Understanding Power Factor and How it Affects Your Electric Bill Presented by Scott Peele PE Understanding Power Factor Definitions kVA, kVAR, kW, Apparent Power vs. True Power Calculations Measurements Power Factor Correction Capacitors System Impacts I2 R losses, Chapter 9 NEC Equipment sizing Power Factor Charges Problems with adding Caps Harmonic resonance Volt rise Power Factor vs Load Factor What is Power Factor Power Factor is the cosine of the phase angle between current and voltage. Power Factor is the ratio of true power to apparent power. Understanding Alternating Current AC 200 Voltage Level Magnitude 150 120 Volts RMS 100 169 volts 50 0 -50 One Cycle .01666 seconds -100 -150 60 Hertz/second -200 0 Duration Time Phase Angle 200 Voltage Level Magnitude 150 120 Volts RMS 100 o 90 50 180 o 0 -50 One Cycle -100 -150 360 -200 o o 0 270 Duration Degrees Three Basic Circuits or Loads Resistive Inductive Capacitive Or any combination Resistive Inductive Inductive Capacitive Resistive Capacitive Resistive Inductive Capacitive Types of Loads Resistive – Incandescent Lamp Resistance heat Inductive – Motors – Contactor Coils – Relays (coils) Capacitive – Capacitors – Start Capacitors – Run Capacitors – Power Factor Correction Capacitors Resistive Loads In Phase 200 150 50 Level Magnitude 100 0 -50 -100 -150 -200 0 Duration Time Inductive Loads Lagging 200 100 Level Magnitude 150 50 0 -50 -100 -150 -200 0 Duration Time Capacitive Loads Leading 200 100 Level Magnitude 150 50 0 -50 -100 -150 -200 0 Duration Time What is Power Power is measured in Watts. Volts X Amps X Power Factor = Watts Watts only equals Volts X Amps when the Power Factor is 1 or unity. Most of the time the Power Factor is less than 1. Power = Watts : True Power Volts X Amps = VA : Apparent Power θ B= Side Adjacent A= Side Opposite Understanding Right Triangles Right Angle 900 Power Triangle True power Power Factor = Hypotenuse θ Power Factor = Cos B= Side Adjacent A= Side Opposite Adjacent side θ =θ Cos Apparent power True power θ B= Side TrueAdjacent Power Apparent power Power Side Opposite A= Reactive Power Factor = Right Angle 900 Watts, KW, Power VAR, kVAR Reactance θ B= True Power A= Reactive Power Understanding Power Triangle Inductive Motors X θ R Resistance Inductive Reactance Graphical representation of resistance, reactance, and impedance Graphical representation of resistance, reactance, and impedance Resistance θ X Capacitors Capacitive Reactance R Imaginary Inductive Motors θ kVAR Reactance Imaginary Real - WATTS – kW (KWH over Time) Cosine of θ POWER FACTOR Capacitive Capacitors True Power 10 HP 460 Volt 4 Pole Motor Transformer Conductor Load Power Factor VA Amps Watts VAR Amps Reactive Amps Resistive 125% 0.82 13203 16.6 10883 7476 9.4 13.7 115% 0.81 12240 15.4 9972 7099 8.9 12.5 100% 0.79 10830 13.6 8592 6593 8.3 10.8 75% 0.73 8771 11.1 6397 6002 7.5 8.0 50% 0.61 7105 8.9 4323 5639 7.1 5.4 25% 0.40 5886 7.4 2331 5405 6.8 2.9 min load 0.17 5399 6.8 911 5322 6.7 1.1 Motor = KW Load (resistive) = KVAR Load (reactive) 10 HP Energy Flow Transformer θ Power Factor = .79 VAR = 6593 A= Reactive Power Conductor B= True Power Measured Amps = 13.6 Watts =8592 Reactive Amps = 8.3 Resistive Amps = 10.8 Motor = KW Load (resistive) = KVAR Load (reactive) 10 HP Adding Capacitance Transformer Conductor VA =8595 Watts =8592 VAR = 1 Measured Amps = 10.8 θ B= True Power VAR = 6593 A= Reactive Power Measured Amps = 8.3 Measured Amps = 13.6 Motor Watts =8592 = KW Load (resistive) = KVAR Load (reactive) 10 HP Energy Savings Transformer Conductor 200 Feet of #12 Gauge wire Saving are calculated on I2 R losses. Using a # 12 gauge wire from Table 9 in the NEC the resistance is 2 ohms per 1000 feet. 200’ @ 2 Ohms/1000’ is .5 ohms. Using this the total saving will be approx. 