I can see no reason for the equation to start at the left margin. Anyway, here's the code
\documentclass[a4paper]{article}
\usepackage[fleqn]{amsmath}
\usepackage{showframe}
\begin{document}
\section*{Test}
\begin{flalign}
U_{i} &= U_{\mathrm{h}i} + U_{\mathrm{r}i} ,
& I_{i} &= \frac{1}{Z_{\mathrm{L}i}}(U_{\mathrm{h}i} - U_{\mathrm{r}i}) && \\
U_{\mathrm{h}i} &= \frac{U_i + Z_{\mathrm{L}i}I_{i}}{2} ,
& U_{\mathrm{r}i} &= \frac{U_i - Z_{\mathrm{L}i}I_{i}}{2} &&
\end{flalign}
\end{document}

With the standard align:
\documentclass[a4paper]{article}
\usepackage[fleqn]{amsmath}
\usepackage{showframe}
\begin{document}
\section*{Test}
\begin{align}
U_{i} &= U_{\mathrm{h}i} + U_{\mathrm{r}i} ,
& I_{i} &= \frac{1}{Z_{\mathrm{L}i}}(U_{\mathrm{h}i} - U_{\mathrm{r}i}) \\
U_{\mathrm{h}i} &= \frac{U_i + Z_{\mathrm{L}i}I_{i}}{2} ,
& U_{\mathrm{r}i} &= \frac{U_i - Z_{\mathrm{L}i}I_{i}}{2}
\end{align}
\end{document}
You get

which agrees with all other equations, since you're using fleqn.
If your aim is to align to the left U and I, then use a phantom. I took the occasion for simplifying your input by defining \rh, \rr and \rL. The macro \prh stands for “a phantom \rh”.
\documentclass[a4paper]{article}
\usepackage[fleqn]{amsmath}
\usepackage{showframe}
\newcommand{\rh}{\mathrm{h}}
\newcommand{\prh}{\hphantom{\rh}}
\newcommand{\rL}{\mathrm{L}}
\newcommand{\rr}{\mathrm{r}}
\begin{document}
\section*{Test}
\begin{align}
U_{i\prh} &= U_{\rh i} + U_{\rr i} ,
& I_{i\prh} &= \frac{1}{Z_{\rL i}}(U_{\rh i} - U_{\rr i}) \\
U_{\rh i} &= \frac{U_i + Z_{\rL i}I_{i}}{2} ,
& U_{\rh i} &= \frac{U_i - Z_{\rL i}I_{i}}{2}
\end{align}
\end{document}
Adapt to the flalign shown above, if you prefer.

flalign? Any reason? – Werner Oct 05 '18 at 17:22flalignalignalignatI have all tried – sun0727 Oct 05 '18 at 17:28=asymmetrical? that looks very odd and quite unlike a normal left aligned equation setting in amsmath. – David Carlisle Oct 05 '18 at 18:01&split the equation and each part should be left aligned – sun0727 Oct 05 '18 at 18:08