Linear MW-only ldquodcrdquo network power flow models are in widespread and even increasing use, particularly in congestion-constrained market applications. Many versions of these approximate models are possible. When their MW flows are reasonably correct (and this is by no means assured), they can often offer compelling advantages. Given their considerable importance in today's electric power industry, dc models merit closer scrutiny. This paper attempts such a re-examination.

DC Power Flow Revisited

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow (OPF) problem, focusing on structural properties rather than algorithms. Part I presents two power flow models, formulates OPF and their relaxations in each model, and proves equivalence relationships among them. Part II presents sufficient conditions under which the convex relaxations are exact.

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Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence

This paper develops an equilibrium modeling framework that captures the interactions among availability of public charging opportunities, prices of electricity, and destination and route choices of plug-in hybrid electric vehicles (PHEVs) at regional transportation and power transmission networks coupled by PHEVs. The modeling framework is then applied to determine an optimal allocation of a given number of public charging stations among metropolitan areas in the region to maximize social welfare associated with the coupled networks. The allocation model is formulated as a mathematical program with complementarity constraints, and is solved by an active-set algorithm. Numerical examples are presented to demonstrate the models and offer insights on the equilibrium of the coupled transportation and power networks, and optimally allocating resource for public charging infrastructure.

Optimal deployment of public charging stations for plug-in hybrid electric vehicles

This paper summarizes diverse concepts for the next generation of power distribution system. The objective is to bring distribution engineering more closely aligned to smart grid philosophy. Issues of design, operation, and control are discussed with regard to new system theoretic as well as component/materials advances. In particular, two transmission engineering techniques are modified for use in distribution engineering: state estimation, and locational marginal pricing. The impact of electronic control in distribution systems is discussed. Because education and training have a great impact on distribution engineering, these topics are discussed as well.

The Next Generation of Power Distribution Systems

State-of-the-art, challenges, and future trends in security constrained optimal power flow

The paper examines the tradeoffs between using a full ac model versus the less exact, but much faster, dc power flow model for LMP-based market calculations. The paper first provides a general discussion of the approximations associated with using a dc model, with an emphasis on the impact these approximations will have on security constrained OPF (SCOPF) results and LMP values. Then, since the impact of the approximations can be quite system specific, the paper provides case studies using both a small 37 bus system and a somewhat larger 12,965 bus model of the Midwest U.S. transmission grid. Results are provided comparing both the accuracy and the computational requirements of the two models. The general conclusion is that while there is some loss of accuracy using the dc approximation, the results actually match fairly closely with the full ac solution.

A comparison of the AC and DC power flow models for LMP calculations

The large size of power systems makes behavioral analysis of electricity markets computationally taxing. Reducing the system into a smaller equivalent, based on congestion zones, can substantially reduce the computational requirements. In this paper, we propose a scheme to determine the equivalent reactance of interfaces of a reduced system based upon the zonal power transfer distribution factors of the original system. The dc power flow model is used to formulate the problem. Test examples are provided using both an illustrative six-bus system and a more realistically sized 12 925-bus system.

PTDF-based power system equivalents

The volatility of the price of electricity in a locational marginal price (LMP) market makes it necessary to introduce financial price risk hedging instruments. The congestion-related and marginal-loss-related revenue surpluses collected by the regional transmission operator (RTO) are proposed to be redistributed to market players. It is important to be able to correctly decompose the LMP into its congestion and marginal-loss components, which are critical for the valuation and settlement of these financial instruments. A new energy reference bus independent LMP decomposition model using an ac optimal power flow (OPF) model is presented to overcome the reference bus dependency disadvantage of the conventional approach. The marginal effect of the generators' output variation with respect to load variation are used as the basis of this decomposition model. The theoretical derivation and a proof are given. The new model achieves a set of reference bus independent results. An example is presented comparing the new model with the conventional model

An energy reference bus independent LMP decomposition algorithm

In order to decrease the cost for those electric logistics vehicles, it’s necessary to consider respond the lower real-time price in the electricity market when the EV is prepared for charging electricity and find an optimal distribution scheme; the key problem is in constructing an optimal model and find proper optimization solving approach. Firstly, based on the constructed information system, the variation characteristics of real-time price and the charging/discharging characteristics of the battery are analyzed. Secondly, the mathematical model of minimizing the cost of electric logistics vehicles is constructed. Various constraints, such as battery capacity limit, road accessibility, and whether a charging station is available, are considered. Then, with the improved dynamic programming, the discussed problem is easy to be solved when being converted into multi-stage decision-making. Finally, an example demonstrates how electric logistics vehicles respond to real-time prices. Those findings can verify the proposed model and solution approach are valid.

Xu Cheng

Papers

A comparison of the AC and DC power flow models for LMP calculations

PTDF-based power system equivalents

An energy reference bus independent LMP decomposition algorithm

Optimal Distribution Scheme for Electric Logistics Vehicle Response to Real-time Price