Constructive heuristic algorithm for the DC model in network transmission expansion planning

A novel constructive heuristic algorithm to the network expansion planning problem is presented the basic idea comes from Garver's work applied to the transportation model, nevertheless the proposed algorithm is for the DC model. Tests results with most known systems in the literature are carried out to show the efficiency of the method.

Fault analysis in four-wire distribution networks

The neutral wire in most existing power flow and fault analysis software is usually merged into phase wires using Kron's reduction method. In some applications, such as fault analysis, fault location, power quality studies, safety analysis, loss analysis etc., knowledge of the neutral wire and ground currents and voltages could be of particular interest. A general short-circuit analysis algorithm for three-phase four-wire distribution networks, based on the hybrid compensation method, is presented. In this novel use of the technique, the neutral wire and assumed ground conductor are explicitly represented. A generalised fault analysis method is applied to the distribution network for conditions with and without embedded generation. Results obtained from several case studies on medium- and low-voltage test networks with unbalanced loads, for isolated and multi-grounded neutral scenarios, are presented and discussed. Simulation results show the effects of neutrals and system grounding on the operation of the distribution feeders.

Continuation load flow using automatically determined branch megawatt losses as parameters

The conventional Newton's method is considered to be inadequate for the computation of the maximum loading point (MLP) of power systems since: (i) it encounters difficulties in the vicinity of the MLP: and (ii) the load flow Jacobian matrix becomes singular at the MLP. It is well known that continuation methods are powerful and useful tools that are able to trace the solution PV curve without experiencing such diffculties. However, continuation methods require a parameterisation so that a modified, well conditioned set of load flow equations is obtained. In particular, the Jacobian matrix associated with this modified set of equations should not be singular at the MLP. The authors propose that the actual power losses in transmission branches (lines and transformers) are used to parameterise the approach. Specific procedures for the automatic determination of the most appropriate parameter (branch) are proposed. Such procedures include the utilisation of fast voltage-stability indices. Simulation results are presented to show that the proposed method is able to trace the whole solution PV curve very efficiently.

Transmission network expansion planning with security constraints

A mathematical model and a methodology to solve the transmission network expansion planning problem with security constraints are presented. The methodology allows one to find an optimal and reliable transmission network expansion plan using a DC model to represent the electrical network. The security (n-1) criterion is used. The model presented is solved using a genetic algorithm designed to solve the reliable expansion planning in an efficient way. The results obtained for several known systems from literature show the excellent performance of the proposed methodology. A comparative analysis of the results obtained with the proposed methodology is also presented.

Constructive heuristic algorithm in branch-and-bound structure applied to transmission network expansion planning

A constructive heuristic algorithm to solve the transmission system expansion planning problem is proposed with the aim of circumventing some critical problems of classical heuristic algorithms that employ relaxed mathematical models to calculate a sensitivity index that guides the circuit additions. The proposed heuristic algorithm is in a branch-and-bound algorithm structure, which can be used with any planning model, such as Transportation model, DC model, AC model or Hybrid models. Tests of the proposed algorithm are presented on real Brazilian systems.

Branch and bound algorithm for transmission system expansion planning using a transportation model

A method for optimal transmission network expansion planning is presented. The transmission network is modelled as a transportation network. The problem is solved using hierarchical Benders decomposition in which the problem is decomposed into master and slave subproblems. The master subproblem models the investment decisions and is solved using a branch-and-bound algorithm. The slave subproblem models the network operation and is solved using a specialised linear program. Several alternative implementations of the branch-and-bound algorithm have been rested. Special characteristics of the transmission expansion problem have been taken into consideration in these implementations. The methods have been tested on various test systems available in the literature.

Specialised branch-and-bound algorithm for transmission network expansion planning

An algorithm is presented that finds the optimal plan long-term transmission for till cases studied, including relatively large and complex networks. The knowledge of optimal plans is becoming more important in the emerging competitive environment, to which the correct economic signals have to be sent to all participants. The paper presents a new specialised branch-and-bound algorithm for transmission network expansion planning. Optimality is obtained at a cost, however: that is the use of a transportation model for representing the transmission network, in this model only the Kirchhoff current law is taken into account (the second law being relaxed). The expansion problem then becomes an integer linear program (ILP) which is solved by the proposed branch-and-bound method without any further approximations. To control combinatorial explosion the branch- and bound algorithm is specialised using specific knowledge about the problem for both the selection of candidate problems and the selection of the next variable to be used for branching. Special constraints are also used to reduce the gap between the optimal integer solution (ILP program) and the solution obtained by relaxing the integrality constraints (LP program). Tests have been performed with small, medium and large networks available in the literature.

