renewable energy utilization · 2017-01-13 · energy systems research laboratory, fiu renewable...
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Energy Systems Research Laboratory, FIU
Renewable Energy Utilization
Professor Osama A. MohammedDepartment of Electrical and Computer Engineering
EEL5285 & EEL 4930All Sections (Spring 2017)
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
What is CoveredPart I: Renewable Energy Systems• Introduction• Electric Systems in Energy Context• Basic Review of Electric Quantifies and Impact of Power Conditioning• Energy Efficiency and operational issues• Energy Generation and operation and control• Alternate and Renewable Energy Sources and its Economics
– Alternate and Renewable Energy Sourceso Wind Energyo Distributed generation technologieso Hydro Power o Wave/ Tidal Powero Cooling and Heat Pumpso The Solar Resource
Part II: Renewable Energy Utilization• Renewable Energy Utilization• Energy Storage including Electric/Pluggable Hybrid Cars• Smart Grid Integration Issues
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Introduction: Notation - Power• Power: Instantaneous consumption of energy• Power Units
Watts = voltage x current for dc (W)kW – 1 x 103 WattMW – 1 x 106 WattGW – 1 x 109 Watt
• Installed U.S. generation capacity is about 900 GW ( about 3 kW per person)
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Introduction: Notation - Energy• Energy: Integration of power over time; energy is what people
really want from a power system• Energy Units
– Joule = 1 Watt-second (J)– kWh = Kilowatthour (3.6 x 106 J)– Btu = 1055 J; 1 MBtu=0.292 MWh; 1MWh=3.4MBtu– One gallon of gas has about 0.125 MBtu (36.5 kWh); one
gallon ethanol as about 0.084 Mbtu (2/3 that of gas)• U.S. electric energy consumption is about 3600 billion kWh
(about 13,333 kWh per person)
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
North America Interconnections
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIUProfessor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
National Transmission Map
Energy Systems Research Laboratory, FIU
Some Regional Transmission Systems
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIUProfessor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
ERCOT -Electric Reliability Council of Texas FRCC -Florida Reliability Coordinating Council MRO -Midwest Reliability Organization NPCC -Northeast Power Coordinating Council RFC –Reliability First Corporation SERC –Southeastern Electric Reliability Corporation SPP -Southwest Power Pool WECC -Western Electricity Coordinating Council
Electric Grid Reliability Regions
Energy Systems Research Laboratory, FIU
Electric Systems in Energy Context• Focuses here is on renewable electric systems, but we first
need to put them in the context of the total energy delivery system
• Electricity is used primarily as a means for energy transportation
• Use other sources of energy to create it, and it is usually converted into another form of energy when used
• About 40% of US energy is transported in electric form, a percentage that is gradually increasing
• Concerns about need to reduce CO2 emissions and fossil fuel depletion are becoming main drivers for change in world energy infrastructure
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
World Energy Consumption
• worldwide energy demand is increasing rapidly (30% increase by 2030)
• World consumption is expected to increase by 36%, most of that growth is from China.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
World Oil Prices are Going Down Since 2009
• Continued demand growth should drive oil prices higher, from IEA World Energy Outlook
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
The 450 Scenario assumes:• Different groups of
countries adopt binding economy-wide emissions targets in successive steps.
• This should reflect their different stages of economic development and their respective responsibility for past emissions.
Energy Systems Research Laboratory, FIU
USA Natural Gas Supplies
• EIA projections of USA natural gas supplies• expanding supplies of USA natural gas prices keep energy prices
down
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Information Administration (EIA) Projections
Energy Systems Research Laboratory, FIU
USA Electricity Production by Fuel
• EIA projections of USA electricity production by fuel
• The projected fuel mix for electricity generation gradually shifts to lower Carbon options
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Expected to Increase
Significantly
Energy Systems Research Laboratory, FIU
USA Energy usage
• the U.S. consumes about 30% of all energy produced in the world
• usage has steadily increased, except during oil crises/major Recessions
• we have about 3% of the world's petroleum reserves, and consume about 25% of the world's petroleum production.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
World distribution of energy resources• petroleum (oil) is
highly concentrated in the Middle East
• natural gas is concentrated in the former Soviet Union and Middle East
• coal is relatively uniform world-wide
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Worldwide Oil Distribution
• Worldwide Oil Distribution.
