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power consumption in alternating current ac

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Unformatted text preview: un/Start (Permanent Split Capacitor, PSC) • Shaded Pole Fractional hp (up to ½ hp) Very small motors (up to 1/10 hp) ASIDE: Reminder (?)… Power Consumption in Alternating Current (AC) Electrical Systems AC I “line” (“hot”) 120 V 60 hz 1) Single Phase AC Power: V load = * ∙ +#! ∙ #! “neutral” single phase volts watts amps “power factor” (dimensionless) = cos / “rms” = root-mean-squared “Power Triangle” Apparent Power (VA) Reactive Power (VAr) / Active Power (W) = * ∙ +#! ∙ cos / #! = 1 for purely resistive load < 1 when current is lagging or leading voltage Example: Device connected to household power (single-phase AC) “hot” watt meter power device “neutral” Readings: = * ∙ +#! ∙ #! 114 volts 7.4 amps pf = 0.77 (114 V) ∙ (7.4 A) ∙ (0.77) = 650 watts 650 watts Note: “Apparent Power” (114 V) ∙ (7.4 A) = 844 watts 3-Phase AC Power A C B LA 3-phase motor LB LC “line-to-line voltages” *010,#! = *34 , *35 , *45 Electrician’s Measurements… LA LB LC *010,#! = *34 = *35 = *45 “line currents” +0,#! = +3 , +4 , +5 balanced? balanced? 3-Phase AC Power = 3 ∙ *010,#! ∙ +0,#! ∙ volts watts amps = 3 ∙ * ∙ + ∙ (End of aside.) AC INDUCTION MOTORS • An induction motor is an AC motor where power is supplied to the rotating device via electromagnetic induction. • In general, the rotor lies within a magnetic field created by the stator. An electric current is induced within the rotor, and the resulting force causes the rotor to turn. • The speed at which the magnetic field rotates depends on the number of magnetic poles in the stator, and is referred to as the “synchronous speed” Synchronous Speed = At 60 Hz AC power: 120 × frequency Number of Poles Poles 2 4 6 8 frequency of AC power supply (e.g. 60 Hz) Synchronous Speed (rpm) 3600 1800 1200 900 • The rotor of an induction motor usually does not rotate at synchronous speed, but lags it slightly. This lag is usually expressed as a percentage of the synchronous speed, called the “slip”. % Slip = Synchronous Speed − Rotor Speed × 100% Synchronous Speed • The “rated speed” is the nominal speed of the rotor when operating at full load. e.g. A motor with synchronous speed of 1800 rpm may operate with rated speed of 1750 rpm (i.e. magnetic field spins at 1800 rpm, rotor spins at 1750 rpm.) • In general, the amount of slip is approximately proportional to the load imposed upon the motor by the driven equipment: 100% Percent of Full-Load Slip 50% 0% 0% 50% No Load 100% Full Load Load Typical Range of Full-Load Efficiency Values by Motor Type: • Squirrel Cage ~ 75 – 95% • PSC ~ 40 – 70% • Shaded Pole ~ 20 – 35% For each category, the full-load efficiency generally will increase with motor hp. Approximate Range of Full Load Efficiency Values for Squirrel Cage Motors (3 phase, induction motors) 100% 95% 90% Full 85% Load Efficiency 80% 75% 70% 65% 1 1.5 2 3 5 7.5 10 15 Motor Rated hp 20 25 30 40 50 Efficiency at part-load can be different than at full-load: Approximate Variation in Motor Part-Load Efficiency for Induction Motors % of Full-Load Efficiency Motor Load (% of Full Load) Usually, motors in HVAC systems do not run at 100% load (fullload)—that is, the brake power required by the driven device (e.g. pump, fan) is less than the motor capacity. For Example Say a centrifugal pump requires ∼32 bhp from an 1800 rpm motor to operate at the required flow and head. The motor selected to drive the pump would likely be 40 hp (i.e. the nearest size that can provide at least 32 hp). boiler Motor power supply Pump flow 95 L/s 204 kPa heat in heat out heating loads Centrifugal Pumps • commonly used in HVAC applications Pump Performance Curve (for a particular pump) 95 L/s, 204 kPa Note: 204 kPa ≈ 68 feet of H20 (head) Say available motors are as follows: Rated hp 20 25 30 40 50 6789:; 92% 93% 93% 94% 95% Recall… Estimating pressure drop (head loss) through a section of piping: flow mean fluid velocity pipe “friction factor” length of pipe section head loss ∆ = + 2 “fitting loss coefficients” gravitational constant pipe diameter 1 ∆ = + 2 ∆ ∝ Head loss through the pipe section is approx proportional to flow velocity squared Also, volumetric flow-rate () is proportional to mean fluid velocity (): =∙ cross-sectional area (for fluid flow) If we consider the bracketed term as fixed/constant for a particular piping section (i.e. once it has been built), then So, head loss through a section of pipe varies approx with volumetric flow () squared: ∆ ∝ “system curve” ∆ Centrifugal Pump Performance Curve For a particular impeller size and rotational speed (rpm). pump curve ∆ Operating Point: At intersection of the two curves operating point ∆ Building Energy Performance – Spring 2012 - Topic 14 - “Coefficient of Performance” Refrigeration System (or Heat Pump): Used to move heat from a colder environment to a warmer environment colder environment cooling warmer environment Refrigeratio...
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