Power Flashcards
National Electric Code (NEC)
- published by National Fire Protection Association (NFPA)
- concerned with safety electrical practices only
- not a guide to efficiency, convenience, or appropriateness
- complying and proper maintenance will result in an installation that is essentially free from hazard
- not necessarily efficient, convenient, or adequate for good service or future expansion of electrical use
- not intended as a design specification nor an instruction manual for untrained persons
mandatory rules of NEC
- identify actions that are specifically required or prohibited
- characterized by the use of the terms “shall” or “shall not”
- exceptions to rules are in italic
permissive rules of the NEC
- actions that are allowed but not required
- are normally used to describe options or alternative methods
- characterized by the use of the terms “shall be permitted” or “shall not be required”
National Electric Safety Code (NESC)
- general purpose is to protect utility personnel and the general public
- specifically “the practical safeguarding of persons during the installation, operation and maintenance of electric supply and communication lines, and associated equipment”
NESC applicability & NEC applicability
NESC applies to everything after the generator except the end-user building
NEC only applies to the end-user building
real power, P
P= Vrms Irms cos θ
- units of watts (W)
- dissipated as heat or converted into mechanical work
- θ is power angle between input voltage and current
- when waveform is a sinusoid:
P = (1/2) Vmax Imax cos θ
purely resistive circuit
- voltage and current in phase (for an AC circuit)
- in resonance (capacitance reactance and inductive reactance cancel)
- cosθ=1
P= Vrms Irms = Vrms^2 / R = Irms^2 R [purely resistive load; pf =1]
energy
ability to do work
power
- rate of flow of energy
- energy per unit time
- as used on the FE exam, it is the RMS quantity unless otherwise stated
reactive power
- power used to provide energy to the magnetic fields of coils of machines or the electric fields of cables, twice per AC cycle
- although not consumed as energy, does represent real current so it produces voltage drop and losses
power triangle
- real power, P
- reactive power, Q
- apparent power, S
- power angel, θ
reactive power, Q
- the power stored and returned without dissipation
- mathematically represented as imaginary
- units: volts-amps reactive (VAR)
- units determine difference in reactive power and real power, real power is in watts
Q = (1/2) Vmax Imax sinθ [sinusoids] Q = Vrms Irms sinθ
apparent power, S
- S = Ieff Veff = (1/2) Im Vm
- magnitude of complex sum of real and reactive power
- units of volt-amps (VA)
- units distinguish apparent power from reactive power (volts-amps reactive) and real power (watts)
- values of S doesn’t show how much is real versus reactive
power angle θ
- overall impedance angle
- same as angle between input voltage and current in the circuit
complex power vector, S
S= V*I = P + jQ
- units of volt-amps (VA)
- I *= complex conjugate of the current
- power angle, θ, and current angle have opposite signs
complex power vector, S continued
- when the current angle is negative, the power factor is lagging
- when the current angle is positive, the power factor is leading
power factor, pf
pf = cosθ
- usually given as a percentage
- positive for both positive and negative angles
- pf=1 for purely resistive load
for inductive circuit,
- lagging power factor
- negative θ
for capacitive circuit,
- leading power factor
- positive θ
power factor correction
- adding reactive power to system to change the system’s power factor
- usually by adding capacitance to a system that is inductive
- when capacitance is storing reactive power, inductance is returning reactive power, and vice versa
Reactive power flow is in power systems and should be minimized, as it
- increases losses
- creates voltage drop
- reduces efficiency
- increases line size (cost)
Maximum Power Transfer
- A fixed network will transfer the maximum power to a load when the load is the complex conjugate of the network equivalent impedance
–> analogous to DC circuits,
using ZL= RL + jXL in place or RL
–> occurs when
Rth + jXth = RL - jXL
net energy exchanged
- inductance and capacitance power transfer
- one direction during part of the half-cycle
- opposite direction during the other part
- source for storage over a cycle is zero
transformer
transfers energy from one circuit to another
- AC current through wire coiled around a magnetic core (the primary winding) generates changing magnetic field
- changing magnetic field induces AC current in secondary winding
