This chapter deals with the computation of an optimal voltage profile using different optimisation strategies. For this purpose, the mathematical model of the optimisation problem is defined and described considering two issues: defining the constraints of the optimisation problem in order to fulfil the actual operating condition of the SVC system and testing different objective functions. A primal dual interior point method is proposed to solve the OPF problem and the structure of the matrices used by the method is described in detail. In particular, in the OPF models, a quadratic formulation of the PF equations is adopted. In this way, no trigonometrical equations are adopted. The main advantage of this formulation is the robustness of the algorithm.

Chapter Contents:

• 10.1 Introduction
• 10.2 The power flow problem in rectangular coordinated
• 10.2.1 The power flow with SVC constraints
• 10.3 The OPF with SVC constraints
• 10.3.1 The maximum loadability with SVC constraints
• 10.3.2 Minimisation of the squared deviation of the bus voltage magnitude from a reference value
• 10.3.3 Constrained maximisation of the loadability with SVC
• 10.4 Solution of the optimisation problem
• 10.4.1 Primal-dual interior point method
• 10.4.2 Reduction of the linear system
• 10.5 Numerical results
• 10.5.1 The New England 39 buses network case
• 10.5.2 The Italian case
• 10.6 Conclusions
• Bibliography

Inspec keywords: mathematical analysis; quadratic programming; power system security; voltage control; matrix algebra

Other keywords: voltage security; mathematical model; SVC system; trigonometrical equation; OPF problem; optimisation strategy; optimal voltage profile computation; primal dual interior point method; matrix algebra; power system; secondary voltage control

Subjects: Algebra; Optimisation techniques; Mathematical analysis; Power system control