Optimal Allocation of Smart Substations in a Distribution System Considering Interruption Costs of Customers

One of the major functions of a smart substation (SS) is to restore power supply to interrupted customers as quickly as possible after an outage. The high cost of a smart substation limits its widespread utilization. In this paper, a smart substation allocation model (SSAM) to determine the optimal number and allocation of smart substations in a given distribution system is presented, with the upgrade costs of substations and the interruption costs of customers taken into account. Besides, the reliability criterion is also properly considered in the model. By linearization strategies, the SSAM is simplified into a mixed integer linear programming problem which could be solved efficiently with commercial solvers. Finally, the performance of the proposed methodology is demonstrated by the standard RBTS-BUS 4 test system and a medium voltage power distribution system in Denmark. Index Terms — distribution system, smart substation allocation, upgrade cost, interruption cost, reliability cost, service restoration, outage management. NOMENCLATURES A. Indices and Sets: f, Sf Index and set of feeders. l, Sl Index and set of line segments. s, Ss Index and set of 10/0.4 kV substations. k, Sk Index and set of types of customers. w, S Index and set of tie switches. z, Sz Index and set of sections. STS w S Set of substations which are located on all sides of a tie switch w. TFS w S Set of substations which are located between substation s ( STS w s S  ) and the feeder supplying power to substation s. Manuscript received on July 9, 2016. This work is jointly supported by National Natural Science Foundation of China (51477151), and Specialized Research Fund for the Doctoral Program of Higher Education of China (20120101110112). L. Sun and F. Wen are both with the College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China (Emails: sunleieee@gmail.com; fushuan.wen@gmail.com). F. Wen is also with Universiti Teknologi Brunei (UTB), Bandar Seri Begawan, Brunei (Email: fushuan.wen@utb.edu.bn). S. You and J. Hu are with the Center for Electric Power and Energy, Department of Electrical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark (Emails: sy@elektro.dtu.dk; junhu@elektro.dtu.dk). Ω f Set of line segments and substations supplied by feeder f. Ω f,z Set of line segments and substations within section z supplied by feeder f. up , f z  Set of substations in the upstream of section z supplied by feeder f. down , f z  Set of substations in the downstream of section z supplied by feeder f. , , SS f l s  Set of substations between line l and substation s supplied by feeder f. B. Parameters lim AIDI S Threshold of the allowed SAIDI value. λf,l Probability of a fault occurred on line segment l at feeder f. pf,s,k Power consumption of type k at substation s supplied by feeder f. , CIC f s C Capital investment cost of upgrading substation s supplied by feeder f. , IC f s C Installment cost of upgrading substation s at feeder f. , MC f s C Maintenance and operation cost of upgrading substation s at feeder f. Nf,s Number of customers supplied by substation s at feeder f. cur , , s f l t Failure duration of substation s when a fault occurs on line l of feeder f in the current distribution system. smart , , s f l t Failure duration of substation s when a fault occurs on line l of feeder f if the fault can be isolated by a smart substation between substation s and line l. uss z t Time spent on opening the closest upstream switch in section z manually. dts z t Time spent on opening the closest downstream switch in section z and closing a tie switch manually. uss_a z t Time spent on opening an upstream switch in section z automatically. Optimal Allocation of Smart Substations in a Distribution System Considering Interruption Costs of Customers Lei Sun, Shi You, Member, IEEE, Junjie Hu, Member, IEEE, Fushuan Wen