Description
Overview of how this mini project fits into the goal of PV system design
The goal of the series of mini-projects is to build a model to allow us to calculate and optimize a PV system. In the first project, you developed a program to calculate the solar insolation on a tilted surface. In Project 2, you developed a program to calculate the efficiency of a solar cell. In Project 3, you calculated the energy output of a PV module.
In Project 4, we will calculate the performance of a simple stand-alone PV system.
In the final project, we will design a PV system to meet certain criteria, such as a minimum availability, zero net energy use, etc.
Mini Project 4
| Figure 1: PV modules for the system. |
The goal of Mini Project 4 is to calculate the performance of a stand-alone PV system. The system we will analyze is one in Monument Valley, Arizona. It is primarily a DC system for lighting an off-grid house, although there is a small inverter included for small appliances such as a screen or laptop. The goal of the project is to calculate the system performance, including expected availability and fraction of power used compared to power generated from the PV modules.
System Description:
The system consists of two PV modules on a fixed pole-mounted mounting as shown in Figure 1. The modules are described in the table below. They are at a tilt angle of 30° from the horizontal, facing due south. They are not matched modules, as they were donated, but the currents are reasonably close.
The system diagram is shown in Figure 2. It is located in Monument Valley Arizona. The closest TMY station is Page Arizona. It consists of the PV modules; a Li-ion battery (SimpliPhi 48V, 72Ah); 4 LED lights at 48V; a charge controller (MorningStar MPPT60); and a small inverter. The label JB in Figure 2 refers to junction boxes, and a disconnect box. The Li-ion battery is 75 Ah. The system voltage is nominally 48V. The lights indicated by the symbol of a light bulb are 4 W each. The lights labeled Soitec lights are an LED “shop” light using 24 W. The inverter has an efficiency of 95%. For this project, we will assume that the inverter’s efficiency is constant and not dependent on the load size.
Individual module area is 19400 cm2 so they are 14.5% efficiency. Figure 2: Details of the two types of PV modules. The PV system consists of two modules, one of Module A and one of Module B. |
In order to analyze the system, we need to know the usage patterns of the load. We need the find the load for every hour of the year. We can assume that the lights go on 2 hours before sunset and turn off at 10 pm. Since you have the TMY data and this includes information for every hour of the year, and you have the equations for sunset/sunrise, you can calculate when the lights are on and off. However, for simplicity you can enter 6 hours in the winter and 3 hours in the summer; I think it’s easier to have the computer figure it out, but your choice. The inverter load consists of a screen and laptop for about 3 hours/day and a chest freezer, which is controlled via a thermostat. You can assume that the freezer is operating 25% of the time during a 24-hour period (on for one hour, off for three hours). The power consumption of the screen is 20W, of the laptop is 30W and of the chest freezer is 95W.
| Figure 3:PV system schematic. |
*** Note: For PV systems, we will often do calculations in Ah (Amp-hour). Ah is defined as Wh/V, where V is the nominal system voltage. If you assume that the MPPT controller performs a power conversion with a conversion efficiency, you can use the P_module * MPPT_efficiency = (Jmp * Vmp) * MPPT_efficiency = Jsc * Voc * FF * MPPT_efficiency to determine the Wh from the module. Since the TMY data has data for every hour of the year, once you find the P_module, the current generated in this time interval given by P_module * MPPT_efficiency / V is the value in Ah.
Project Description:
The general approach to PV system calculations is to calculate the generation from the modules (and where it goes), the load, the battery state of charge, and battery input/output for each hour of the year. So, take the TMY program from Project 1 and PV module information from Project 3. For this project, we will use the module information from the installed modules rather than what you calculated in Project 2. Don’t remove the code – you will probably use it in the Final Project.
The project is divided into two parts:
Part 1: Calculate the system parameters
Part 2: Analyze the system.
Part 1: Calculation of PV System Hourly Parameters
- Calculate and plot (1) the energy (Wh) and (2) Ah from the PV modules for every hour of the year including the effect of tilt angle. In the caption or graph also identify the location, the tilt of the modules, and the nominal or nameplate rating of the modules (which is 2 modules at 285W each or 0.57 kW) and the total kWh generated in the year. You can assume that the MPPT controller performs a power conversion with an efficiency of 95%.
Output: Plot the energy density output from the module and in the graph title give the total energy density generated over the course of a year in kWh. In a separate plot, graph the Ah from the PV modules over the course of a year.
- Calculate and plot the load for every hour of the year, in the caption also giving the total kWh and Ah of the load in one year.
The load is calculated by finding the power of the load in each one hour period, and multiplying by the time it is “on” in that hour. E.g., a 20 W load running the full hour is 20Wh in that time period. A 1500 W toaster (not that the system has a toaster, but as an example), might be on 6 min in a one-hour period (e.g. it is on for 0.1 hour), so the load in that hour is (1500 W) (0.1h) = 150Wh.
Output: Plot the load energy and in the graph title give the total energy consumed by the load over the course of a year in kWh.
- Calculate the following parameters for every hour: PV Ah going to load; PV Ah “dumped”; -Battery state of charge; Load Ah from battery; Load Ah unavailable. There is a possible flow chart (there are lots of ways you can program it) in the programming notes section.
Plot the battery state of charge and one other of the above plots for every hour of the year.
Assume that the battery is fully charged at the beginning of the year.
Output: Plot the battery state of charge for every hour of the year.
Part 2: Analysis of PV System
- Calculate and print out the availability of the system, where availability is defined as the ratio of the total powered load to the total requested load.
- Calculate and print out (1) the average battery state of charge of the system; (2) the lowest battery state of charge and the time of year when this occurs.
- Calculate and print out the ratio between the energy provided to the load and that generated by the PV system.
Output: Print the availability, average BSOC, date and value of lowest BSOC, fraction of used and unused solar power.
Programming Notes
The program for the most part continues to combine Project 1 and Project 3. It adds back in the angle-dependence calculations from Project 1 into the calculation of the Wh in each hour used to find the Amp-hour from the module in Project 3.
Generating the load profile can be a bit inconvenient using Python or Matlab. Generating one load like this works fine, but inputting a user-friendly way to generate the load profile is more of a challenge. For this project, and also the next one, we don’t need generalized loads, so a “hard-wired” approach where the load is not changeable as a user input is fine.
Another approach is that this is one of the cases where the table format of Excel can be easier. To keep the graphical convenience of Excel, one approach is to save the Excel load file and read it into your program.
The final component of the program is two-fold: (1) to determine what happens to the Amp-hour generated from the PV (does it go to the load, the battery or get dumped); and (2) determine how many Ah we can get from the battery to power the load (calculate the battery state of charge every hour of the year and calculate the amount of power from the battery to the load).
A possible flowchart for calculating this is shown below; there are of course many other possible routines to find the above parameters.
