energy flow in electrical grids - math.arizona.edugabitov/teaching/131/...references the papers used...
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Authors: Safatul Islam Deanna Johnson, Homa Shayan, Jonathan UtegaardMentors: Aalok Shah, Ildar Gabitov
ENERGY FLOW IN ELECTRICAL GRIDS
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OVERVIEW
Image Source: http://www.altenergymag.com/articles/09.04.01/smartgrid/grid.jpg
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MOTIVATION
Along a feed line voltage fluctuates
Desire: Reduce voltage drop at end of line
Determine maximum length supporting consumption
Goal: Create low-parametric ODE Model of a feeder
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APPLICATIONS
Superbowl Power Outage
PV systemsSmart Grids
Transporting Energyhttp://deepresource.files.wordpress.com/2012/04/smart-grid-concept.png
http://assets.inhabitat.com/wp-content/uploads/sunpower_main.jpghttp://energy.gov/sites/prod/files/styles/topic_hero/public/Wind.jpg?itok=uYcFe4cS
http://www.mediaite.com/wp-content/uploads/2013/02/cbs-power.jpg
Image Sources:
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BACKGROUND
Alternating Current
Voltage
Current
Power
Reactive Power
Real Power
v = Voltagei = Currentp = Power
Image Source: http://prismglow.com/electronics/eees/ch02/ch2_2/inst-e,i,p-inaccircuit.gif
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BACKGROUND
Other Basic Equations S = Apparent Powerz = impedancex = inductancer = resistance
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SET-UP
Feed Line
Load
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DEVELOPING THE MODEL
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PROBLEM FORMULATION
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MATLAB/RESULTS
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INITIAL AND BOUNDARY VALUE PROBLEMS
IVP
End Voltage vs. LengthPower Utilization vs.
Length
BVP
Voltage vs. PositionPower vs. Position
Graphs generated from each problem:
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MATLAB CODE
IVP
ode45 used to solve the system of rescaled ODEs
BVP
bvp4c was used to solve the original system of ODEs
Requires a guess of the solution
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End Voltage vs. Lengthp = -1, q = -0.5
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End Voltage vs. Lengthp = -1, q = 0
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p = -1, q = -0.5 p = -1, q = 0
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Two End Voltages for One Length
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POWER UTILIZATION VS. LENGTH
Power utilization = Initial Injected Power = P(0) Power Consumed p*L
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Power Utilization vs. Lengthp = -1, q = -.5
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Voltage Along the Line
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Voltage Along the Line
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Power Along the Line
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OUR GRAPHS VS. ARTICLE
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FUTURE WORK
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FUTURE WORK
Major Assumption:
Uniform consumption of loads p
In reality
Slight variations across a line
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OUR PLAN
Monte Carlo Method
Let p(l) = p0 + w(l)
Substitute for p in DistFlow ODEs
Solve for boundary value problem
Repeat
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Expectations
Verify the previous researcher’s approach to statistical similarity as valid
Averaged results will align with previous findings
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REFERENCES
The papers used for this presentation were:
M. Baran and F. Wu, “Optimal sizing of capacitors placed on a radial distribution system,” Power Delivery, IEEE Transactions on, vol. 4, no. 1, pp. 735 –743, jan 1989.
D Wang, K Turitsyn and M Chertkov, “DistFlow ODE: Modeling, Analyzing and Controlling Long Distribution Feeder”, Proceedings of, the 51st IEEE Conference on Decision and Control (2012) [http://arxiv.org/abs/1209.5776]
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QUESTIONS?
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