Fig. 9

Normalised mapping of optimal power flows according to equation (11) with the estimated flows of the low resolution model \({\hat{f}}_{(c,d),t}\) on the x-axis and the aggregated flows on the y-axis. The first row shows results on the \(60\%\), the second row on the \(100\%\) reduction target. Instead of presenting the raw data, we plot a two dimensional histogram and outline the \(95\%\) and \(85\%\) percentiles of the corresponding probability density function (PDF) using contour plots. The black line depicts the origin (perfect correlation), the dashed one a line with the slope of the bivariate correlation coefficient \(\rho\). \(\alpha\) is the angle between the two lines