Quantum-Enhanced DC Optimal Power Flow

Harrow-Hassidim-Lloyd (HHL) is a quantum computation algorithm that can solve a system of linear equations in a logarithmic time scale; hence, an exponential speed-up over best-known classical computers, which have polynomial time complexity, is accessible. This paper studies the integration of HHL into the DC optimal power flow problem. Optimality conditions are formulated as a system of equations in the form of $Ax=b$ that is solved by HHL. The performance of HHL for A-matrices appearing in DCOPF problems is discussed. The initialization of HHL for encoding data from classical data to a quantum state in an efficient manner is also investigated. The impact of HHL calculation error on DCOPF convergence and solution accuracy is analyzed. Qiskit module is used to test the HHL-based DCOPF problem on a 3-bus system. The impact of quantum computers and HHL errors on DCOPF is simulated for the IEEE 14- bus system.