A Mixed-Integer Quadratically Constrained Programming Model for Hybrid DG and Capacitor Placement in Terms of Load Components and Consumption Types

The integration of simultaneous distributed generation (DG) and capacitor allocation strategies has shown considerable promise in reducing power losses, mitigating voltage deviations, and lowering operational expenses within power systems. Achieving these benefits hinges on the optimal placement of DG units and shunt capacitors, which in turn depends on accurate modeling of electricity demand. However, such modeling is inherently challenging due to the variable nature of electrical loads, which fluctuate with voltage levels and are influenced by consumer types. Electrical loads are typically represented by a combination of constant-power, constant-current, and constant-impedance components. Establishing a clear relationship between these components and consumer categories is essential for precise load modeling. Despite its critical role, this aspect has been largely overlooked in existing studies on DG and capacitor placement. This article presents a novel mathematical framework that links load components to consumer types, thereby enhancing the flexibility and effectiveness of DG and capacitor placement strategies. The proposed formulations aim to improve system performance and economic efficiency, offering a significant advancement in the optimization of power systems.