# Increasing Photovoltaic Systems Efficiency Through the Implementation of Statistical Methods
## 3 Methodology
### Application of STEM Method Focused on Economic Efficiency  
The managerial approach based on a STEM-type statistical analysis is currently applied to product competitiveness analysis. As mentioned, this method is used for the first time in photovoltaic power plants, which are considered market-promoted products. The process was applied to five existing PV plants with six known characteristics, three of which represent the subset of characteristics whose value is directly proportional to the quality of the product, and the other three represent the subset of characteristics whose value is inversely proportional to the quality of the product, as described in the next section. The technical level method can evaluate product quality based on the von Neumann-Morgenstern utility principle and the Cobb-Douglas production functions [9]. A form relation defines the absolute technical level H\({}_{\text{ai}}\)[10, 11]. \[H_{ai}=a\cdot\prod_{j\in S_{1}}\left(\frac{K_{ij}}{K_{1j}}\right)^{\gamma_{j} }\cdot\prod_{j\in S_{2}}\left(\frac{K_{ij}}{K_{1j}}\right)^{-\gamma_{j}} \tag{2}\]  
where  
* \(S_{1}\) represents the subset of characteristics whose value is directly proportional to the quality of the product;
* \(S_{2}\) represents the subset of characteristics whose value is inversely proportional to the quality of the product;
* \(i\) represents the product for which the technical level is calculated;
* \(1\) represents the reference product (any of the analysed products can be considered a reference);
* \(a\) is a constant that defines the technical level of the reference product (usually \(a=1000\), to differentiate the products sufficiently);
* \(j\) is the characteristic of the product;
* \(K_{ij}\) is the value of the characteristic \(j\) for product \(i\);* \(\gamma_{j}\) represents the weight of the characteristic \(j\). The relative technical level can also be calculated with the relation: \[H_{ri}=H_{ai}\cdot 100/max(H_{ai})\] (3)  
The product with the highest technical level has a value of 100, while the others have values below this. The primary challenge is determining the weights of the characteristics, \(\gamma_{j}\), to apply the above relations. Two methods are primarily known for this: the MISENIT and STEM methods [10; 11]. The MISENIT method is based on the elasticity of the operating expense function, which is the property of a function that changes when its argument changes. The STEM method is less finesse than the previous one. Still, it allows, on the other hand, a faster calculation of the weights, given that the analyst must be a specialist in exploiting the respective products. To accomplish this, the characteristics are compared two by two, defining a matrix with the elements \(a_{j1/2}\) established as follows:  
\[a_{j}= \begin{cases}4,&\quad K_{j1}\;\gg\;K_{j2}\\ 2,&\quad K_{j1}>K_{j2}\\ 1,&\quad K_{j1}\;\approx\;K_{j2}\\ 0,&\quad K_{j1}<K_{j2}\end{cases}  \tag{4}\]  
where \(K_{j}\) are the quality characteristics. The signs that intervene have the following meanings:  
(\(\gg\))--much more important;  
(\(>\))--more important;  
(\(\approx\))--equivalent;  
(\(<\))--less important. Under these conditions, the weights of the characteristics are calculated with Relation (5):  
\[\gamma_{j}=\frac{\sum_{j2}a_{j1/2}}{\sum_{j1}\sum_{j2}\left(a_{j1}\right)\cdot \left(a_{j2}\right)} \tag{5}\]  
The STEM method algorithm flowchart shows the computing steps for the relative technical level evaluation:  
According to Figure 1, the first step of the presented algorithm involves selecting parameters from sets S1 and S2, respectively. For PV power plants, the three parameters whose value is directly proportional to the electricity supplied are the panel's efficiency, expressed in percentages, the installed power of the panel, described in Wp, and the presence of a tracking-type orientation system.