Magnetics, Transformers, Harmonics

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ECE 333 (398RES)Renewable Energy Systems

• Lecture 5
• Magnetics, Transformers, Harmonics
• Professor Tom Overbye
• Department of Electrical andComputer Engineering

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Announcements

• Finish reading Chapter 1 and 2
• Be reading Chapter 3
• Homework 2 is 2.2, 2.9, 2.10, SP1. Due date is
  Feb 5.

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SP1 (Special Problem 1)

• A delta connected load with each Z 8?30 ohms
  is supplied from a balanced three phase wye
  connected generator through lines having series
  impedance of 0.25 ? 30 ohms. The line-to-line
  voltage measured at the load is 208 volts (for
  the angle, please use load Vab as the reference,
  such that Vab 208 ? 0 volts).
• a. Calculate the three load phase currents
  (magnitude and angle).
• b. Calculate the magnitude of the line-to-line
  voltage at the generator.
• c. Calculate the power factor at the generator
  (be sure to indicate leading or lagging).

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In the News UI Wind Turbine

• UIUC has been looking at building a wind
  turbine(s) for years, with maximum power output
  of 1.5 MW
• Cost has increased, with current value around
  4.5 million
• Would produce perhaps 3000 MWh per year
• Student Sustainability Committee has recently
  raised its contribution to 500,000 (funded by a
  student fee)
• Project is currently on hold because of budget
  constraints
• Let your voice be heard! Email Dick Warner,
  Director UIUC Office of Sustainabilty,
  dickw_at_illinois.edu, Jaclyn ODay, UIUC Student
  Body President, joday2_at_illinois.edu, or Robert
  Gregg, UIUC Graduate Senator, rgregg_at_illinois.edu.

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Inductance Example

• Calculate the inductance of an N turn coil wound
  tightly on a torodial iron core that has a radius
  of R and a cross-sectional area of A. Assume
• 1) all flux is within the coil
• 2) all flux links each turn

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Inductance Example, contd
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Transformers Overview

• Power systems are characterized by many different
  voltage levels, ranging from 765 kV down to
  240/120 volts.
• Transformers are used to transfer power between
  different voltage levels.
• The ability to inexpensively change voltage
  levels is a key advantage of ac systems over dc
  systems.
• In this section well development models for the
  transformer and discuss various ways of
  connecting three phase transformers.

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Distribution Transformer Picture
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Transmission Level Transformer
230 kV surge arrestors
115 kV surge arrestors
Oil Cooler
Oil pump
Radiators W/Fans
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Ideal Transformer

• First we review the voltage/current relationships
  for an ideal transformer
• no real power losses
• magnetic core has infinite permeability
• no leakage flux
• Well define the primary side of the
  transformer as the side that usually takes power,
  and the secondary as the side that usually
  delivers power.
• primary is usually the side with the higher
  voltage, but may be the low voltage side on a
  generator step-up transformer.

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Ideal Transformer Relationships
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Current Relationships
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Current/Voltage Relationships
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Impedance Transformation Example

• Example Calculate the primary voltage and
  current for an impedance load on the secondary

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Real Transformers

• Real transformers
• have losses
• have leakage flux
• have finite permeability of magnetic core
• 1. Real power losses
• resistance in windings (i2 R)
• core losses due to eddy currents and hysteresis

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Transformer Core losses
Eddy currents arise because of changing flux in
core. Eddy currents are reduced by laminating the
core
Hysteresis losses are proportional to area of BH
curve and the frequency
These losses are reduced by using material with a
thin BH curve
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Effect of Leakage Flux
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Effect of Finite Core Permeability
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Transformer Equivalent Circuit
Using the previous relationships, we can derive
an equivalent circuit model for the real
transformer
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Simplified Equivalent Circuit
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Calculation of Model Parameters

• The parameters of the model are determined based
  upon
• nameplate data gives the rated voltages and
  power
• open circuit test rated voltage is applied to
  primary with secondary open measure the primary
  current and losses (the test may also be done
  applying the voltage to the secondary,
  calculating the values, then referring the values
  back to the primary side).
• short circuit test with secondary shorted, apply
  voltage to primary to get rated current to flow
  measure voltage and losses.

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Residential Distribution Transformers
Single phase transformers are commonly used in
residential distribution systems. Most
distribution systems are 4 wire, with a
multi-grounded, common neutral.
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Power System Harmonics

• So far class has talked about fundamental
  frequency analysis. Many traditional loads only
  consume power at the fundamental frequency.
  However, some loads, mostly electronic-based,
  tend to draw current in non-linear pulses, which
  gives rise to harmonics.
• If current has half-wave-symmetry (values are
  equal and opposite when separated by T/2) then
  there are no even harmonics

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Switched-Mode Power Supply Current
Source www.utterpower.com/commercial_grid.htm
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Quick Review of Fourier Analysis
.
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Harmonic Current Specturm

• The below figure shows the harmonic current
  components for an 18-W, electronic-ballast
  compact fluorescent lamp.

Source Fig 2.34 of Renewable and Efficient
Electric Power Systems by Masters
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Key Problems with Harmonics

• A key problem with the third harmonic is neutral
  current since the fundamental 120 degree phase
  shift becomes 360 degrees for the third harmonic
  so the third harmonic values do not cancel (also
  true for other triplen harmonics)
• Delta-grounded wye transformers prevent triplen
  harmonic currents from flowing into the power
  grid
• Harmonics cause transformer overheating since
  core losses are proportional to frequency
• Harmonic resonance, particularly with shunt
  capacitors (can be around 5th or 7th harmonic
  values)