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.

This paper presents an innovative tuning strategy for the design of multiple-loop lag-lead compensators for uninterruptible power supplies (UPSs) based on the H-infinity robust control theory. Taking into account an average model of a UPS, the parameters of a double-loop controller are synthesized such that the upper bound on the two-norm of the input-to-output operator is minimized while guaranteeing local stability of the closed-loop system for all admissible load variations. The stabilization conditions are cast in terms of linear matrix inequalities that are solved via standard software packages. To improve regulation dynamics, a newer technique to compute the root-mean-square value of the output voltage is also proposed. Practical results considering a commercial UPS system demonstrate the effectiveness of the proposed approach as a tool for tuning multiloop controllers

This paper deals with the synthesis problem of multiple resonant controllers for uninterruptible-power-supply systems in a robust control framework. The controller parameters aiming the tracking of sinusoidal reference signals (with zero steady-state error) and the rejection of harmonic components of the output voltage (when supplying energy to time-varying nonlinear loads) are determined by means of a convex optimization problem subject to a set of linear-matrix-inequality constraints. Results from a 5.0-kVA experimental setup are considered to illustrate and validate the proposed approach.

This paper presents the computer simulation of the multistage model for distribution expansion planning with distributed generation, as described in Part I. The simulations deal with the planning of an electrical power distribution network in three stages, in five different situations: 1. each of the three stages planned independently; 2. multistage planning; 3. multistage planning with distributed generation; 4. multistage planning with distributed generation and constraints on investment; and 5. multistage planning with distributed generation considering three load levels. The influence of additional constraints is analyzed in terms of the computational effort required to find the optimum solution to the problem.

This paper presents a general mathematical model of a five-phase induction machine including the effects of higher space and time harmonics in the air gap field. These harmonic waves play a decisive role in the behavior of machines with more than three phases. Mathematical expressions for the calculation of the self and mutual inductances are presented, and results are compared with values obtained by finite element analysis and measurements. Based on the air gap field distribution produced by the stator and rotor, all the field harmonics are included in a direct and simple way in the self-inductances. The mutual inductances are obtained from a Fourier series description of the air gap field, resulting in a different inductance for each harmonic field. The machine equations are then simplified using coordinate transformations, which result in equivalent d-q models and equivalent circuits for given harmonic groups. In their final form, the equations are appropriated for the simulation of the machine behavior and developing new control strategies including higher space and time harmonics. Finally, practical results of a prototype machine are compared with simulations demonstrating the accuracy of the model

In this brief, we propose a particular structure for resonant controllers and a tuning method of the Ziegler-Nichols type for their tuning. Performance criteria for resonant controllers are also defined. The effectiveness of the tuning rules is illustrated by their application and corresponding performance assessment in a test batch consisting of four representative classes of processes. The control performance is analyzed in detail for one particular example, shedding light on the virtues and limitations of the control structure and of the tuning method.