Novel Linearized Power Flow and Linearized OPF Models for Active Distribution Networks With Application in Distribution LMP

The locational marginal price (LMP) methodology has been discussed for distribution networks/systems under the smart grid initiative. In this paper, a new distribution LMP (DLMP) formulation is presented which includes reactive power prices and voltage constraints. To solve DLMP, three modeling tools, namely, linearized power flow for distribution (LPF-D), loss factors for distribution (LF-D), and linear optimal power flow for distribution (LOPF-D) are proposed. LPF-D solves not only voltage angles but also magnitudes through linear expression between bus injections and bus voltages, specifically for distribution systems. LF-D is solved recursively based on the radial topology of typical distribution systems. With the integration of LPF-D and LF-D, conventional optimal power flow (OPF) can be reformulated as LOPF-D which is essentially a linear programming model. Test results on various systems show that: 1) LPF-D efficiently yields very close results if compared with AC power flow; 2) LOPF-D provides very close dispatch results in both real and reactive power if compared with ACOPF; and 3) the proposed DLMPs calculated with LF-D and LOPF-D give accurate price information if compared with the prices from ACOPF. Further, these three tools are not limited to DLMP but can be potentially applied to other distribution analyses.