This paper presents a model for use in the problem of multistage planning of energy distribution systems including distributed generation. The expansion model allows alternatives to be considered for increasing the capacity of existing substations, for installing new ones, for using distributed generation, and for the possible change to feeders in terms of addition and removing feeders sections; combining, subdividing, and load transfer between feeders; and replacement of conductors. The objective function to be minimized is the present value of total installation costs (feeders and substations), of operating and maintaining the network, and of distributed generation. The model takes operational constraints on equipment capacities and voltage limits together into account with logical constraints, aimed at reducing the search space. This paper presents: (1) an extension to the linear disjunctive formulation to represent the inclusion, exclusion, and replacement of branches and (2) a generalization of constraints related to the creation of new paths which can be applied in more complex topologies. The resulting mixed integer linear model allows the optimal solution to be found using mathematical programming methods, such as the branch-and-bound algorithm. The validity and efficiency of the model are demonstrated in Part II of this paper.

Multistage Model for Distribution Expansion Planning With Distributed Generation—Part I: Problem Formulation

This paper presents a model for solving the multistage planning problem of a distribution network. The objective function to be minimized is the net present value of the investment cost to add, reinforce or replace feeders and substations, losses cost, and operation and maintenance cost. The model considers three levels of load in each node and two investment alternatives for each resource to be added, reinforced or replaced. The nonlinear objective function is approximated by a piecewise linear function, resulting in a mixed integer linear model that is solved using standard mathematical programming. The model allows us to find multiple solutions in addition to the optimal one, helping the decision maker to analyze and choose from a pool of solutions. In addition to the optimization problem, reliability indexes and associated costs are computed for each solution, based on the regulation model used in Brazil. Numerical results and discussion are presented for an illustrative 27-node test network.

Distribution System Planning With Reliability

Multistage distribution system expansion planning considering distributed generation using hybrid evolutionary algorithms

Integrated distribution network expansion planning incorporating distributed generation considering uncertainties, reliability, and operational conditions

In this paper, we propose a flexible mixed-integer linear programming formulation of the AC OPF problem for distribution systems, using convexification and linearization techniques. The proposed formulation allows the representation of discrete decisions via integer decision variables, captures the nonlinear behavior of the electrical network via approximations of controllable accuracy, and can be solved to global optimality with commercial optimization solvers. The formulation is based on conventional variables that describe network behavior, which ensures its flexibility and the possibility of application to various distribution system problems, as we indicate with case studies.

http://www.pee.ufrj.br/teses/textocompleto/2013032603.pdf

A Flexible Mixed-Integer Linear Programming Approach to the AC Optimal Power Flow in Distribution Systems

A new model for distribution system planning

The power transfer capability (PTC) of AC transmission lines is increased by using series capacitor and shunt reactor compensation. This paper presents a method to calculate the degree of series capacitor and shunt reactor compensation in order to increase the power transfer capability of overhead transmission lines. This method is based on linear programming which takes into consideration line modelling, series and shunt compensation, voltage and reactive power constraints, and power factor before and after compensation. The proposed method has been applied to the existing 500 kV transmission line interconnected between the High-Dam generation station and Cairo load center in Egypt. Copyright © 2005 John Wiley & Sons, Ltd.

M. M. El-Metwally

Papers

A new model for distribution system planning

A linear programming method for series and shunt compensation of HV transmission lines

Effect of load characteristics on maximum power transfer limit for HV compensated transmission lines