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In real-time applications involving power flow equations, measuring ofvoltage phase angle difference of the connected buses is essential. However, itneeds special techniques to measure voltage angle difference, which may enlargethe computational burden of the working controller and hence, may make thecontrol process slow. In this paper, authors investigate the approximation ofangle difference to zero and its effects on the convergence speed and optimalsolutions of a distributed algorithm. To test this approximation, a distributednonlinear algorithm is proposed to optimize the multi-objective function whichincludes 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 andfinally, propose a condition to make such approximation. Importance of makingthis approximation in terms of fast convergence of the algorithms is alsoillustrated.

Effect of the Approximation of Voltage Angle Difference on the OPF algorithms in the Power Network