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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 affinetransformations of the complex plane, we deduce simple-to-apply formulas forcalculating the $G$-derviation between $n$-gons on the complex plane. We applythese formulas for defining new measures of asymmetry of triangles. These newmeasures can be applied in Electric Power Engineering for evaluating thequality of 3-phase electric power. One of such measures, namely the affinedeviation, is espressible via the unbalance degree, which is a standardcharacteristic of quality of three-phase electric power.

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