# Quadratic exponential method (by Andersen) in Heston model

I am having trouble understanding the reasons that led Andersen to define his QE scheme to efficiently simulate Heston Stochastic volatility model (you may check the celebrated scheme here).

The gist of it is that for "sufficiently large" values of the process modelling the variance, the scheme adopts the form: $$V(t+dt) = a(b + Z)^2$$ where $a,b$ are certain constants and $Z$ is a standard Gaussian random variable. For low values of $V$ he thinks that it is better to use: $$V(t+dt) = \Psi^{-1}(U_V;p,\beta)$$ where $U_V$ is drawn from a uniform distribution, and $$\Psi^{-1}(u) = \Psi^{-1}(u;p,\beta) = \left\{ \begin{array}{rl} 0 &\mbox{ if 0\leq u \leq p} \\ \beta^{-1}\ln\left(\frac{1-p}{1-u} \right) &\mbox{ if p<u\leq1} \end{array} \right.$$

Andersen deduces this scheme by saying:

The first step is based on an observation that a non- central chi-square with moderate or high non-centrality parameter can be well-represented by a power-function applied to a Gaussian variable.

But then he gives little detail about why this observation is useful to develop his scheme, and why he thinks that when the variance his low the scheme needs to change its form. If somebody knows the mechanics behind his reasoning, I would be very glad if you could provide more insight into the subject.