In this work, we compared the performance of the ordinary Newton-Raphson method for calculating power flows against three quasi-Newton methods: chord, “good” and “bad” Broyden's methods. First, we illustrated compared the performance of each method on systems of equations of different sizes. Secondly, we compared these methods on power flow calculation for grids of different sizes. We found that an ill-suited initial approximation strongly affects the quasi-Newton methods and makes them slower than the Newton-Raphson one. Finally, in order to fix this issue, we introduced a mixed-method: a few iterations of Newton-Raphson are used to determine a more accurate initial approximation, which can then be used in quasi-Newton methods. Numerical tests showed that this approach outperforms ordinal Newton-Raphson and quasi-Newton methods.