Effect of the approximation of voltage angle difference on the OPF algorithms in the power network

In real-time applications involving power flow equations, measuring of voltage phase angle difference of the connected buses is essential. However, it needs special techniques to measure voltage angle difference, which may enlarge the computational burden of the working controller and hence, may make the control process slow. In this paper, authors investigate the approximation of angle difference to zero and its effects on the convergence speed and optimal solutions of a distributed algorithm. To test this approximation, a distributed nonlinear algorithm is proposed to optimize the multi-objective function which includes power loss, voltage deviation and cost of reactive power generation, by controlling the reactive power generations from distributed generators. Authors investigate the reasons which may outlaw making this approximation and finally, propose a condition to make such approximation. Importance of making this approximation in terms of fast convergence of the algorithms is also illustrated.