---
title: "Current-Voltage(I-V) Features of Photovoltaic Modules"
author: "Jiqi Liu, Alan Curran, Justin S. Fada, Xuan Ma, Wei-Heng Huang, Jennifer L. Braid, Roger H. French"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{IV features}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
Data Description
-----------------------------------

The dataset consists of current-voltage($I-V$) features obtained by $I-V$ feature extraction from $I-V$ curves of photovoltaic (PV) modules. 
The features have been extracted using the ddiv package algorithm for brand A PV modules under damp heat indoor accelerated exposures for up to 3000 hours. 
The I-V curves were measured in a step-wise manner after every 500h of exposure time, and provided by the SunEdison company. 
The I-V features include max power ($P_{mp}$), short circuit current ($I_{sc}$), current at max power ($I_{mp}$), fill factor ($FF$), series resistance ($R_s$), shunt resistance ($R_{sh}$), open circuit voltage($V_{oc}$), voltage at max power ($V_{mp}$). $R_{sh}$ is too noisy to contain for modeling. 
After checking the correlation between $I_{sc}$, $I_{mp}$, $V_{oc}$, $V_{mp}$, $FF$, $R_s$, we find that $FF$, $R_s$, $V_{mp}$ are highly correlated, and therefore only choose one of these three variables to be included in the model. Here we choose $I_{sc}$, $I_{mp}$, $R_s$ and $V_{oc}$ to be contained in the model and these four I-V features show no indication of high correlation. 
The trend of the I-V features are related with the mechanisms of PV degradation. 
The variable '$dy$' is time that has been converted into decimal years so that $dy$=1 corresponds to 1 year of exposure time. 
We use this dataset to build an <S|M|R> network model with time ($dy$) as the exogenous stressor variable, four I-V features ($I_{sc}$, $I_{mp}$, $R_s$ and $V_{oc}$) as mechanistic endogenous variables and maximum power ($P_{mp}$) as the endogenous response variable.

Load data and run code to build netSEM 
------------------------------------------
```{r, message=FALSE, eval=FALSE}

## Load the acrylic data set
data("IVfeature")

## Run netSEMp1 model
ans1 <- netSEMp1(IVfeature, exogenous = "dy", endogenous = "Pmp")
## Plot the network model for principle 1
plot(ans1, cutoff = c(0.25, 0.5, 0.8))

## Run netSEMp2 model
ans2 <- netSEMp2(IVfeature, exogenous = "dy", endogenous = "Pmp")
## Plot the network model for principle 2
plot(ans2, cutoff = c(0.25, 0.5, 0.8))
```


Network diagram for data
--------------------------

The direct <S|R> path from dy to $P_{mp}$ has an $adj. R^2$ of 0.757. 
Considering the path with one mechanism, the paths contain $I_{mp}$ or $R_s$ are likely to be as good as the direct path. 
The path from $dy$ to $R_s$ has an $adj. R^2$ of 0.761 and the path from $R_s$ to $P_{mp}$ has an $adj. R^2$of 0.912. 
The path from dy to $I_{mp}$ has an $adj. R^2$ of 0.683 and the path from $I_{mp}$ to $P_{mp}$ has an $adj. R^2$ of 0.829. 
And we further use the pathwayRMSE function to calculate the root mean squared error(RMSE) of the direct path and the two paths with $I_{mp}$ or $R_s$. 
The RMSE for the direct path is 2.8998, for the path contain $I_{mp}$ is 3.3007, for the path contain $R_s$ is 2.9053. 
So overall, the predicted accuracy of the direct path and the path contain $R_s$ are very similar and the latter one with $R_s$ informs us about the active the degradation mechanism.


```{r, out.width="675px", echo=FALSE, fig.cap="IVfeature netSEMp1 model"}
knitr::include_graphics("IVfeature1.png")
```

```{r, out.width="800px", echo=FALSE, fig.cap="IVfeature netSEMp2 model"}
knitr::include_graphics("IVfeature2.png")
```

Reference
--------------------------
1. ddiv: Data Driven I-v Feature Extraction, R package,  https://CRAN.R-project.org/package=ddiv.  

2. J. Liu, Alan Curren, Justin S. Fada, Xuan Ma, Wei-Heng Huang, C.Birk Jones,
E. Schnabel, M. Kohl, Jennifer L. Braid, and Roger H.French, “Cross-correlation 
Analysis of the Indoor Accelerated and Real World Exposed Photovoltaic Systems 
Across Multiple Climate Zones,” in IEEE WCPEC-7 Conference, HI, 2018. DOI:  https://doi.org/10.1109/PVSC.2018.8547840



Acknowledgment
--------------------------
This material is based upon work supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under Solar Energy Technologies Office (SETO) Agreement Number DE-EE0007140.