Maximum Power Transfer Theorem Project Objective: Write a computer program (using Matlab) that demonstrates the Maximum Power Transfer Theorem. Use your computer model to demonstrate that the theoretical maximum amount of electrical power that can be transferred from any power source is 50 % and occurs when the load resistance (RL) is equal to the Thevenin resistance (RT) of the power source. Alternatively you may demonstrate that the theoretical maximum amount of electrical power that can be transferred from any power source is 50 % and occurs when the ratio of load resistance (RL) to the Thevenin resistance (RT) equals 1 (RL/ RT ＝ 1). Research: Develop a derivation of the Maximum Power Transfer Theorem. You may use a combination of Internet resources, your physics, or engineering dynamics textbooks to assist in the derivation. Be sure to properly cite these resources in your final report (see below). Assignment: Your modeling assignment is two-fold: 1.Write a program that will model the Maximum Power Transfer Theorem. The programming language can be Matlab. The program must meet the following minimum requirements: a.The program must be structured with clear input, output, and computational processing sections. b.Documentation for the program must be embedded in the program. c.Produce a plot that illustrates the maximum Power Transfer Theorem (see Figure 1). The plot must be properly titled, axis labeled and identified. (NOTE: if your programming language does not provide the graphing capabilities needed to produce the plot illustrated in Figure 1, then the program must produce a table of values equivalent to the plot). d.The x-axis variable must use a minimum of 100 steps. e.The program must identify the maximum of the curve. f.The program must identify the point at which the maximum occurs. 2.You must write a brief report that includes the following sections: a.Table of Contents, List of Figures, List of Tables (if present). b.Introduction – Introduces the purpose of the program and describes its operation in general terms c.Background – Provide the mathematical derivation of the Maximum Power Transfer Theorem. Describe how the theoretical background for the derivation including any assumptions and all mathematical steps from the beginning assumptions to the final form of the equation. Properly cite all sources (using APA format) used to complete the derivation. d.Program – Lists the lines of code. e.Output – Contains the output of a run which will include: i.The plot generated. ii.The identified maximum f.Conclusion – Indicate if the program identified the maximum electrical power that can be transferred as predicted by the Maximum Power Transfer Theorem. Figure 1 – Plot of Maximum Power Transfer Theorem (RL/ RS versus Pload) RL ＝ Load resistance (in ohms) RT ＝ Thevenin resistance of the power source (in ohms) v1 ＝ Velocity of the upstream wind v2 ＝ Velocity of the downstream wind
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