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Abstract-This paper proposes a hierarchical economic dispatch (HED) mechanism for computing distribution locational marginal prices (DLMPs). The HED mechanism involves three levels: The top level is the national (regional) transmission network, the middle level is the distribution network, while the lowest level reflects local embedded networks or microgrids. Each network operator communicates its generalized bid functions (GBFs) to the next higher level of the hierarchy. The GBFs approximate the true cost function of a network by a series of affine functions. The concept of Benders cuts are employed in simulating the GBFs. The AC optimal power flow (ACOPF) is convexified and then used for dispatching generators and calculating GBFs and DLMPs. The proposed convexification is based on the second order cone reformulation. A sequential optimization algorithm is developed to tighten the proposed second order cone relaxation of ACOPF. The properties of the sequential tightness algorithm are discussed and proved. The HED is implemented in the GAMS grid computing platform. The GBFs and DLMPs are calculated for the modified IEEE 342 node low voltage test system. The numerical results show the utility of the proposed HED and GBF in implementing DLMP.

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Optimal power flow (OPF) is the fundamental mathematical model to optimize power system operations. Based on conic relaxation, Taylor series expansion and McCormick envelope, we propose three convex OPF models to improve the performance of the second-order cone alternating current OPF (SOC-ACOPF) model. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods. A heuristic algorithm to recover feasible ACOPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The proposed SOC-ACOPF models are examined through IEEE case studies under various load scenarios and power network congestions. The quality of solutions from the proposed SOC-ACOPF models is evaluated using MATPOWER (local optimality) and LINDO-GLOBAL (global optimality). We also compare numerically the proposed SOC-ACOPF models with other two convex ACOPF models in the literature. The numerical results show robust performance of the proposed SOC-ACOPF models and the feasible solution recovery algorithm.

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