Volt/VAR Optimization in Transmission Networks with Discrete-Control Devices

Voltage (Volt) and reactive-power (VAR) control in transmission networks is critical for reliability and increasingly needs fast, implementable decisions. This paper presents a transmission Volt/VAR Optimization (VVO) framework that co-optimizes discrete control of on-load tap-changing transformers (OLTCs) and capacitor banks (CBs) with AC power flow (ACPF) physics to improve voltage stability and minimize VAR generation. The framework follows a relax-round-resolve pipeline: a continuous relaxation proposes targets, a rounding step selects feasible discrete settings, and a final solve enforces AC power flow physics. Extensive experiments on IEEE, PEGASE, and RTE systems show consistent improvements in voltage and VAR quality metrics with modest generator redispatch while preserving economic operation and achieving compatible runtimes with real-time transmission operations.