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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