Structural Vulnerability of Energy Distribution Systems; Incorporating Infrastructural Dependencies Arild Helseth, Arne T. Holen Department of Electric Power Engineering The Norwegian University of Science and Technology (NTNU) Trondheim, Norway helseth@elkraft.ntnu.no Abstract—In this paper a method for assessing the struc- tural vulnerability of two coupled energy distribution systems is proposed. The co-existing of an electric power distribution system and a district heating system is described and modelled, under the assumption that the operation of the district heating system is directly dependent on electric power. The structural vulnerability of the two systems subject to single failures or a set of simultaneous failures in the power system is found. Thus, the consequences of power system failures for the energy supply as a whole are quantified. Index Terms—Power distribution, district heating, vulnera- bility, reconfiguration, network constraints, genetic algorithms (GAs), linear programming I. I NTRODUCTION Reliability analysis of electric power systems is a rather mature field of study, covering all essential parts of the system [1], [2]. Analysing simultaneous failures in addition to single failures at distribution level will normally not significantly influence the reliability indices, due to low probability of occurrence and modest increase in consequences. Thus, most methods for reliability analysis of distribution systems focus on single failures. On the other hand, simultaneous failures may be a result of extraordinary circumstances – such as adverse weather, mali- cious attacks and loss of supporting infrastructures – and will challenge the use of both human and equipment resources. The occurrence of simultaneous failures are not easily predicted and the use of generic failure rates and repair times may not be appropriate for analysing the system impact of these. In this work we emphasise on finding the consequences of multiple simultaneous failures, leaving considerations on probability of occurrence and duration of such failure sets to the judgement of the analyst. Interruptions of electricity supply may also degrade the performance of parallel energy infrastructures, e.g. district heating and natural gas systems, which are more or less dependent on electricity for proper operation. Consequently, in order to capture the consequences of power system failures for the energy supply as a whole, these parallel infrastructures and their links to the power system should be modelled. In this paper a method for assessing the structural vulnera- bility of two coupled energy distribution systems is proposed. The overall aim is to find the vulnerability of the energy system as a whole to single or simultaneous failures in the power system. The structural vulnerability of the systems with respect to failures in the power system is defined as the consequences caused in both systems. Thus, the concept of vulnerability, as defined here, is not related to the probability of such failure sets to occur. Several recent studies have addressed the concept of vul- nerability in electric power systems, ranging from graph theoretical investigations in [3]–[5] to investigations based on more physical models in [6], [7]. These studies all refer to the transmission system, and there is a large gap between the applied definitions of vulnerability. In [8], the vulnerability to failures at distribution level is analysed using a network ana- lytic approach. Here, the electrical properties of the network are neglected and vulnerability is defined as the degree of loss or damage to the system when exposed to a perturbation of a given type and magnitude. Some studies have been conducted regarding infrastructural dependency modelling. In [9] a general overview of different kinds of interdependencies in critical infrastructures is given. A network analytic approach is presented in [10], identifying vulnerabilities in local distribution systems of electricity, nat- ural gas and water. Furthermore, [11] and [12] describe and analyse the impact of natural-gas system reliability on electric power transmission systems. The proposed method is described and illustrated for an electric power distribution system (EPDS) co-existing with a district heating system (DHS). The operation of the DHS is directly dependent on electricity. The following section describes the system modelling approach and the correspond- ing underlying assumptions for both the EPDS and DHS. Section III presents a screening strategy used for finding the most critical failure sets in the EPDS. A limited number of failure sets are fully analysed for both systems. In section IV, a simple example is elaborated, before the method is applied in a case study in section V. II. SYSTEM MODELLING Two simple systems, an EPDS and a DHS, are presented below, and a method suitable for finding the systems’ vulner- abilities to failures in the EPDS is elaborated. Both the EPDS and the DHS are modelled as networks, comprising a set of