- DC current produces constant magnetic field, can’t induce current
- magnetic flux mostly in core (much higher permeability in free space)
used for changing voltages, matching impedances, isolating circuits
- voltage increase of decreases according to ratio of turns in primary and secondary windings
- for impedance matching, turns ratio is chosen so that impedance can be seen by source through transformer matches source impedance
turns ratio, a
- ratio of primary to secondary windings
- also called ratio of transformation
a = N1/N2
step-down transformer
- turns ratio >1
- decreases voltage
step-up transformer
- turns ratio < 1
- increases voltage
ideal transformer
- power absorbed by primary windings equals power generated by secondary windings
IpVp = IsVs - windings have neither resistance nor reactance
turns ratio (ideal transformer)
a = l Vp/Vs l = l Is/ Ip |
input impedance, Z1
- Real primary circuits have input impedance
- Anything attached to the transformer, such as a microphone will contribute to input impedance
- the input impedance contributes to the impedance seen by the source
power
- concerned with voltage and current
- mathematically modeled as having real and imaginary parts
- isn’t real and imaginary; it is dissipated & stored
“real” power
dissipated in resistors or rotating machine mechanical load
“imaginary” power
- stored in electric and/or magnetic fields during one part of the half-cycle
- returned during the other part of the half-cycle
three-phase power
most common way to transmit large amounts of power over long distances
- Power that would take six conductors using single-phase systems can be transmitted with just three conductors
- There is loss in the lines for only the direction from source to load (single-phase systems have loss both ways)
- Three wires are used to transmit power (some systems also have a neutral wire)
Phase Vectors
- rotate counterclockwise as time (phase) goes by
- B-phase vector passes the origin
- followed by the C-phase vector
- sequence is A-B-C
balanced three-phase system
- voltages and currents on three wires all of same magnitude
- out of phase by 120 degrees
- vector sum of voltages and currents is zero
benefits of three- phase energy distribution system
- more efficient
- smaller conductors than single -phase
- provides same power with three wires as single-phase systems with six wires
- smoother waveform and less ripple to be filtered when rectified
- can produce a magnetic field that rotates in a specified direction, simplifying design of electric motors
benefits of three-phase motor versus single-phase
- provides a uniform torque, not a pulsating one
- does not require additional starting windings or associated switches
- physical size is smaller, with same horsepower rating
balanced load
- three equal loads with same real and reactive parts
- magnitude and phase of voltage and current are same in each load
- power factor is same for each phase
Because of these traits, a balanced system can be analyzed on per-phase basis (known as one-line analysis)
delta-wired systems
- three loads each connected to two of the three phase conductors
- no neutral wire
- line-to-neutral voltage and current do not physically exist
wye equivalent
- can still represent the delta system
- can compare the line terminal voltage to the neutral even though the neutral does not physically exist
three-phase delta configuration
has three phases and no neutral wire
- only voltages to be considered are line-to-line voltages
- two currents to be considered
- -> line currents that flow in the lines
- -> phase currents which flow in the resistors, shown as load in the diagram
line currents
out of phase with the line-to-line (phase) currents
wye-wired systems
- have three loads connected together at one node
- each load connected to the three-phase conductors
- may or may not have a neutral wire
- line-to-line voltage and current physically exist
three-phase wye configuration
- three phases and a neutral wire
- line-to-neutral voltages are between the lines and the neutral: Van, Vbn, and Vcn
- line-to-line voltages are between the legs: Vab, Vbc, and Vca
line-to-neutral voltage
- differ from each by 120 degrees (1/3 cycle)
- go through maxima in regular order
- led by phase voltage by 30 degrees
line-to-line voltage
- expressed in terms of phase voltages
- lags the phase voltage by 30 degrees
Phase Sequence
- Va reaches peak before Vb
- Vb reaches peak before Vc
- ABC sequence
transmission lines
- necessary for distributed power
- modeled as lossless when the source and load are close together
- modeled with lumped parameters when the source and load are further apart
transmission line resistance
