A Hybrid Quantum–Classical Variational Linear Solver for Power Flow Analysis in Smart Grids with V2G Integration

This paper presents a simulation-based proof of concept for integrating an existing Variational Quantum Linear Solver (VQLS) with a Newton-type AC power flow procedure for smart grids with vehicle-to-grid (V2G) participation. The novelty of the work lies not in proposing a new VQLS algorithm but in its engineering integration with a reduced Jacobian-based power flow subproblem and V2G operating scenarios. The proposed framework linearizes the nonlinear AC power flow equations and applies a four-qubit Real-Amplitudes VQLS circuit with the COBYLA optimizer to approximate a selected 16×16 reduced Jacobian system. The complete voltage profile is then reconstructed through the hybrid quantum–classical procedure. The method is evaluated using a modified IEEE 33-bus radial distribution system with an aggregated V2G unit connected at Bus 18. The main optimization run shows a rapid reduction and subsequent stabilization of the VQLS cost, while the resulting bus-voltage profile follows the overall trend of the Newton–Raphson reference solution. A separate 50-iteration assessment also reduces the cost substantially but does not reach the reference tolerance of 10−4. The V2G scenario analysis shows that prescribed V2G active-power support can reduce active power losses under both normal and stressed operating conditions, with loss reductions of 26.26%, 27.85%, and 30.52% in the base peak-load, N-1 contingency support, and dynamic railway-peak support cases, respectively. A resource-scaling assessment using a normalized classical computation index and a VQLS circuit-depth index is included only to illustrate resource-growth trends, not to establish computational superiority. The results support the feasibility of the proposed integration under ideal statevector simulation, but no quantum speedup or advantage over established classical solvers is claimed.