Objectives Revie Capacitors and Inductors Learn about Transformers 3 Phase vs. 1 phase F&N vs. 1 phase F&F Electricity Pricing

Capacitors Consists of two conductive plates separated by a dielectric layer.

Dynamic System t (or ) is time

Example Find i as a function of C , R and VB

Solving Differential Equation The transient response is the time required for the capacitor to fully charge, and is equivalent to about 5 time constants or 5T. 5T

We need a resistor

Solving the Differential Equation time required for the inductor to get full current is equivalent to about 5 time constants or 5T.

Summary

High voltage systems

Ref: Tao and Janis (2001)

Transformers Change - Voltage [E] and - Current [I] Across a transformer I1E1 = I2E2 Es/Ep = Ns/Np

Single-Phase vs. Three-Phase For three phase: P=√3 E I Ref: Tao and Janis (2001)

Grounding What is electrical ground? Why do we ground electrical devices/systems? Protect equipment Lightening strike Protection of people Sometimes need ungrounded power If the hot side touches ground, it can put out of service our circuit Isolate ungrounded systems

Neutral and 3-phase system If system is well balanced the current through the neutral wire is 0

Why Three-Phase? Larger loads Smaller wire sizes (because higher voltages) P = EI = I2R= E2/R (E = IR) More efficient use of neutral wire 3 needed for efficient operation of equipment

Power Factor Difference between power supplied and power that does useful work “working power” P=E I cos θ θ is the phase difference between current and voltage For circuits that contain reactance (Inductor and Capacitors) For three phase P=√3 E I cos θ Commercial buildings pay for power factor.

Electricity Billing Electrical Use (energy) Peak Demand (power) Power factor Which is largest portion of residential bill? What about for commercial buildings?

Example: September cost of Electricity for ECJ Assume ECJ is 120,000 ft2 and that it needs, on average, 8 W/ft2 for 8 hours a day, 6 W/ W/ft2 for 4 hours a day, and 4 W/ft2 for 12 hours a day Use Austin Energy Large Primary summer service rate 1.5¢/kWh, 12.60 $/peak kW/month Assume no power factor charges

Solution large primary service $/kW $/kWh Daily $ 12.60 $ 0.015 hours $ 12.60 $ 0.015 hours kW kWh 8 960 7680 demand $12,096.00 4 720 2880 energy $ 7,344.00 12 480 5760 TOTAL 16320 Total $19,440.00

Other Pricing Strategies Time of use pricing Becoming more common for residential and commercial Electricity cost related to actual cost Requires meter Interruptible pricing Utility can shut off electricity for periods of time

Conductors Material Form Composition Voltage class Insulation Covering Temperature rating AWG American Wire Gage

Wiring method –Raceways Electric tubes Rigid conduits Wire ways Bus ducts Underflow Different variation www.hhrobertson.com/

Design issues with conductors Material (copper/aluminum) Size of conductor (pg. 365) Conduit requirements Location Residential or Commercial With or without raceways Compression fittings or set screws Threaded connections NEC and local codes