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- 1. School of Engineering & TechnologyIntroduction to Electrical Engineering Rajneesh Budania Jaipur National University June 29, 2012
- 2. Outline• Basics of Electric Circuits• AC Power• Power Generation and Transmission 2 YAGTP3918 icfi.com
- 3. Basics of Electric Circuits• Current is the flow of electrons; must be induced by electromotive force or voltage.• Opposition to flow of power in a material is measured by the resistance (R) of the material. I• Ohm’s law – Current (I) is proportional to Voltage (V), where the constant of proportionality is 1/R. (1/R is the conductance) V R – I = V/R or V = IR – Resistance of 1 Ohm will allow a current of 1 Ampere to flow when a voltage of 1 Volt is applied across it. 3 YAGTP3918 icfi.com
- 4. Basics of Electric Circuits• Flow of current governed by conservation rules called Kirchoff’s Laws – Kirchhoff’s Current Law: Sum of currents entering a point must equal sum of currents leaving that point. – Kirchhoff’s Voltage Law: The algebraic sum of all voltages in a loop must equal zero. i1 i2 4 YAGTP3918 icfi.com
- 5. Basics of Electric Circuits• Voltage and current can be direct or alternating DC• Direct voltage or current (DC) – From sources such as batteries• Alternating voltage or current (AC) – From sources such as generators – Alternates between plus and minus (60 AC times a second in the US) – Current and voltage typically specified as the root mean square (RMS) 5 YAGTP3918 icfi.com
- 6. Basics of Electric Circuits 200 Peak = 163 V 150 100 RMS = 115 V 50 0 0 45 90 135 180 225 270 315 360 405 450 495 540 585 -50 -100 -150 -200 6 YAGTP3918 icfi.com
- 7. Basics of Electric Circuits• Faraday’s Law: Changing magnetic flux through a loop of wire induces a voltage in the wire• Simple AC generator – Spinning loop of wire between magnets generates AC voltage – Replacing wire loop with a coil of wire with N turns creates N times the voltage 7 YAGTP3918 icfi.com
- 8. Choice of AC Power For Transmission System• First U.S. generating station at Pearl Street in Manhattan produced DC power, beginning in 1882.• “Battle of the Currents” fought throughout the 1880s, with Thomas Edison promoting DC and George Westinghouse promoting AC• Backbone of AC power system theory formulated by Serbian-American scientist Nikola Tesla, originally employed by Edison, and later by Westinghouse Thomas Edison George Westinghouse Nikola Tesla 8 YAGTP3918 icfi.com
- 9. Advantages of DC Power in the 1880s• Less dangerous, due to lower voltages used, and relative effect of DC vs AC on the human nervous system• Lower losses than AC at same voltage level• DC generators and motors readily available in the 1880s 9 YAGTP3918 icfi.com
- 10. Advantages of AC Power• AC systems allow use of transformers to easily convert between different voltages• Higher transmission voltages mean lower currents, and lower losses• Voltage drop is less significant at high voltage, removing limit to system size 10 YAGTP3918 icfi.com
- 11. Basics of AC Circuits• Power consuming components in the network include – Resistors – Inductors – Capacitors 11 YAGTP3918 icfi.com
- 12. Basics of AC Circuits• Behavior of voltage and current, and hence power, depends on the characteristics of the device – Resistors: current and voltage in phase (Phase angle is zero) – Inductors: current lags voltage by 90⁰ – Capacitors: current leads voltage by 90⁰• Combined effect of these components is called Impedance – Effect of resistors depends on their resistance, while that of inductors and capacitors depends on their reactance – Resulting phase angle will not be zero or ± 90⁰, but will depend on relative effect of the components 12 YAGTP3918 icfi.com
- 13. Basics of AC Circuits• Power in an electric circuit is derived as the product of voltage and current – P = VI• When voltage and current are in phase, instantaneous power is never less than zero• This is the best case scenario – No “non-useful” power 13 YAGTP3918 icfi.com
