Laboratory "Optimization of Dynamic Systems"

Learning Objectives:

1) Test a number of the computer modeling techniques that we have learned in the ME529 laboratory with the construction of an model of a nonlinear dynamic (thermal) system

2) Introduce penalty functions as a means for imposing constraint on system optimization algorithms

3) Use optimization to define ideal conditions of operation for a dynamic system

Task - Thermal Photovoltaic Panel Model:

Dynamic Model:

A photovoltaic (PV) panel generates electricity from the sun, but there are a number of consideration that determine how much value it will generate.  Its orientation, its temperature, and the time varying price of electricity; all determine what the value of the panel will be.  For this homework, we will compare a couple of options for configuring and orienting a PV system to maximize the economic value of the array.  

Problem 1) Simulate the thermal behavior of this single solar photovoltaic panel over the first day (24*60*60 seconds) of the year.  Model the solar panel as a thermal capacitance (using thespec sheet value for mpanel and a referenced value forcp from glass) and a thermal resistance (due to convection to the ambient air). With your system dynamics model you should be able to calculate the temperature of the panel as a function of time. 

The global goal is to maximize the amount of money that your solar panel can earn.  You will have to construct a cost function to sum the amount of money that your solar panel will produce. 

My house allows the panels to be mounted to the roof and oriented at A=180 degrees (pointing direct South) and ? = 23deg (equal to my roof pitch).  Use those values for this initial simulation. 

Please calculate the value that your panel can accrue over the 24 hours of Jan 1, 2015.  Plot a variety of dynamic inputs and states to cursorily validate your simulation. 

Problem 2) Compare the difference in value accrued over the entire year (365days/yr*24hrs/day*3600 sec/hr) between these two scenarios of PV system mounting.

1. Mounting the panel directly to the roof, where only 1 side of the panel is cooled by the convection to the ambient air.

2. Mounting the panel on a rack to the roof, where both sides of the panel is cooled by convection to the ambient air.  This can be modeled by considering the area of convection to be 2x the area considered above. 

How much money could the racking system cost (per panel) to realize value for the PV system?

Problem 3) Assuming that I could mount the PV panel at any orientation (A, α) what is the optimal orientation that realizes maximum value from our PV system?   Getting the data in and out of Simulink can be a bit tricky, here is my augmented cost function:

Problem 4) You can see that the panel can reach over the 85C maximum temperature if it is not rack mounted.  Make the convection only happen on the top side of the panel, and add a constraint so that the panel never reaches over 85C. What is the optimal orientation (A, α) that results in the temperature of the panel never going over 85C? Plot temperature to verify that the constraint is met.

Attachment:- Lab Assignment.rar