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      Figure 0.1 Stages of solving an optimization problem.

      This book will focus on stages two and three, associated with power system operations models. In particular, we are interested in models with a geometric characteristic called convexity, that present several advantages, namely:

In summary, convex problems have both theoretical and practical advantages for power systems operation. This book studies both aspects. The book is oriented to bachelor and graduated students of power systems engineering. Concepts related to power systems analysis such as per-unit representation, the nodal admittance matrix, and the power flow problem are taken for granted. A previous course of linear programming is desirable but not mandatory. We do not pretend to encompass all the theory behind convex optimization; instead, we try to present particular aspects of convex optimization which are useful in power systems operation. The book is divided into two parts: In the first part, the main concepts of convex optimization are presented, including a distinct chapter about conic optimization. After that, selected applications for power systems operation are presented. Most of the solvers for convex optimization allow mixed-integer convex problems. Therefore, we include models that can be solved in this framework too. The student is recommended to do numerical experiments in order to acquire practical intuition of the problems.

      All applications are presented in Python, which is a language that is becoming more important in power systems applications. Students are not expected to have previous knowledge in Python, although basic concepts about programming (in any language) are helpful. Our methodology is based on many examples and toy-models. We made a great effort in showing the most simple model with a clean code. Of course, these toy-models are an oversimplification of the real problem; however, they allow us to understand the model and its coding. In practice, we may have complex models that combine different aspects such as the economic dispatch, the unit commitment and/or the optimal power flow. A real operation model may require a sophisticated platform that integrates the model with the supervisory control and data acquisition system (SCADA) operating in real-time. The development of such a real industrial model is beyond the objectives of this book.