- 14. Basics of AC Circuits1.50 Voltage has zero Average value of power is greater average value than zero; instantaneous value is never less than zero Current has zero1.00 average value0.500.00 0 45 90 135 180 225 270 315 360 405 450 495 540-0.50-1.00 Voltage and current are in phase-1.50 14 YAGTP3918 icfi.com
- 15. Basics of AC Circuits• When voltage and current are not in phase, instantaneous power is sometimes less than zero• “Useful” power is scaled by a function of the phase angle – P = VI*Cos (α) – P = Cos (α) is called the power factor• It is possible to decompose the power into two components – First component never less than zero – Second component has a zero average 15 YAGTP3918 icfi.com
- 16. Basics of AC Circuits 1.50 Average value of power Current has zero average value is greater than zero 1.00 Voltage has zero average value 0.50 0.00 0 45 90 135 180 225 270 315 360 405 450 495 540 -0.50 -1.00 Phase angle -1.50 16 YAGTP3918 icfi.com
- 17. Basics of AC Circuits 1 Instantaneous Power Component 1: Never less than zero. 0.8 Average = 0.28 0.6 0.4 0.4 0.28 0.2 0 0 45 90 135 180 225 270 315 360 -0.2 Component 2: -0.4 Has zero average. Peak = 0.4 -0.6 17 YAGTP3918 icfi.com
- 18. Basics of AC Circuits• Component that is never less than zero represents power consumed by resistive elements – Average value is greater than zero – Can be transformed into useful work – Specified using the average value, P (measured in MW)• Component with zero average value represents power in inductive and capacitive elements – Always 90 degrees out of phase with first component – Specified using peak value, Q (measured in MVAr) – Average value is zero – Not available for useful work; stored and returned to circuit as charge accumulations (capacitive) or magnetic fields (inductive) – Important for voltage support 18 YAGTP3918 icfi.com
- 19. Basics of AC Circuits• Complex Power S = P + jQ – P is “active” or “real” power – Q is “reactive” or “imaginary” power• Apparent Power |S| = sqrt (P2 + Q2) 19 YAGTP3918 icfi.com
- 20. Single Phase AC vs. Three Phase AC• Single Phase – Two wires – Uneven torque on generator – Varying power over the AC cycle• Three Phase – Triple the power transmission, but number of wires only increases to three – Constant torque on generator or motor – Constant power – Sum of current on three phases equals zero• Why not more phases? – More expensive generators, more transformers, more complicated tower and wiring structure 20 YAGTP3918 icfi.com
- 21. Power Generation and Supply• Utilities produce power using 3-Phase generation – Three equal phases of electricity different only in timing – Requires fewer conductors to deliver the power – 3 or 4 instead of 6 for three single phase circuits – Instantaneous power is fixed; motors can operate with no variation in torque – Reduced line losses – higher line voltage relative to single phase for the same power; additional reduction if flow on neutral is zero 21 YAGTP3918 icfi.com
- 22. Three Phase Load Connection: Delta vs. Wye• Delta – Higher voltage: Voltage difference between phases is 1.732 times higher than phase to ground voltage. – No neutral connection; currents add to zero.• Wye – Lower voltage, lower power draw – Optional neutral connection 22 YAGTP3918 icfi.com
- 23. Power Transmission – Characteristics ofTransmission Lines• A transmission line has characteristics of a resistor, inductor and capacitor• Resistor: The line has a resistance that depends on the characteristics of the conductor material – Results in 3% to 7% losses in transmission lines• Inductor: The line acts like many small inductors connected in series, yielding an inductive reactance• Capacitor: The line acts like a perfect conductor with many small capacitors in parallel between the line and the neutral or the ground, resulting in a capacitive reactance – Usually ignored for short lines (less than 50 to 75 miles) – Correction factor required for long lines (greater than 200 miles) 23 YAGTP3918 icfi.com
