Reliability cost is considered as an inevitable criterion in expansion planning studies of distribution systems. However, nonlinear expressions of reliability indices aggravate complexity of planning studies. To address this issue, this letter proposes a novel method to linearize mathematical model of the reliability-based distribution expansion planning problem. Using this variant of reliability indices, reliability costs can easily be involved in mixed-integer linear programming (MILP) model of distribution expansion planning. Validity of the derived expressions is tested by simulation results.

The judicious placement of disconnecting switches is an efficient means to enhance the reliability of distribution networks. Aiming at optimizing the investment in these switches, this paper presents a mathematical programming-based model considering the installation of remote-controlled and manual switches at various locations in the distribution network. The proposed model not only yields the optimal location and type of switches in the main feeders but also specifies the optimal type of tie switches, i.e., backup switches at the reserve connection points. Incentive reliability regulation in the form of a reward-penalty scheme is incorporated into the proposed model to take the distribution service reliability worth into account realistically. In addition to this cost, the revenue lost due to energy undelivered during the distribution network faults is considered to determine the unreliability costs more accurately. In order to estimate such reliability-related costs, a novel reliability assessment technique is developed and integrated into the proposed switch optimization model. Formulated as an instance of mixed-integer linear programming, the proposed model is applied to a test distribution network, and the outcomes are investigated in detail. INDEX TERMS Electricity distribution system, mixed-integer linear programming, reliability, reward-penalty scheme, switch optimization. NOMENCLATURE INDICES

This paper aims at proposing a mixed-integer linear formulation to incorporate reliability oriented costs into the expansion planning model of electricity distribution networks. In this respect, revenue lost associated with the undelivered energy caused by network interruptions, as well as costs incurred by the widely-used reward-penalty regulations are considered as the major reliability related costs from distribution companies point of view. A set of mixed-integer linear equations is proposed to calculate the most common distribution system reliability indices, i.e. EENS, SAIFI, and SAIDI. It is found that these equations can also facilitate the formulation of radiality constraint in the presence of DG units. Moreover, application of the proposed method is investigated through various case studies performed on two test distribution networks with 24 and 54 nodes.

Continuity of supply plays a significant role in modern distribution system planning and operational studies. Accordingly, various techniques have been developed for reliability assessment of distribution networks. However, owing to the complexities and restrictions of these methods, many researchers have resorted to several heuristic optimization algorithms for solving reliability-constrained optimization problems. Therefore, solution quality and convergence to global optimality cannot be guaranteed. Aiming to address this issue, two salient mathematical models are introduced in this paper for topology-variablebased reliability evaluation of both radial and radially-operated meshed distribution networks. Cast as a set of linear expressions, the first model is suitable for radial networks. The second model relies on mixed-integer linear programming and allows handling not only radial networks but also radially-operated meshed distribution grids. Therefore, the proposed formulations can be readily incorporated into various mathematical programming models for distribution system planning and operation. Numerical results from several case studies back the scalability of the developed models, which is promising for their further application in distribution system optimization studies. Moreover, the benefits of the proposed formulations in terms of solution quality are empirically evidenced. Mahmud Fotuhi-Firuzabad (F'14) received the M.Sc. degree in electrical engineering from the