introduction to electrical engineering

School of Engineering & Technology

Introduction to Electrical Engineering

School of Engineering & Technology

Rajneesh Budania

Jaipur National University

June 29, 2012

Outline

• Basics of Electric Circuits

• AC Power

• Power Generation and Transmission

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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.

• Ohm’s law I

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• Ohm’s law

– Current (I) is proportional to Voltage (V), where the constant

of proportionality is 1/R. (1/R is the conductance)

– 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.

• 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

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• Voltage and current can be direct

or alternating

• Direct voltage or current (DC)– From sources such as batteries

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– From sources such as batteries

• Alternating voltage or current (AC)– From sources such as generators

– Alternates between plus and minus (60

times a second in the US)

– Current and voltage typically specified as

the root mean square (RMS)

200 Peak = 163 V

RMS = 115 V

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0 45 90 135 180 225 270 315 360 405 450 495 540 585

• Faraday’s Law: Changing magnetic flux through a loop of wire induces a

voltage in the wire

• Simple AC generator

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• 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

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

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Nikola Tesla, originally employed by Edison, and later by Westinghouse

Thomas Edison George Westinghouse Nikola Tesla

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

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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

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• Voltage drop is less significant at high voltage, removing limit

to system size

Basics of AC Circuits

• Power consuming components in the network include

– Resistors

– Inductors

– Capacitors

• 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

• 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

Voltage has zero

average value

Current has zero

average value

Average value of power is greater

than zero; instantaneous value is

never less than zero

0 45 90 135 180 225 270 315 360 405 450 495 540

Voltage and current

are in phase

• 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

1.50Current has zero

average value

Voltage has zero

average value

Average value of power

is greater than zero

0 45 90 135 180 225 270 315 360 405 450 495 540

Phase angle

Instantaneous Power Component 1:

Never less than zero.

Average = 0.28

0 45 90 135 180 225 270 315 360

Component 2:

Has zero average.

Peak = 0.4

• 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

• Complex Power S = P + jQ

– P is “active” or “real” power

– Q is “reactive” or “imaginary” power

• Apparent Power |S| = sqrt (P2 + Q2)

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

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

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

Power Transmission – Characteristics of

Transmission 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)

Power Transmission – Characteristics of

Transmission 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

Power Transmission – Operation of Transmission

• 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

• 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)

Power Transmission – Reactive Power Compensation

115 kV XL R

Q = 60 MVAr

P = 100 MW

• No reactive compensation

• Real Power = 100 MW

• Reactive Power = 60 MVAr

• Power Factor = Cos (α) = 0.857

• Apparent Power = 117 MVA

Power Transmission – Reactive Power Compensation

115 kV XC XL R

Q = 10 MVAr

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

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)

Power Transmission – Isolation Transformers

• No electrical connection between primary and secondary

creates galvanic isolation

PP NE =

Power Transmission – Auto-transformers

• Shared coil, lighter, cheaper, but no isolation

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

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

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

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)

A-B 1/3 -1/3

sA-C 2/3 1/3

BC (Reference Bus)~

sA-C 2/3 1/3

B-C 1/3 2/3

~A 60 MW

40 MW20 MW

(Reference Bus)~Gen 2

~A 60 MW

50 MW10 MW

(Reference Bus)~Gen 2

• 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

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

U.S. Transmission / Distribution System

Structure

• 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

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

• Line Sag

– Line heating from loading close to capacity causes lines to sag

– Sag limits the distance between transmission towers

Aluminum Conductor

Steel Core

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°

V1 sin(θ1) V2 sin(θ2)

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

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

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

introduction to electrical engineering

ac voltage

current ac

current leads voltage

current lags voltage

choice of ac power

average value of power

current dc

basics of ac circuits1

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