Electric power engineering. Modal components in three- phase a.c. systems. Quantities and transformations

2015 ◽  
Keyword(s):  
Electric Power ◽  
Power Engineering ◽  
Electric Power Engineering ◽  
Three Phase

scholarly journals $G$-deviations of polygons and their applications in Electric Power Engineering

2021 ◽  
Vol 55 (2) ◽  
pp. 188-200
Author(s):  
T. Banakh ◽  
O. Hryniv ◽  
V. Hudym
Keyword(s):  
Electric Power ◽  
Complex Plane ◽  
Metric Space ◽  
Power Engineering ◽  
Affine Transformations ◽  
Electric Power Engineering ◽  
Standard Characteristic ◽  
Three Phase ◽  
Measures Of Asymmetry

For any metric space $X$ endowed with the action of a group $G$, and two $n$-gons $\vec x=(x_1,\dots,x_n)\in X^n$ and $\vec y=(y_1,\dots,y_n)\in X^n$ in $X$, we introduce the $G$-deviation $d(G\vec x,\vec y\,)$ of $\vec x$ from $\vec y$ as the distance in $X^n$ from $\vec y$ to the $G$-orbit $G\vec x$ of $\vec x$ in the $n$-th power $X^n$ of $X$. For some groups $G$ of affine transformations of the complex plane, we deduce simple-to-apply formulas for calculating the $G$-deviation between $n$-gons on the complex plane. We apply these formulas for defining new measures of asymmetry of triangles. These new measures can be applied in Electric Power Engineering for evaluating the quality of 3-phase electric power. One of such measures, namely the affine deviation, is espressible via the unbalance degree, which is a standard characteristic of quality of three-phase electric power.

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