- 24. Power Transmission – Characteristics ofTransmission Lines• The line has a resultant impedance that depends on the relative effects of the resistance, inductance and capacitance• It can be represented using the PI model• In an AC circuit the inductive reactance is typically much larger than the resistance 24 YAGTP3918 icfi.com
- 25. Power Transmission – Operation of TransmissionLines• Inductive reactance creates a reactive power demand (and a loss of reactive power) in the line that results in a drop in voltage at the receiving end• As line becomes more reactive, current must increase for a given amount of Real Power• Increase in current further increases reactive losses (recall that reactance >> resistance)• Increased reactive losses results in larger voltage drop at receiving end• Relatively higher inductive reactance implies that it is inefficient to deliver reactive power over long distances; it is better to compensate for reactive demand locally – Reactive power compensation devices include static devices (capacitors, inductors, etc) and dynamic (generators, synchronous condensers, etc) 25 YAGTP3918 icfi.com
- 26. Power Transmission – Reactive Power Compensation i XL R Q = 60 MVAr 115 kV α P = 100 MW • No reactive compensation • Real Power = 100 MW • Reactive Power = 60 MVAr • Power Factor = Cos (α) = 0.857 • Apparent Power = 117 MVA 26 YAGTP3918 icfi.com
- 27. Power Transmission – Reactive Power Compensation i XC XL R Q = 10 MVAr115 kV α P = 100 MW • Reactive power compensation provided by capacitor • Real Power = 100 MW • Reactive Power = 60 MVAr – 50 MVAr = 10 MVAr • Power Factor = Cos (α) = 0.995 • Apparent Power = 101 MVA 27 YAGTP3918 icfi.com
- 28. Power Transmission - Transformers• Used to convert power between different voltages via magnetic coupling between coils of wire• Types of transformers include – Isolation transformers – Auto-transformers – Variable tap transformers – Phase Angle Regulators (PARs) 28 YAGTP3918 icfi.com
- 29. Power Transmission – Isolation Transformers• No electrical connection between primary and secondary creates galvanic isolation EP N P = ES N S Ep Es IP NS = IS NP 29 YAGTP3918 icfi.com
- 30. Power Transmission – Auto-transformers• Shared coil, lighter, cheaper, but no isolation 30 YAGTP3918 icfi.com
- 31. Power Transmission – Adjustable Transformers• Variable tap transformers allow voltage to be adjusted• Phase Angle Regulators (PARs) are combinations of series/parallel connected transformers that draw reactive power and change the power system phase angle at their location, allowing power flows to be regulated Phase Angle Regulator 31 YAGTP3918 icfi.com
- 32. Power Flow Analysis• Determine bus voltages (magnitude and angles), generator dispatch and real and reactive power flows• At generator buses specify real power and bus voltage magnitude (PV) – These can be regulated by the generator control systems• At load buses specify real and reactive power (PQ) – Assume we have knowledge of expected demand• Select slack bus – Necessary because losses depend on actual flow and are not known a priori – Makes up for line losses and any demand not served by other generators – Voltage at slack bus is specified as 1 per unit and phase angle as 0 32 YAGTP3918 icfi.com
- 33. Power Flow Analysis (continued)• Fundamental quantities to be solved are voltage magnitude and voltage phase angle at each bus – With voltage known, all real and reactive power can be determined• Electrical parameters of transmission equipment (transmission lines, transformers, etc) are known• Real and reactive power absorbed at any bus should equal that delivered to the bus• Solve the Load Flow problem iteratively – Nonlinear with no closed form solution 33 YAGTP3918 icfi.com