• Concentration of resources in the Middle East has a dramatic impact on world politics and finance.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Worldwide Natural Gas Distribution
• Distribution of natural gas reserves worldwide
• Concentration of resources in the former Soviet Union is important, but overseas export is difficult.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Worldwide Coal Distribution
• Distribution of coal reserves worldwide
• Since coal distribution is relatively uniform, coal the universal energy source.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Sources of Energy in the US
Source: EIA Energy Outlook 2009
Petroleum, 38.9
Coal, 22.6
Natural Gas, 24.1
Nuclear, 9.3
Hydro, 2.6
Biomass, 3 Other, 1.4
CO2 Emissions (millions of metric tons, and per quad measure)Petroleum: 2598, 64.0 Natural Gas: 1198, 53.0Coal: 2115, 92.3
About 86% Fossil Fuels
1 Quad = 293 billion kWh (actual)
1 Quad = 98 billion kWh (used, taking into account efficiency)
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Electric Generation by Fuel/State
Source: 2006 EIA Data
EIA: Energy Information Administration
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Energy Consumption in the World• The total world-wide energy consumption was 472
quad (2006), a growth of about 19% from 2000 values for example.
• A breakdown of this value by fuel source is 171.7 quad (36.3%) from petroleum, 127.5 (27.0%) from coal, 108.0 (22.9%) from natural gas, 29.7 (6.3%) from hydroelectric, 27.8 (5.9%) from nuclear, 4.7 (1.0%) other used as electric power, 2.8 (0.6%) other not used as electric power
• World-wide total is 86.2% fossil-fuel, and (currently) less than 1.0% in the focus area of this class
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Historical and Projected US Energy Consumption
EnergyinQuad
Source: EIA Annual Energy Outlook, 2010This data says we will be 81% Fossil in 2035!!
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
The World: Top Energy Users (in Quad), 2006 Data
• USA – 99.9• China – 73.8• Russia – 30.4• Japan – 22.8• India – 17.7• Germany – 14.6• Canada – 14.0• France – 11.4• UK – 9.8• Brazil – 9.6
World total is 472; Average per 100 Million people is about 7.32. If world used US averagetotal consumption would be about 2148 quad!
Source: US DOE EIA
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
A quad is a unit of energy equal to 1015 (a short-scale quadrillion) BTU, or 1.055 ×1018 joules (1.055 exajoules or EJ) in SI units.
Energy Systems Research Laboratory, FIU
Per Capita Energy Consumption in MBtu in Some Countries per Year (2006 data)
• Iceland: 568.6 Norway: 410.8• Kuwait: 469.8 Canada: 427.2 • USA: 334.6 Australia: 276.9• Russia: 213.9 France: 180.7• Japan: 178.7 Germany: 177.5• UK: 161.7 S. Africa: 117.2• China: 56.2 Brazil: 51.2• Indonesia: 17.9 India: 15.9• Pakistan: 14.2 Nigeria: 7.8• Malawi: 1.9 Afghanistan: 0.6
Source http://www.eia.doe.gov/pub/international/iealf/tablee1c.xls
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Global Warming: What is Known is CO2 in Air is Rising
Source: http://www.esrl.noaa.gov/gmd/ccgg/trends/
• Value was about 280 ppm in 1800, 389 in 2010
• Rate of increase is about 2 ppm per year
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
The Worldwide Air Temperature is Rising (at Least Over the Last 150 Years)
Source: http://www.cru.uea.ac.uk/cru/info/warming/
Baseline is 1961 to 1990 mean
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Monthly Worldwide Temp. Data, Last 40 Years (Celsius, 1961-1990 Deviation)
http://hadobs.metoffice.com/hadcrut3/diagnostics/global/nh+sh/monthly
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIUProfessor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Monthly Worldwide Temp. Data, Last 40 Years (Celsius, 1961-1990 Deviation)
Energy Systems Research Laboratory, FIU
U.S Annual Average Temperature
Source: http://www.noaanews.noaa.gov/stories2009/images/1208natltemp.png
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Eventual Atmospheric CO2 Stabilization Level Depends Upon CO2 Emissions
Regardless of what we doin the short-term the CO2 levels in the atmosphere will continue to increase.
