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• A two-stage robust planning model for the coupled system is proposed. • The uncertainty of renewable energy, load and traffic demand are jointly considered. • The interactions between transportation and active distribution system are explored. • A two-level method is used to solve the proposed robust optimization model. Widespread utilization of electric vehicles has incurred more uncertainties and led to profound interdependencies across the power grid and transportation network. This creates an urgent demand for uncertainty modelling tools. Under this context, this paper proposes a two-stage robust optimization model for expansion planning of coupled active distribution and transportation. This model identifies the best type, location and capacity for roads, distribution lines, distributed generations, static VAR compensators, on-load tap changers, energy storage systems and charging facilities. From a system-level perspective, the steady-state pattern of the traffic flow in a transportation network is characterized by the Wardrop user equilibrium. In the active distribution system, the conic relaxation-based branch flow equations are employed, and the operating status of related devices are formulated by the linearized convex constraints. Considering the interdependency between two coupled systems, a deterministic expansion planning model is first established. Furthermore, with multiple uncertainties considered, a two-stage robust optimization model is proposed to optimize the investment and operation strategies coordinately, and thus a robust optimal solution is achieved. A two-level algorithm based on a combination of the column-and-constraint generation and outer approximation technique is developed for solving the two-stage model. The results demonstrate that the robust approach can effectively reduce the operation cost of coupled systems under the worst-case scenarios. Moreover, a comparative analysis indicates that operation costs in both systems increase linearly as the uncertainty level of traffic demand increases, while increasing that of the power load does not show an obvious change in the traffic operation cost. [ABSTRACT FROM AUTHOR]

• A planning model of coupled transportation and active distribution system is proposed. • Scenario generation technique is extended to incorporate traffic demand. • Scenario-based user equilibrium constraint is derived and embedded into the model. • A three dimensional piecewise method is designed to relax the bivariate expressions. • The importance of considering interdependencies of the coupled system is verified. The widespread utilization of electric vehicles has inspired the emerging trend of coupled transportation and distribution system, which entails the systematic methodologies to model the new planning problems. This paper proposes a scenario-based comprehensive expansion planning model for a coupled transportation and active distribution system. With the aim of minimizing the investment and operation costs, this model determines the best alternatives, locations and sizes for candidate assets, including traffic roads, distribution lines, distribution generators, capacitor banks, static var compensators, voltage regulators, energy storage systems and charging facilities, as well as their operation strategies. First, a generated scenario method is extended to incorporate the uncertainty of the traffic flow demand. Based on multiple scenarios, the steady-state distribution of traffic flow is characterized by the Wardrop user equilibrium principle, and the corresponding equivalent constraints are derived and incorporated into the model. For active distribution system, we formulate the operation constraints for related infrastructures. Considering the interdependency between the two systems, an expansion planning model is proposed, which simultaneously optimizes the investment and operation strategies. Due to the nonlinear nature of the model, we have developed a three-dimensional piecewise linear approximation and applied second order cone relaxation to reformulate the model as a mixed-integer second order conic program; thus, the global optimal solution can be found in a reasonable time frame. Results on a test system reveal that the variations of both systems have some influences on each other, indicating the significance of considering the interdependencies between transportation and active distribution system. [ABSTRACT FROM AUTHOR]

• The structure of urban multi-energy network is provided. • Three energy flows are generally defined and their convex relaxations are performed. • A mixed user equilibrium is applied to describe rational route and charging choices. • A two-stage bound-tightening algorithm is proposed to strengthen convex relaxations. The ever-growing interdependence among power distribution, natural gas networks and transportation infrastructure entails efficient and coordinated optimization techniques. This paper proposes an operational optimization model of urban multi-energy networks that encompasses the synergies among the above components, energy converters and electric vehicles. The proposed model defines and encapsulates three energy flows in a convex optimization problem. In the distribution network, the conic relaxation-based branch flow equation is employed to characterize the alternating current power flow. The static characteristics of gas flow are described via the Weymouth equation with convex envelop relaxations. In the transportation network, the traffic flow patterns associated with the interplay among routing and charging behaviors are studied. Since these behaviors are amenable to the Wardrop principle such that the travel cost cannot be reduced by unilaterally altering travel choice, a mixed user equilibrium model is established to describe the related traffic flows. Although the relaxation quality has been improved by deriving the tighter bounds of the variables, to date, bound-tightening approaches have not yet been effectively applied to multi-energy network problems. To strengthen convex relaxations, we enhance the proposed model with a two-stage approach. The first stage improves the variable bounds through sequential optimality-based bound contraction. The second stage iteratively and successively solves the model with a dynamic bound-tightening algorithm. Based on case studies, the interdependence among energy networks is discussed. In addition, the numerical experiments corroborate the solution quality and computational efficiency benefits of the proposed approach. [ABSTRACT FROM AUTHOR]