- 34. Power Flow Analysis – PTDFs• The Load Flow solution shows generation dispatch and power flow on transmission lines• Line flows are compared to transmission line limits to ensure no line is overloaded• Line flows can be adjusted using their sensitivities to bus injections• These sensitivities are called Power Transfer Distribution Factors (PTDF)• PTDFs are important for Transmission Loading Relief (TLR) 34 YAGTP3918 icfi.com
- 35. Power Flow Analysis – PTDFs Gen 1 ~ Bus A A B C A-B 1/3 -1/3 Reference Reference Bus Bus Line A-C 2/3 1/3 B-C 1/3 2/3Gen 2 B ~ C (Reference Bus) 35 YAGTP3918 icfi.com
- 36. Power Flow Analysis – PTDFs Gen 1 ~ A 60 MW 20 MW 40 MW Gen 2 B ~ 20 MW C (Reference Bus) 36 60 MW YAGTP3918 icfi.com
- 37. Power Flow Analysis – PTDFs Gen 1 ~ A 60 MW 10 MW 50 MW Gen 2 B ~ 40 MW C (Reference Bus) 30 MW 37 90 MW YAGTP3918 icfi.com
- 38. Power Flow Analysis – PTDFs• PTDF of transaction from Gen 1 on Line A-C is 2/3• PTDF of transaction from Gen 2 on Line A-C is 1/3• Gen 1 has a larger impact on flows on Line A-C than Gen 2• To relieve congestion on Line A-C by 1 MW – Reduce Gen 1 by 1.5 MW; or – Reduce Gen 2 by 3 MW 38 YAGTP3918 icfi.com
- 39. Power Transmission – Loop Flows• Loop flows arise whenever there are multiple paths for power to travel on between two points• Power cannot be directed to flow on specific paths• Flow on all lines is in inverse proportion to impedances, according to Kirchhoff’s laws• When one path becomes overloaded, it can prevent additional power transmission on other paths, even when they have spare capacity 39 YAGTP3918 icfi.com
- 40. U.S. Transmission / Distribution SystemStructure• Generation at medium voltage (4,000 – 13,000 volts)• Power transformed to high voltage (115kV to 765kV for transmission)• Stepped down to medium voltage for distribution• Stepped down to customer voltage for end usage 40 YAGTP3918 icfi.com
- 41. Power Line Physical Characteristics• Conductor Types – Standard high voltage line type is Aluminum Conductor Steel Reinforced (ASCR); aluminum has a low resistance, and is cheaper than copper – Lower resistance copper wires often used for underground cabling where cooling is an issue• Line Sag – Line heating from loading close to capacity causes lines to sag – Sag limits the distance between transmission towers Aluminum Conductor Steel Core 41 YAGTP3918 icfi.com
- 42. Stability• System could operate at x or y for some power transfer P• At x, system maintains stability after disturbance• At y, system loses stability after disturbance• System typically operated well below 90° P V1 sin(θ1) V2 sin(θ2) 42 YAGTP3918 icfi.com
- 43. Power Quality• Voltage – U.S. standard is ±5% from nominal voltage – Voltage drop along transmission lines determined by load – Transformer taps and reactive compensation used to maintain voltage – Out-of-range voltage can damage equipment• Frequency – U.S. standard on order of ±1% of nominal frequency (±0.6 Hz)• Harmonics – Components of voltage/current waveform not at 60Hz – Cause additional losses in transformers and lines – Can damage or cause malfunctioning of sensitive equipment 43 YAGTP3918 icfi.com
- 44. Summary• AC voltage is sinusoidal in nature; described by magnitude and phase angle• Power has two components – Real and Reactive• Real power describes average power delivered; it is non-zero• Reactive power describes magnitude of oscillatory portion of power delivered; has zero average• Starting with predictions of demand and generator setpoints, and knowledge of system characteristics, Power Flow used to solve for voltage magnitudes and voltage phase angles; all other parameters can be derived from these 44 YAGTP3918 icfi.com
- 45. Summary• Decoupling in power system operation – Voltage phase angles depend mainly on real power – Voltage magnitudes depend mainly on reactive power• Real power flow on lines depends on voltage angles• Changes in real power flow on lines can be calculated using linearized sensitivities known as PTDFs• Voltage angle typically kept small to maintain system stability 45 YAGTP3918 icfi.com

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