A multi-stage MINLP-based model for sub-transmission system expansion planning considering the placement of DG units Mehdi Jalali, Kazem Zare ⇑ , Mehrdad Tarafdar Hagh University of Tabriz, P.O. Box 51666-15813, Tabriz, Iran article info Article history: Received 7 July 2013 Received in revised form 18 May 2014 Accepted 29 May 2014 Keywords: Sub-transmission substation expansion planning Distributed generation Feeder routing abstract This paper presents a new multi-stage model, based on the mixed integer nonlinear programming (MIN- LP) approach, to determine the optimal sub-transmission system expansion planning (SSEP). This model considers the placement of distributed generation (DG) units in distribution networks over the planning periods. The SSEP determines the facilities which should be installed and/or reinforced so that the system serves the forecasted demand at the lowest cost while satisfying the operational constraints. These con- straints include the maximum allowable voltage drop, and the operation capacity of substations, MV feeders, and DG units. Meanwhile, the proposed model presents the optimal planning of existing and new sub-transmission substations, as well as the routes of medium voltage (MV) feeders. Moreover, the allocation and operation planning of DG units over the planning period is considered, as well. On the other hand, the expanding limitations of existing and candidate sub-transmission substations and DG units are considered as the expansion constraints in the SSEP problem. The effectiveness of proposed MINLP-based model is demonstrated using several case studies. Ó 2014 Elsevier Ltd. All rights reserved. Introduction Sub-transmission system is a part of an electric power trans- mission network, which connects the energy sources in extra high voltage transmission networks to the medium voltage load points in distribution networks [1]. Sub-transmission system expansion planning (SSEP) problem determines the facilities which should be installed and/or reinforced so that the system serves the fore- casted demand at the lowest cost while satisfying the operational constraints. This target is achieved by optimal sitting and sizing of network elements, such as substations, MV feeders and distrib- uted generation (DG) units. DGs are defined as the small power resources which are located close to the load points [2–4]. The role of DG units has been increased, since the last decade, by providing different benefits such as cost reduction, reliability of supply, ancil- lary services, emission reduction, and postponement of the trans- mission and distribution expansion planning. Appetency of the distribution network operators (DNO), DG owners (DGO), and socio-political requirements cause the use of DG units to be increased [5–7]. On the other hand, the active and reactive power injections from DG units, typically installed close to the load cen- ters, are seen as a cost-effective solution for distribution system improvement. So, DG units are considered as a remarkable option of distribution system planning in the future [8]. The challenge between the integration of DG units in power systems and the existing protection schemes is an important problem which is dis- cussed in [9–11]. Many approaches have been presented for distribution system planning. However, a little of them has focused on the placement and expansion planning of sub-transmission substations. Some papers, such as [12], determine the location, type and capacity of the new equipments that should be expanded and/or added to the distribution system through a static approach, which considers only one planning horizon. Some other approaches, like the succes- sive method, pseudo-dynamic method, and dynamic method, con- sider the time variety of the demand during the planning period in the expansion planning. In the successive method, a static planning is conducted for each time period to meet the maximum load level of that period with respect to the layout planning of the previous stage. Since the optimal solution of each period is dependent to the obtained results from the previous stages, the successive method often leads to the local minima [12,13]. In the pseudo dynamic methodology, the total planning period is divided into two separate sections [14,15]. In the first section, based on the static planning method, a system is designed that can serve the maximum demand of the horizon year in an optimal manner. Then, the non-elected substations are eliminated from the set of candi- date substations. Moreover, the maximum installable capacity of http://dx.doi.org/10.1016/j.ijepes.2014.05.044 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel./fax: +98 411 3300829. E-mail addresses: m.jalali90@ms.tabrizu.ac.ir (M. Jalali), kazem.zare@tabrizu.ac. ir (K. Zare), tarafdar@tabrizu.ac.ir (M.T. Hagh). Electrical Power and Energy Systems 63 (2014) 8–16 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes