Applied Mathematics is a way to use math to solve problems in the real world, like in economics, engineering, and medicine. 

My objective was to determine an optimal location for a gas-powered electrical power plant to help meet the energy shortfall in southern CA by building a mathematical model using linear programming.

Where is the best place to build a gas-powered plant in Southern California? You create a mathematical model using linear programming to find out.

You place a coordinate grid over a map and test each location. Each spot gets scored based on distance to cities, power loss during transmission, and environmental and property costs. An objective equation combines these factors to rank the locations.

The model shows the best spot is about 50 miles east of Lancaster. During high summer demand, two locations closer to Los Angeles also become feasible.

Project Title
Energy Enigma

Abstract

Objectives/Goals

My objective was to determine an optimal location for a gas-powered electrical
power plant to help meet the energy shortfall in southern CA by building a mathematical model using linear programming. I hypothesized that the optimal location would be centrally located to the major cities of southern CA, those with the greatest power consumption, because the distribution from this location would have minimal line
loss.

Methods/Materials

To determine the best location to construct a power plant, I developed a set of
functions in an Excel spreadsheet. I placed a coordinate plane over a map of southern CA and established nodes within the state boundaries. I determined whether a given  node was within the natural gas pipeline corridor by calculating linear inequalities to represent the boundaries of the corridor. To find the distance from a given node to the major cities, I used the distance formula and weighted the distances by the city populations. I used the weighted distances to calculate the power loss from a potential plant to
consumers. I used the power loss to calculate a hypothetical sales price, decreasing this sales price with
increasing power loss. I expressed environmental and property costs by assigning higher costs to nodes within 50
miles of a major city. I devised an optimizing objective equation that combined the sales price and
production costs (constraints)
and then used this equation to find the locations (feasible solutions) that
balanced a low production cost
with a high sales price.

Results

The mathematical model shows that the best location to construct a power plant
is about 50 miles east of
Lancaster. Second and third best locations are east of Riverside and
Bakersfield, respectively. I changed
the constraints to approximate hot summer conditions and found that in addition
to the regions above, two
locations closer to LA were also feasible solutions during periods of high
demand.

Conclusions/Discussion

The optimal location for a power plant is not centrally located to the major
cities included in my
experiment, as I hypothesized. The model showed that the best locations are
outside the Clean Air Zones
and areas of high property costs and within the gas corridor, but still close to
the population centers. The
environmental, property, and production costs associated with running a power
plant in the LA basin
shifted the optimal locations further from the major cities than I had
anticipated.

Summary Statement

My project is a mathematical model using linear programming and multiple
constraints to determine an
optimal location for a gas-powered electrical power plant to help meet the
energy shortfall in southern
California.


Optimal Power Plant Location in Southern California

How to determine the best location for an electrical power plant

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Math is all about numbers, patterns, and solving problems. Computer science is about using math and technology to create computer programs and solve real-world problems. Together, they help us understand how things work, how to solve problems, and how to use technology to make our lives better!

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Optimal Power Plant Location in Southern California

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