Abstract:

This paper describes the experience of the author in the supervision of PhD students enrolled in electrical engineering programmes. The main goal of the paper is to present a set of high-level techniques that the authors has found to be effective in teaching graduate students how to carry out research and successfully publish paper in international peer-reviewed journals.
A PhD programme differs substantially from an undergraduate programme. In an undergraduate programme, for each module, students learn how to solve a set given problems. In a PhD, students learn to invent the problems themselves. This involves a creative process that is, in general, very hard to teach.

The final paper will provide the following contributions.
1. A discussion on the didactic challenges of teaching “how to do research”.
2. A variety of techniques that the author and his students have found to be effective “to have ideas” for carrying out research.

Specifically, the methodology described in the paper consists in utilizing one or a combination of the following techniques.
- Formal analogy between two different problems. For example, [1] shows the analogy between the Euler integration method for ordinary differential equations and the Newton-Raphson technique to find the zeros of a set of nonlinear equations.
- Take a well-known problem and try to solve a dual (opposite) problem. For example, time delays are generally assumed to worsen the dynamic response of a control system. In [2], the authors have shown that delays can be, under certain circumstance, be effectively used to improve the dynamic response of certain power system controllers.
- Exploring mathematical techniques that have never been applied to a specific engineering problem. For example, in [3], the authors show that the
Filippov theory of discontinuous right-hand side systems can be effectively applied to properly calculate, under certain conditions, the dynamics of the limiters of power electronic converter controllers.

The final paper will not only discuss successful stories but also the challenges that the PhD students supervised by the author face when taught the techniques above and the risks associated. It is not uncommon, in fact, that an idea does not lead to the expected results. This is a common aspect of research but it is even more so for the technique described above.

The main conclusion of the paper is that the proposed techniques can be learnt and, as any other skill, can be developed and improved with time by the students. These techniques are also general enough to be applicable to any STEM topic. Another relevant conclusion is that students that can master one or more of the techniques above learn a “way of thinking” rather than just a specific application. The final paper will duly elaborate on this point through real-life examples based on the 20-year long experience in PhD students’ supervision by the author.

[1] F. Milano, Implicit Continuous Newton Method for Power Flow Analysis, IEEE Transactions on Power Systems, vol. 34, no. 4, pp. 3309-3311, July 2019.
[2] G. Tzounas, R. Sipahi, F. Milano, Damping Power System Electromechanical Oscillations Using Time Delays, IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 68, no. 6, pp. 2725-2735, June 2021.
[3] M.A.A. Murad, F. Milano, Chattering-Free Modelling and Simulation of Power Systems with Inclusion of Filippov Theory, Electric Power System Research, Elsevier, vol. 189, 106727, December 2020.

Keywords:

Electrical energy systems, electrical engineering education, PhD programme, research, creativity.