The eventual stabilizationlevels depend upon how quickly CO2 emissions are curtailed.
Emissions from electricity production are currently about 40% of the total
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
And Where Might Temps Go?
http://commons.wikimedia.org/wiki/File:Global_Warming_Predictions.png
Note that the modelsshow rate of increase valuesof between0.2 to 0.5 C per decade.The rate from1975 to 2005was about 0.2 C per decade.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
World Population Trends Country 2005 2015 2025 %Japan 127.5 124.7 117.8 -7.6Germany 82.4 81.9 80.6 -2.2Russia 142.8 136.0 128.1 -10.3USA 295.7 325.5 357.4 20.8China 1306 1361 1394 6.7India 1094 1251 1396 27.6World 6449 7230 7941 23.1Source: www.census.gov/ipc/www/idb/summaries.html; values in
millions; percent change from 2005 to 2025
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Energy Economics• Electric generating technologies involve a tradeoff
between fixed costs (costs to build them) and operating costs
• Nuclear and solar high fixed costs, but low operating costs
• Natural gas/oil have low fixed costs but high operating costs (dependent upon fuel prices)
• Coal, wind, hydro are in between• Also the units capacity factor is important to
determining ultimate cost of electricity• Potential carbon “tax” major uncertainty
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Ball park Energy Costs
Source: http://www.oe.energy.gov/DocumentsandMedia/adequacy_report_01-09-09.pdf
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIUProfessor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
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Natural Gas Futures Contract 1 (Dollars per Million Btu)
Natural Gas Prices Since 1994
Energy Systems Research Laboratory, FIU
Natural Gas Prices 1990’s to 2010
Marginal cost for natural gas fired electricity price in $/MWh is about 7-10 times gas price
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Coal Prices have Fallen Substantially Recently
Source: http://www.eia.doe.gov/cneaf/coal/page/coalnews/coalmar.html#spot
Prices are on the order of $1 to $2 per Mbtu
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIUProfessor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Current Average weekly coal commodity spot prices in different US Regions (dollars per short ton ) [1 short ton= 0.907184 metic ton]
Week ending Week ago12/18/15 12/25/15 12/28/15 12/31/15 01/08/16 change
Central Appalachia12,500 Btu, 1.2 SO2 $43.50 NA $43.50 $43.50 $42.25 $-1.25
Northern Appalachia13,000 Btu, < 3.0 SO2 $48.95 NA $48.95 $48.95 $48.60 $-0.35
Illinois Basin11,800 Btu, 5.0 SO2 $32.60 NA $32.60 $32.60 $32.20 $-0.40
Powder River Basin8,800 Btu, 0.8 SO2 $10.90 NA $10.90 $10.90 $9.70 $-1.20
Uinta Basin11,700 Btu, 0.8 SO2 $40.65 NA $40.65 $40.65 $39.05 $-1.60
Source: With permission, SNL Energy
Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Average weekly coal commodity spot prices dollars per MbtuWeek ending Week ago
12/18/15 12/25/15 12/28/15 12/31/15 01/08/16 change
Central Appalachia12,500 Btu, 1.2 SO2 $1.74 NA $1.74 $1.74 $1.69 $-0.05
Northern Appalachia13,000 Btu, < 3.0 SO2 $1.88 NA $1.88 $1.88 $1.87 $-0.01
Illinois Basin11,800 Btu, 5.0 SO2 $1.38 NA $1.38 $1.38 $1.36 $-0.02
Powder River Basin8,800 Btu, 0.8 SO2 $0.62 NA $0.62 $0.62 $0.55 $-0.07
Uinta Basin11,700 Btu, 0.8 SO2 $1.74 NA $1.74 $1.74 $1.67 $-0.07
Source: With permission, SNL Energy
Energy Systems Research Laboratory, FIU
Support for Renewable Energy
• The White House issued report about how the stimulus is going. Renewable energy projects were very much included. For example the largest solar PV installation in US, 579 MW Solo Star Site in California.