11.8 watts. NOTE: This is only if the I2 X R = Watts capacitor is at the motor. 2.8 2 X .5 = 3.92 3 X 3.92 = 11.76 Motor = KW Load (resistive) = KVAR Load (reactive) 10 HP Capacitor Sizing Transformer Conductor Utility Meter II22 R R Savings Losses Capacitor to large then var flow in both directions and one may increase cost. Motor = KW Load (resistive) = KVAR Load (reactive) Based on one month operation at 8 hours a day Example of Power Factor Charge PF Charge Factor NC Charge $0.40 Max Billing kW 8.592 Power Factor kW Charge $10.25 kWh Charge $0.03854 0.79 Calc kVA Calc kVAR 10.8759 6.6681 kW 8.6 kWh 2064 Less than .85 then a $0.40 charge For kVar – (kW X.62) In this Case $0.54 PF Charge $0.54 kW Charge $88.15 kWh Charge $79.55 Total Charge $168.23 10 Horse Power Motor VA Watts VAR VA 14000 Watts VAR 125% 115% 12000 100% 10000 75% 8000 50% 6000 25% Min 0.40 0.17 4000 2000 0 0.82 0.81 0.79 0.73 Power Factor 0.61 Power Factor vs Amps Volts Amps VA kW Power Factor VAR Amps Reactive Amps Resistive 208 83 10000 10 1 0 0 83 208 88 10526 10 0.95 3287 28 83 208 92 11111 10 0.9 4843 41 83 208 98 11765 10 0.85 6197 52 83 208 104 12500 10 0.8 7500 63 83 208 111 13333 10 0.75 8819 74 83 208 119 14286 10 0.7 10202 85 83 208 139 16667 10 0.6 13333 111 83 208 166 20000 10 0.5 17321 144 83 Power Factor vs Amps 180 160 140 120 100 kW Amps 80 Power Factor 60 40 20 0 1 2 3 4 5 6 7 8 9 10 HP Voltage Rise Transformer Conductor 200 Feet of #12 Gauge wire kVAR * Xsource /kVA/100 = Voltage Rise % Note This does not include the wire inductance that will cause some additional rise in voltage. Note: With this voltage rise an increase in kW and kwh can occur. Motor = KW Load (resistive) = KVAR Load (reactive) System VAR Requirements Power Plant Generator MVAR (Met by Power Plant Generator) T/D Substatio n Transmission Circuit KVAR MW KW Distribution Circuit L L Industrial Load Commercial Load = KW Load (resistive) Substation Capacitor Bank L Residential Load = KVAR Load (reactive) System VAR Requirements Power Plant Generator (Met by Power T/D Substation) T/D Substatio n Transmission Circuit KVAR MW KW Distribution Circuit Substation Capacitor Bank L L Industrial Load Commercial Load = KW Load (resistive) L Residential Load = KVAR Load (reactive) System VAR Requirements Power Plant Generator (Met by T/D Sub and Feeder Capacitors) T/D Substation Transmission Circuit KVAR MW KW Distribution Circuit Substation Capacitor Bank L Industrial Load Feeder Capacitor Bank L Commercial Load = KW Load (resistive) L Residential Load = KVAR Load (reactive) Things We have Talked About And Other Things to Talk About Phase Angle Power Factor I2R Loss Power Factor Penalty Voltage Rise Harmonic resonance Load Factor --- Power Factor Harmonic Resonance X Source Equivalent Circuit XT 3 PHASE AC INPUT X Source XT XC Harmonic Source Harmonic Filters L1 XF XC L2 L3 L1 L2 L3 Power Factor Vs Load Factor They have no relation Load Factor is kW at 100% operation Yielding so many kWh vs. Actual kWh Example Hours in a Month = 30 X 24 = 720 Hours Load is at 8 kW 8 X 720 = 5760 kWh Actual kWh by load is 3240 Load Factor then is 3240/5760 Load Factor = .56 BOTTOM LINE ON Understanding Power Factor and How it Affects Your Electric Bill z Very small charge with penalty most customer have no Power Factor Penalty z None or very small savings or possible increase cost when using Power Factor Correction Devices Questions

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