Distribution Locational Marginal Pricing by Convexified ACOPF and Hierarchical Dispatch

Abstract

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.

Second-order cone AC optimal power flow: convex relaxations and feasible solutions

“…A computer with 2.4 GHz CPU and 8 GB RAM is deployed for the computations (except the computations in Section 4.2). It is worth to mention that voltage phase angle solutions can be obtained from solving the proposed SOC-ACOPF models directly since voltage phase angle is one of the decision variables in all the SOC-ACOPF models (see constraint (7) in Model P, constraints (17), (18) in Model R, constraints (40)-(45) in Model T and constraints (72), (73) in Model E). The convergence of MOSEK solver is guaranteed by the convexity of all the proposed SOC-ACOPF models.…”

“…For radial networks, sufficient conditions regarding network property and voltage upper bound under which the proposed relaxed ACOPF can give global ACOPF solution are derived in [14]. Recent applications of SOCP based convex ACOPF model in distributional locational marginal pricing (DLMP), transmission-distribution coordination and decentralized power system operation can be found in [17][18][19].…”

“…The complementarity conditions in the Karush-Kuhn-Tucker (KKT) system of DCOPF are used in [32] to recover feasible solution of ACOPF. A sequential algorithm to improve the tightness of some relaxed constraints of a SOCP-based ACOPF model is proposed in [17]. The performance of this algorithm for large power networks remains to be improved.…”

A Modified Benders Decomposition Algorithm to Solve Second-Order Cone AC Optimal Power Flow

“…The SOC-ACOPF model, as a convex relaxation of the nonconvex ACOPF model, is summarized here in (1) [26]. The convexity, accuracy and applicability of this model have been proved by our work in [26]. The objective function (1a) can be any convex function of the decision variables.…”

“…To compare our SOC-ACOPF model with the SOCP-based ACOPF model in [27], we implement both models in GAMS and solve the models for various IEEE test cases by MOSEK solver. Note we implement the active power loss constraint (1d) in GAMS coding of the SOC-ACOPF model which is different from the implementation in our work in [26]. Accordingly, there are some minor numerical differences compared with the results in [26].…”