• Cost of residential solar is projected to decrease from $0.21 per kWh in 2009 to $0.10 in 2015 and $0.06 by 2030; wholesale parity is $0.05.
http://www.whitehouse.gov/sites/default/files/uploads/Recovery_Act_Innovation.pdf
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Solar Star (I and II) United States 34°49′50″N
118°23′53″W579 2015
Topaz Solar Farm United States 35°23′N 120°4′W 550 2014
Desert Sunlight Solar Farm
United States 33°49′33″N
115°24′08″W550 2015
Copper Mountain Solar Facility United States 35°47′N
114°59′W458 2015
Largest Solar Plants in the US
Energy Systems Research Laboratory, FIU
Wind is the Major Electric Renewable Growth Area Right Now
Source: EIA Energy Consumption by Energy Source, July 2009
2009 Data:Total: 94.5Coal: 19.7NG: 23.3Petro: 35.3Nuc.: 8.35Bio: 3.88Geo: 0.36Hydro: 2.68Wind: 0.70Solar: 0.11
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Growth in US Wind Power Capacity
Source: AWEA Wind Power Outlook 2nd Qtr, 2010
The quickdevelopmenttime for windof 6 monthsto a year means thatchanges infederal tax incentivescan have an almostimmediateimpact onconstruction
AMERICAN WIND ENERGY ASSOCIATION - www.awea.org
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Basic Review--Phase Angles• Angles need to be measured with respect to a
reference - depends on where we define t=0 • When comparing signals, we define t=0 once
and measure every other signal with respect to that reference
• Choice of reference is arbitrary – the relativephase shift is what matters
• Relative phase shift between signals is independent of where we define t=0
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Example: Phase Angle Reference• Pick the bottom wave as the reference
1 sin4
v V t
2 sin 0v V t
1 sin 0v V t
2 sin4
v V t
1 2 4
1 2 4
• Or pick the top as the reference- it does not matter!
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Important Properties: RMS
• RMS = root of the mean of the square• RMS for a periodic waveform
• RMS for a sinusoid (derive this for homework)
21 ( )o
o
t T
RMSt
V v tT
let ( ) cos( )pv t V t
2p
RMSV
V
T period
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Important Properties: Instantaneous Power
• Instantaneous power into a load
p(t)= ( ) ( )v t i t( )v t
+
-
( )i t
( )= cos( )
( )= cos( )p V
p I
v t V t
i t I t
( )= ( ) ( )p t v t i t
( )= cos cos 22p p
V I V IV I
p t t
“Passive sign convention” –current and power INTO load
1cos cos cos cos2
Identity
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Important Properties: Average Power
• Average power is found from
• Find the average power into the load (derive this for homework)
( )= cos cos 22p p
V I V IV I
p t t
1 ( )o
o
t T
tP p t dt
T
T period
P= cos2p p
V IV I
P= cosRMS RMS V IV I or
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Important Properties: Real Power
• P is called the Real Power
• cos(θV-θI) is called the Power Factor (pf)
• We’ll review phasors and then come back to these defintions…
P= cosRMS RMS V IV I
P= Re{VI*}
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Why Do We Use Phasors?• Simplifies calculations
- Turns derivatives and integrals into algebraic equations
- Makes it easier to solve AC circuits
d A j Adt
R( )R i (t)= Rv t
R
L( )L (t)= Ldi tv L
dt
C( )C (t)= Cdv ti C
dt
=V RI
=Lj IV V j LI
I=Cj V 1VI j C
LjX j L
1cjX j
C
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Complex PowerVV= RMSV
II= RMSI
Asterisk denotes complex conjugate
*
*
VI
VI cos sinRMS RMS V I
RMS RMS V I RMS RMS V I
V I
V I jV I
SApparentpower
PReal Power
QReactive Power
S = P+jQ
SQ
P
(θV-θI)
Power triangle
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Apparent, Real, Reactive Power
• P = real power (W, kW, MW)• Q = reactive power (VAr, kVAr, MVAr)• S = apparent power (VA, kVA, MVA)• Power factor angle• Power factor
*
*
*
VI
VI
VI cos sinRMS RMS V I
RMS RMS V I RMS RMS V I
S P jQ
V I
V I jV I
V I cos( )pf
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Distribution System Capacitors for Power Factor Correction
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Reactive Power Compensation
• Reactive compensation is used extensively by utilities• Capacitors are used to correct the power factor• This allows reactive power to be supplied locally• Supplying reactive power locally leads to decreased
line current, which results in– Decrease line losses– Ability to use smaller wires– Less voltage drop across the line
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Balanced 3 Phase () Systems• A balanced 3 phase () system has
• three voltage sources with equal magnitude, but with an angle shift of 120
