Transmission dispatch for loss minimisation using linearised power flow equations in mixed integer programming

• We demonstrated the danger of using only the active power in transmission dispatch problems.
• We proposed a model that accounts for the active and reactive power useful in transmission line switching.
• We proposed a new multi period formulation of transmission dispatch based on load duration curve.
• The global set of switchable lines obtained from multi period transmission formulation minimises losses better.

Transmission dispatch is a nonlinear optimisation problem due to the nonlinearity of the power flow equations. In the open literature, linearisation of power flow that yields only the active power is used for transmission dispatch problems. The solutions obtained are unacceptable when verified in nonlinear power flow equations, especially for smart grid applications because of the instability issues that result from such formulations. This paper overcomes this limitation by proposing a model that accounts for both active and reactive power in transmission dispatch problem formulations. Furthermore, this paper develops new formulations for transmission dispatch that covers the overall spectrum of operation of a power system network based on the load duration curve rather than the single period considered in the open literature. Transmission dispatch is considered in the context of minimising active power losses in this paper. The advantage of the proposed approach is that it gives acceptable results when verified with nonlinear power flow compared to the classical approach used in transmission dispatch problems. Also, the paper demonstrates that the global set of switchable lines that can minimise the active power losses of a network is obtainable from the multi-period formulations based on the consideration of varying load levels. The results indicate that only this set of switchable lines can reduce losses and ensure the stability of a network, hence useful for smart grid applications.