- can be ignored if the conductor is good and the length of the line is short
- increases as the frequency increases because the effective cross-section decreases
transmission line inductance
exhibited externally and internally if a conductor is long enough
external inductance
- produced by a long straight wire with a current
- greatly increased by the presence of other conductors near the wire
internal inductance
- caused by the skin effect
- typically insignificant compared to external inductance
shunt capacitance
capacitance between conductors
single-phase systems
shunt capacitance depends on conductor diameter and spacing, also dielectric properties of insulation
polyphase systems (three-phase)
shunt capacitance depends on geometric arrangement of the conductors
short-length transmission lines
60 Hz lines that are less than 80 km long
medium-length transmission lines
- 60 Hz lines between 80 km and 240 km (50 mi and 150 mi) long
- modeled as either T- or pi- models
long transmission lines
- 60 Hz lines greater than 240 km (150mi) long
- modeled with partial differential equations and distributed parameters
short-length transmission lines
- modeled as a series impedance with resistance and inductance
- shunt reactance is excluded from model because coupling is insignificant
medium- length transmission line
- modeled as T- model, pi-model, or series of T-model and pi-model sections
- lumps series impedance as two components and shunt admittance as single component
generation stations
generate very high voltages which is stepped down for sub transmission, distribution substation, primary distribution, and secondary mains
the higher voltage:
- the more efficient transmission
- the greater the danger of faults
- the greater the consequences for faults
overcurrent protection
- required by the NEC to reduce probability of fire, electrical arcing
- many protective devices, including fuses and circuit breakers
- multiple-level protection at facilities often includes protection such as feeder circuits, sub feeder panels, and branch circuit panels
AC Machines
- Motors convert electrical energy into mechanical energy
- Generators convert mechanical energy into electrical energy
- AC machines have rotating magnetic fields
- DC machines have constant magnetic fields and commutators
- The energy must always convert to magnetic energy first
synchronous generators
constant magnetic field in the rotating part that induces currents in the stationary windings of the machine
synchronous motors and induction motors
stator magnetic field rotates at synchronous speed, ns
ns= 120f/p
induction motors
- essentially constant- speed drives
- receive power through induction – no brushes
- rotating transformer secondary (the rotor) with a stationary primary (the stator)
- EMF induced as stator field moves pas rotor conductors
- rotor windings have reactance, the rotor fields lags the induced EMF
slip
slip = (ns- n) / ns
- to have a change in flux linkage, rotor must turn at less than the synchronous speed
- typically 2% to 5%
DC Machine
- device that produces DC potential
- constant magnetic field in the stator (called the field)
- magnetic field of the rotor (called the armature) responds to the stator field
- field can be a permanent magnet or can be an electromagnet powered by the current of the armature circuit
- magnetic flux generated by the field current, If, is approximately
Φ = KfIf
magnetic field, B
- produced either by permanent magnets or electromagnets
- rotated, wires in the field cross the lines of magnetic flux and current flows in the field
commutator
insures that the polarity of the output voltage is correct with time
DC generator
- simplified model ignores the resistance loss in the armature and field windings
-terminal voltage for simplified model
Va= KanΦ [in volts]
n is rotational speed [rpms]
Φ is magnetic flux
DC motor
- very similar to a DC generator, only the direction of current is reversed
- power (for the motor model in the DC machine equivalent circuit)
Pe= Ph + Pm = Ia^2 Ra+ IaE - ignoring power dissipated as heat for the DC machine equivalent circuit
Pm= Va Ia
servomotor
- particular type of motor
- precise control of the position or speed
- sensors and feedback systems allow control
back electromotive force (emf), Eg
- not a physical voltage
- a mathematical model for electrical power converted to mechanical work
V= IR + Kew
T =kTI
KT= KE
line regulation
measures the ability to maintain a constant output voltage regardless of changes in the input voltage
load regulation
measures the ability to maintain a constant output voltage regardless of changes in size of the load (current draw)
