A Partially Distributed Fixed-Time Economic Dispatch Algorithm With Kron's Modeled Power Transmission Losses
Shivanshu Tripathi, Anoop Jain, Abhisek K. Behera
Abstract
A partially distributed economic dispatch algorithm, which renders optimal value in fixed time with the objective of supplying the load requirement as well as the power transmission losses, is proposed in this article. The transmission losses are modeled using Kron's <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B\text{-}$</tex-math></inline-formula> loss formula, under a few (standard) assumptions on the values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B\text{-}$</tex-math></inline-formula> coefficients. The total power supplied by the generators is subject to time-varying equality constraints due to the time-varying nature of the transmission losses. Using Lyapunov stability and optimization theory, we prove the convergence of the proposed algorithm to the optimal value within a fixed time, which depends on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B\text{-}$</tex-math></inline-formula> loss coefficients, cost function parameters associated with each generator, and the interaction topology among them. Finally, two test cases, including an IEEE-57 bus system, are simulated to illustrate the performance of the proposed algorithm.