Efficient linear programming algorithm for the transmission network expansion planning problem

The transmission network planning problem is a non-linear integer mixed programming problem (NLIMP). Most of the algorithms used to solve this problem use a linear programming subroutine (LP) to solve LP problems resulting from planning algorithms. Sometimes the resolution of these LPs represents a major computational effort. The particularity of these LPs in the optimal solution is that only some inequality constraints are binding. This task transforms the LP into an equivalent problem with only one equality constraint (the power flow equation) and many inequality constraints, and uses a dual simplex algorithm and a relaxation strategy to solve the LPs. The optimisation process is started with only one equality constraint and, in each step, the most unfeasible constraint is added. The logic used is similar to a proposal for electric systems operation planning. The results show a higher performance of the algorithm when compared to primal simplex methods.

Power system transmission network expansion planning using AC model

An optimisation technique to solve transmission network expansion planning problem, using the AC model, is presented. This is a very complex mixed integer nonlinear programming problem. A constructive heuristic algorithm aimed at obtaining an excellent quality solution for this problem is presented. An interior point method is employed to solve nonlinear programming problems during the solution steps of the algorithm. Results of the tests, carried out with three electrical energy systems, show the capabilities of the method and also the viability of using the AC model to solve the problem.

Analysis of heuristic algorithms for the transportation model in static and multistage planning in network expansion systems

The usefulness of the application of heuristic algorithms in the transportation model, first proposed by Garver, is analysed in relation to planning for the expansion of transmission systems. The formulation of the mathematical model and the solution techniques proposed in the specialised literature are analysed in detail. Starting with the constructive heuristic algorithm proposed by Garver, an extension is made to the problem of multistage planning for transmission systems. The quality of the solutions found by heuristic algorithms for the transportation model is analysed, as are applications in problems of planning transmission systems.

Transmission-expansion planning using the DC model and nonlinear-programming technique

The paper presents a constructive heuristic algorithm (CHA) for solving directly the long-term transmission-network-expansion-planning (LTTNEP) problem using the DC model. The LTTNEP is a very complex mixed-integer nonlinear-programming problem and presents a combinatorial growth in the search space. The CHA is used to find a solution for the LTTNEP problem of good quality. A sensitivity index is used in each step of the CHA to add circuits to the system. This sensitivity index is obtained by solving the relaxed problem of LTTNEP, i.e. considering the number of circuits to be added as a continuous variable. The relaxed problem is a large and complex nonlinear-programming problem and was solved through the interior-point method (IPM). Tests were performed using Garver's system, the modified IEEE 24-Bus system and the Southern Brazilian reduced system. The results presented show the good performance of IPM inside the CHA.

Test systems and mathematical models for transmission network expansion planning

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.

Transmission system expansion planning by a branch-and-bound algorithm

A branch and bound (B& B) algorithm using the DC model, to solve the power system transmission expansion planning by incorporating the electrical losses in network modelling problem is presented. This is a mixed integer nonlinear programming (MINLP) problem, and in this approach, the so-called fathoming tests in the B&B algorithm were redefined and a nonlinear programming (NLP) problem is solved in each node of the B& B tree, using an interior-point method. Pseudocosts were used to manage the development of the B&B tree and to decrease its size and the processing time. There is no guarantee of convergence towards global optimisation for the MINLP problem. However, preliminary tests show that the algorithm easily converges towards the best-known solutions or to the optimal solutions for all the tested systems neglecting the electrical losses. When the electrical losses are taken into account, the solution obtained using the Garver system is better than the best one known in the literature.

New approach to four-phase transmission systems: analysis of the transient response and the possible voltage surges

This study describes a technical analysis of a four-phase line as a transmission system alternative. An analysis in the frequency and the time domains is performed to evaluate the electrical characteristics and the transient response of a generic four-phase system compared with those of a conventional three-phase transmission system. The technical features of this non-conventional system are discussed and reviewed based on the current literature. Thus, a new analysis of the four-phase system is presented that emphasises several technical characteristics that have not been discussed in previous studies.

Generalised single-equation load flow method for unbalanced distribution systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)