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Review of AC Circuits

Review of AC Circuits. Smith College, EGR 325 March 27, 2006. Objectives. Power calculations and terminology Expand understanding of electrical power from simple linear circuits to a high voltage power system. Overview. Basic Circuits Sinusoidal waveform representation

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Review of AC Circuits

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  1. Review of AC Circuits Smith College, EGR 325March 27, 2006

  2. Objectives • Power calculations and terminology • Expand understanding of electrical power • from simple linear circuits to • a high voltage power system

  3. Overview • Basic Circuits • Sinusoidal waveform representation • Root mean square • Phase shift • Phasors • Complex numbers • Complex impedance • Electric Power • Complex: real & reactive power • Power factor and power factor correction

  4. ac Waveform

  5. N S Rotor How AC is Generated Stator Windings

  6. f N S X How AC is Generated v 2700 900 Angle 3600 1800

  7. v w t AC Phasor Representation

  8. V1 v 1 V2 v 2 w t q Reference

  9. V1 v 1 V2 v 2 w t q Reference

  10. Phasors

  11. Representing Power

  12. Power Calculations • P = VI • P = I2R • P = V2/R • S = VI • S = I2Z • S = V2/Z

  13. Resistance  Impedance • Resistance in  • Capacitance in F • Inductance in H • Z = R + jX

  14. V I Instantaneous Electric Power [p(t)] Fixed average Zero average

  15. Instantaneous vs. Average Power

  16. Instantaneous vs. Average Power • Instantaneous power is written as • The average of this expression is

  17. p p Q(t) wt w t q Real & Reactive Power – Time Domain

  18. V I Complex Power IMPORTANT is the power factor angle Real Power Reactive Power

  19. Example: Current Flow

  20. Example: Power Flow

  21. Power System Operations

  22. Operating Challenges • Load is stochastic and is not controlled • Power flows cannot be directed or controlled • Electricity cannot be stored • Everything happens in real-time • Generation can be controlled

  23. Power System Variables • Generators produce complex power • S = P + jQ • Real power, P, able to perform useful work • Reactive power, Q, supports the system electromagnetically • Single system frequency, f • Voltage profile, V

  24. Real Power Flow – Voltage Relation • In normal system operation, frequency/real-power dynamics are decoupled from voltage/reactive-power Voltage (pu) Power (pu)

  25. Real Power and Frequency • P and f dynamics are coupled • Demand > Supply: frequency will decrease (more energy drained from system than produced, acts like brakes on the turbines) • Supply > Demand: frequency will increase (more energy in the power system than consumed, acts like an accelerator so turbines spin faster) • Generation-based frequency regulation • Generator inertia • Generator governors

  26. Frequency Problems • Imbalances in supply and demand beyond the capabilities of these generator controls • Load may be dropped, or “shed” by operators • Equipment protection may disconnect generators • Operators may disconnect regional tie lines

  27. Reactive Power Analogy • Voltage and reactive power allow real power to flow • Reactive power • Energy stored in capacitance and inductance • Supports the electromagnetic fields along transmission lines • Cannot be transmitted long distances • Analogy • Inflatable water pipes

  28. Voltage Collapse • The real power demanded is above the transfer capability of a transmission line • Return to the water pipe analogy • Load draws too much power – dips into the stored reactive power – “collapses” the pipe • Equations: P = V*I, I = V/Z • Load wants more power: Decrease apparent impedance (Z), to increase current draw (I), which allows increased P • But, if P at limit, result is to decrease V

  29. Real Power Flow – Voltage Relation Voltage (pu) Power (pu)

  30. Power System Response to Outages • Power flows on the paths of least impedance • As elements are removed (fail), the impedance changes and so power flows change  Instantaneously • Human and computer monitoring of and reaction to problems is on a much slower timescale

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