This paper presents a holistic modeling framework for the interdependent transportation network and power distribution network. From a system-level perspective, on-road fast charging stations would simultaneously impact vehicle routing in the transportation system and load flows in the distribution system, therefore tightly couple the two systems. In this paper, a dedicated traffic user equilibrium model is proposed to describe the steady-state distribution of traffic flows comprised of gasoline vehicles and electric vehicles. It encapsulates route selections, charging opportunities, electricity prices, and individual rationalities of minimum travel expense in a convex traffic assignment problem over an extended transportation network. An adaptive path generation oracle is suggested to solve the problem in a tractable manner. Economic operation of the power distribution system is formulated as an alternating current optimal power flow problem. Convex relaxation is performed. The optimal generation dispatch and nodal electricity prices can be computed from a second-order cone program. It is revealed that an equilibrium state will emerge due to the rational behaviors in the coupled systems, which is characterized via a fixed-point problem. A best-response decomposition algorithm is suggested to identify the network equilibrium through iteratively solving the traffic assignment problem and the optimal power flow problem, both of which entail convex optimization. Illustrative examples are presented to validate related concepts and methods.

This paper proposes a two-stage two-level model for the energy pricing and dispatch problem faced by a smart grid retailer who plays the role of an intermediary agent between a wholesale energy market and end consumers. Demand response of consumers with respect to the retail price is characterized by a Stackelberg game in the first stage, thus the first stage has two levels. A risk-aversive energy dispatch accounting for market price uncertainty is modeled by a linear robust optimization with objective uncertainty in the second stage. The proposed model is transformed to a mixed integer linear program (MILP) by jointly using the Karush-Kuhn-Tucker (KKT) condition, the disjunctive constraints, and the duality theory. We propose a heuristic method to select the parameter in disjunctive constraints based on the interpretation of Lagrange multipliers. Moreover, we suggest solving an additional linear program (LP) to acquire a possible enhanced bidding strategy that guarantees a Pareto improvement on the retailer's profit over the entire uncertainty set. Case studies demonstrate the proposed model and method is valid.

This paper conducts an interdisciplinary study on the coordinated operation of both transportation system and power system. We consider an electrified transportation network enabled by wireless power transfer technology and coupled with a power distribution network (PDN) in the future city. The independent system operator, which is a public entity, is eligible to manage generation assets and charge congestion tolls (CTs) on electrified roads with the purpose of minimizing social cost. The route choices of electric vehicles are amenable to the Wardrop user equilibrium (UE) principle, such that no one can reduce his travel cost by changing route unilaterally. The traffic UE pattern further influences the spatial distribution of the electrical loads of the PDN. The power flow of the PDN is modeled through Dist-Flow equations. To find out the best generation schedule and CTs, we propose an optimal traffic-power flow model, which is a mixed integer nonlinear program with traffic UE constraints and further reformulated as a mixed integer second-order cone program, whose global optimal solution is accessible with reasonable computation effort. Case studies corroborate the benefits from the joint operation of the coupled networks, and demonstrate that ignoring the interdependency between the two critical infrastructures may lead to an insecure operation.

Integration of electricity and heat distribution networks offers extra flexibility to system operation and improves energy efficiency. The energy hub (EH) plays an important role in energy production, conversion and storage in such coupled infrastructures. This paper provides a new outlook and thorough mathematical tool for studying the integrated energy system from a deregulated market perspective. A mathematic program with equilibrium constraints (MPEC) model is proposed to study the strategic behaviors of a profit-driven energy hub in the electricity market and heating market under the background of energy system integration. In the upper level, the EH submits bids of prices and quantities to a distribution power market and a heating market; in the lower level, the two markets are cleared and energy contracts between the EH and two energy markets are determined. Network constraints of physical systems are explicitly represented by an optimal power flow problem and an optimal thermal flow problem. The proposed MPEC formulation is approximated by a mixed-integer linear program via performing integer disjunctions on the complementarity and slackness conditions and binary expansion technique on the bilinear product terms. Case studies demonstrate the effectiveness of the proposed model and method.

This paper proposes a two-stage distributionally robust optimization model for the joint energy and reserve dispatch (D-RERD for short) of bulk power systems with significant renewable energy penetration. Distinguished from the prevalent uncertainty set-based and worst-case scenario oriented robust optimization methodology, we assume that the output of volatile renewable generation follows some ambiguous distribution with known expectations and variances, the probability distribution function (pdf) is restricted in a functional uncertainty set. D-RERD aims at minimizing the total expected production cost in the worst renewable power distribution. In this way, D-RERD inherits the advantages from both stochastic optimization and robust optimization: statistical characteristic is taken into account in a data-driven manner without requiring the exact pdf of uncertain factors. We present a convex optimization-based algorithm to solve the D-RERD, which involves solving semidefinite programming (SDP), convex quadratic programming (CQP), and linear programming (LP). The performance of the proposed approach is compared with the emerging adaptive robust optimization (ARO)-based model on the IEEE 118-bus system. Their respective features are discussed in case studies.

Global warming and environmental pollution concerns have promoted dramatic integrations of renewable energy sources all over the world. Associated with benefits of environmental conservation, essentially uncertain and variable characteristics of such energy resources significantly challenge the operation of power systems. In order to implement reliable and economical operations, a robust energy and reserve dispatch (RERD) model is proposed in this paper, in which the operating decisions are divided into pre-dispatch and re-dispatch. A robust feasibility constraint set is imposed on pre-dispatch variables, such that operation constraints can be recovered by adjusting re-dispatch after wind generation realizes. The model is extended to more general dispatch decision making problems involving uncertainties in the framework of adjustable robust optimization. By revealing the convexity of the robust feasibility constraint set, a comprehensive mixed integer linear programming based oracle is presented to verify the robust feasibility of pre-dispatch decisions. A cutting plane algorithm is established to solve associated optimization problems. The proposed model and method are applied to a five-bus system as well as a realistic provincial power grid in China. Numeric experiments demonstrate that the proposed methodology is effective and efficient.