQA

Back 19

Meter can only provide the total values and not the phase values

Front 20

Single-Phase PQA

Back 20

Does not give accurate readings to an unbalanced load

Front 21

The VOLTS/AMPS/HERTZ screen

Back 21

Displays:

Vrms (phase-to-phase)

Vrms (phase-to-neutral)

Vpeak

V crest factor

A crest factor

Arms

Apeak

Frequency (Hz)

Front 22

Crest Factor (CF)

Back 22

Indicates the amount of waveform distortion.

1.41 = no waveform distortion

1.8 or greater = high waveform distortion

Front 23

Crest factor (CF)

Back 23

Is the ratio of peak values to rms values of the waveform

(Peak-to-rms ratio)

Front 24

Calculate Crest factor

Back 24

(PR÷) Vpeak ÷ CF = Vrms or

(RP×) Vrms × CF = Vpeak

Front 25

Power and Energy screen

Back 25

Displays:

Kw

kVA

kVA Reactive

Pf

Amps rms

Volts rms

Front 26

Polarity marks

Back 26

Indicate if the load is inductive (lagging) or capacitive (leading 90°)

Front 27

Three-Phase PQA

Back 27

Have six (6) to (9) nine inputs. Nine lead analyzers have 4 BNC inputs (miniature quick connect/disconnect)

Front 28

Phasor diagrams

Back 28

Are drawn for both single-phase & three-phase circuits

Front 29

Resistance and Reactance

Back 29

Are not measured or detected by a PQA

Front 30

Phasor diagrams

Back 30

Are used to interpret data from PQA readings

Front 31

In a 120/208 V balanced or unbalanced delta source (panel)

Back 31

208 V (greater voltage) would be the VP

Front 32

Three-Phase PQA

Back 32

Should be used to analyze a three-phase unbalanced load

Front 33

To correct the Pf of a circuit that contains an induction motor

Back 33

The motor and capacitors are connected in parallel

Front 34

Unity Pf (useful work)

Back 34

Is when the ratio of power to apparent power in one (1)

Front 35

A small Pf ( lagging)

Back 35

Indicates that most of the applied voltage & current is not doing useful work

Front 36

The Pf angle

Back 36

Is equal to the phase angle between the VP (phase voltage) and the IP (phase current)

Front 37

Greek letter theta (θ)

Back 37

Is used to represent Pf angle or cos θ

Front 38

Power factor correction equipment (PFC)

Back 38

Can be installed by consumers to avoid paying a penalty for low Pf loads

Front 39

Power loss (Line loss)

Back 39

= I2×R

Where:

·Power loss is measured in watts

·Current is measured in amperes

·Resistance is measured in ohms

Front 40

If current is reduced

Back 40

The line loss (I2R) is reduced

Front 41

Reactive power (Q)

Back 41

Is used by circuits with inductive components like motors, coils and ballasts (lagging Pf)

Front 42

A synchronous condenser

Back 42

Is used without any load connected to the end of the motor shaft

Front 43

Two types of equipment used for Pf correction

Back 43

·Capacitors or Capacitor banks

·Synchronous Motors

Front 44

Two main reasons for Pf correction

Back 44

·To reduce energy costs

·To increase system capacity

Front 45

Capacitive Reactance (Xc)

Back 45

The current of the capacitor leads the voltage by 90°, the reactive component of the current of the inductor lags the voltage by 90°. When the capacitor is in parallel with an inductive load, it supplies reactive power 180° out-of-phase with the reactive power of the motor.

Front 46

Capacitive Reactance (XC)

Back 46

The current through a capacitor leads the voltage across that capacitor by 90°, so capacitors have a leading out-of-phase reactive component.

Front 47

Adding capacitors to an inductive circuit

Back 47

To correct the overall Pf, will cause the line current (IA) to be reduced.

Front 48

Adding capacitors to an inductive circuit

Back 48

To correct the overall Pf, will cause the net VARS supplied to the circuit to decrease.

Front 49

Adding capacitors to an inductive circuit

Back 49

To correct overall Pf, will cause the circuit to draw fewer VA, fewer vars, watts will stay the same.

Front 50

Calculate microfarad rating of each capacitor (to correct Pf to unity)

Back 50

Calculate each unbalanced load separately.

1. ST1 = VL×IL×1.732

2. QT1 = VA×sin (cos-1)

3. QTOTAL = QT1+QT2+QT3

4. QP = QTOTAL÷3 (each capacitor)

5. XC = V2÷P(QP)

6. C = 1÷(2pie×Hz×XC)

Front 51

For a capacitor bank to correct the overall Pf to unity

Back 51

VARS (produced by the capacitors) = VARS (produced by the remainder of the circuit)

Front 52

Calculate Pf correction

Back 52

Old Pf .75

1. PTotal = VL×IL×1.732×Pf .75

Calculate VA & VAR (old)

New Pf .92

1. New VA = PTotal÷Pf .92

Calculate VAR (new)

VAR (old) - VAR (new) = VAR

Front 53

Major concern when disconnecting capacitors

Back 53

Stored energy levels of the capacitors

Front 54

Ratio for leading/greater reactive power (same capacitance)

Back 54

Delta Wye

3 : 1

Front 55

Three important ratings when selecting a capacitor bank

Back 55

·Voltage rating

·Current rating

·kVAR rating

Front 56

Safe way of disconnecting a capacitor bank

Back 56

A Three-Phase disconnect that automatically discharges the capacitors

Front 57

If capacitors are connected at the motor terminals

Back 57

The rating or setting of overloads must be reduced CEC 26-222 (3)

Front 58

Two locations where Pf correction capacitors may be installed

Back 58

·A distribution centre

·At the terminals of individual motors