• equal loads on each phase• equal impedance on the lines connecting the
generators to the loads • Bulk power systems are almost exclusively 3• Single phase is used primarily only in low voltage,
low power settings, such as residential and some commercial
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Advantages of 3 Power
• Can transmit more power for same amount of wire (twice as much as single phase)
• Torque produced by 3 machines is constrained
• Three phase machines use less material for same power rating
• Three phase machines start more easily than single phase machines
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Three Phase Transmission Lines
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Three Phase - Wye Connection• There are two ways to connect 3 systems
• Wye (Y)• Delta ()
an
bn
cn
Wye Connection VoltagesVVV
VVV
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Wye Connection Line Voltages
Van
Vcn
Vbn
VabVca
Vbc
-Vbn
(1 1 120
3 30
3 90
3 150
ab an bn
bc
ca
V V V V
V
V V
V V
Line to linevoltages arealso balanced
(α = 0 in this case)
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Delta Connection
IcaIc
IabIbc
Ia
Ib
a
b
*3
For the Delta phase voltages equalline voltages
For currentsI
3II
3
ab ca
ab
bc ab
c ca bc
Phase Phase
I I
II II I
S V I
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Delta-Wye Transformation
Y
phase
To simplify analysis of balanced 3 systems:1) Δ-connected loads can be replaced by
1Y-connected loads with Z3
2) Δ-connected sources can be replaced byY-connected sources with V
3 30Line
Z
V
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Per Phase Analysis
• Per phase analysis allows analysis of balanced 3 systems with the same effort as for a single phase system
• Balanced 3 Theorem: For a balanced 3system with• All loads and sources Y connected• No mutual Inductance between phases
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
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, we’ll development models for the transformer and will later discuss various ways of connecting three-phase transformers.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Distribution Transformer
115 – 35 kV distribution transformer
Radiators W/FansLTC
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Transmission Level Transformer230 kV surge arrestors
115 kV surge arrestors
Oil Cooler
Radiators W/FansOil pump
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Large Power Transformer
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Residential Distribution Transformers
Single phase transformers are commonly used in residential distribution systems. Most distributionsystems are 4 wire, with a multi-grounded, commonneutral.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Power System Harmonics• So far we 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
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Quick Review of Fourier Analysis0
1 2 3
1 2 3
n0
n0
f(t) cos cos2 cos32
sin sin 2 sin32where 2 ,
2a ( )cos , 0,1,2,
2 ( )sin , 1,2,
T
T
a a t a t a t
b t b t b t
f T
f t n t dt nT
b f t n t dt nT
.
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Switched-Mode Power Supply Current
Source: www.utterpower.com/commercial_grid.htm
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Current Waveform with Harmonics
• Example- A diode bridge rectifier current waveform
• Top picture - DC & Fundamental only
• Middle picture- Up to 7th harmonic
• Bottom picture- Up to 15th harmonic
-15
-10
-5
0
5
10
15
50.1 50.12 50.14 50.16 50.18 50.2 50.22 50.24
-15
-10
-5
0
5
10
15
50.1 50.12 50.14 50.16 50.18 50.2 50.22 50.24
-15
-10
-5
0
5
10
15
50.1 50.12 50.14 50.16 50.18 50.2 50.22 50.24
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Harmonic Current SpecturmThe 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
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Total Harmonic Distortion (THD)
22
1 2 3
2 2 2 2
( ) 2 cos cos2 cos3
But the square term is simplied by recognizing( ) ( 2 2 2and noting that the average value of the product of two sinusoids of d
rms avg avgI i I t I t I t
a b c a b c ab ac bc
22 22 2 231 21 2 3
2 2 22 3 4
1
iffering frequency is zero. This leaves
22 2 2
A common metric for distortion is total harmonic distortion (THD)
THD
rmsII II I I I
I I II
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017
Energy Systems Research Laboratory, FIU
Efficiency and Home Energy Use• Whole-house energy efficiency approach –
find out which parts consume the most energy
http://www1.eere.energy.gov/consumer/tips/home_energy.html
Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017