VAr planning using genetic algorithm and linear programming

A combined methodology consisting of successive linear programming (SLP) and a simple genetic algorithm (SGA) solves the reactive planning problem. The problem is divided into operating and planning subproblems; the operating subproblem, which is a nonlinear, ill-conditioned and nonconvex problem, consists of determining the voltage control and the adjustment of reactive sources. The planning subproblem consists of obtaining the optimal reactive source expansion considering operational, economical and physical characteristics of the system. SLP solves the optimal reactive dispatch problem related to real variables, while SGA is used to determine the necessary adjustments of both the binary and discrete variables existing in the modelling problem. Once the set of candidate busbars has been defined, the program implemented gives the location and size of the reactive sources needed, if any, to maintain the operating and security constraints.

Optimal reactive power dispatch using stochastic chance-constrained programming

Deterministic Optimal Reactive Power Dispatch problem has been extensively studied, such that the demand power and the availability of shunt reactive power compensators are known and fixed. Give this background, a two-stage stochastic optimization model is first formulated under the presumption that the load demand can be modeled as specified random parameters. A second stochastic chance-constrained model is presented considering uncertainty on the demand and the equivalent availability of shunt reactive power compensators. Simulations on six-bus and 30-bus test systems are used to illustrate the validity and essential features of the proposed models. This simulations shows that the proposed models can prevent to the power system operator about of the deficit of reactive power in the power system and suggest that shunt reactive sourses must be dispatched against the unavailability of any reactive source. © 2012 IEEE.

Optimal Reactive Power Planning Using Risk Analysis

In this paper, the optimal reactive power planning problem under risk is presented. The classical mixed-integer nonlinear model for reactive power planning is expanded into two stage stochastic model considering risk. This new model considers uncertainty on the demand load. The risk is quantified by a factor introduced into the objective function and is identified as the variance of the random variables. Finally numerical results illustrate the performance of the proposed model, that is applied to IEEE 30-bus test system to determine optimal amount and location for reactive power expansion.

Optimal reactive power flow via the modified barrier Lagrangian function approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A decentralized approach for optimal reactive power dispatch using a Lagrangian decomposition method

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

TWO DECOMPOSITION APPROACHES APPLIED TO THE MULTI-AREA OPTIMAL REACTIVE POWER FLOW PROBLEM

This paper applies two methods of mathematical decomposition to carry out an optimal reactive power flow (ORPF) in a coordinated decentralized way in the context of an interconnected multi-area power system. The first method is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). The second method uses a decomposition technique based on the Karush-Kuhn-Tucker (KKT) first-order optimality conditions. The viability of each method to be used in the decomposition of multi-area ORPF is studied and the corresponding mathematical models are presented. The IEEE RTS-96, the IEEE 118-bus test systems and a 9-bus didactic system are used in order to show the operation and effectiveness of the decomposition methods.

Multi-areas optimal reactive power flow

This paper describes a method for the decentralized solution of the optimal reactive power flow (ORPF) problem in interconnected power systems. The ORPF model is solved in a decentralized framework, consisting of regions, where the transmission system operator in each area operates its system independently of the other areas, obtaining an optimal coordinated but decentralized solution. The proposed scheme is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). An implementation of an interior point method is described to solve the decoupled problem in each area. The described method is successfully implemented and tested using the IEEE two area RTS 96 test system. Numerical results comparing the solutions obtained by the traditional and the proposed decentralized methods are presented for validation. ©2008 IEEE.

Penalty-based nonlinear solver for optimal reactive power dispatch with discrete controls

The optimal reactive dispatch problem is a nonlinear programming problem containing continuous and discrete control variables. Owing to the difficulty caused by discrete variables, this problem is usually solved assuming all variables as continuous variables, therefore the original discrete variables are rounded off to the closest discrete value. This approach may provide solutions far from optimal or even unfeasible solutions. This paper presents an efficient handling of discrete variables by penalty function so that the problem becomes continuous and differentiable. Simulations with the IEEE test systems were performed showing the efficiency of the proposed approach. © 1969-2012 IEEE.

Fluxo de potência ótimo reativo via método da função lagrangiana barreira modificada

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

Transmission system expansion planning by an extended genetic algorithm

The paper presents an extended genetic algorithm for solving the optimal transmission network expansion planning problem. Two main improvements have been introduced in the genetic algorithm: (a) initial population obtained by conventional optimisation based methods; (b) mutation approach inspired in the simulated annealing technique, the proposed method is general in the sense that it does not assume any particular property of the problem being solved, such as linearity or convexity. Excellent performance is reported in the test results section of the paper for a difficult large-scale real-life problem: a substantial reduction in investment costs has been obtained with regard to previous solutions obtained via conventional optimisation methods and simulated annealing algorithms; statistical comparison procedures have been employed in benchmarking different versions of the genetic algorithm and simulated annealing methods.

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.

Transmission network expansion planning considering uncertainty in demand

This paper presents two mathematical models and one methodology to solve a transmission network expansion planning problem considering uncertainty in demand. The first model analyzed the uncertainty in the system as a whole; then, this model considers the uncertainty in the total demand of the power system. The second one analyzed the uncertainty in each load bus individually. The methodology used to solve the problem, finds the optimal transmission network expansion plan that allows the power system to operate adequately in an environment with uncertainty. The models presented are solved using a specialized genetic algorithm. The results obtained for several known systems from literature show that cheaper plans can be found satisfying the uncertainty in demand.

Transmission network expansion planning in full open market considering security constraints

This paper presents a mathematical model and a methodology to solve the transmission network expansion planning problem with security constraints in full competitive market, assuming that all generation programming plans present in the system operation are known. The methodology let us find an optimal transmission network expansion plan that allows the power system to operate adequately in each one of the generation programming plans specified in the full competitive market case, including a single contingency situation with generation rescheduling using the security (n-1) criterion. In this context, the centralized expansion planning with security constraints and the expansion planning in full competitive market are subsets of the proposal presented in this paper. The model provides a solution using a genetic algorithm designed to efficiently solve the reliable expansion planning in full competitive market. The results obtained for several known systems from the literature show the excellent performance of the proposed methodology.

A resolução do problema de despacho ótimo de reativos pelo método da função Lagrangiana-barreira relaxada

This work presents the application of the relaxed barrier-Lagrangian function method to the optimal reactive dispatch problem, which is a nonlinear nonconvex and large problem. In this approach the inequality constraints are treated by the association of modified barrier and primal-dual logarithmic barrier method. Those constraints are transformed in equalities through positive auxiliary variables and are perturbed by the barrier parameter. A Lagrangian function is associated to the modified problem. The first-order necessary conditions are applied generating a non-linear system which is solved by Newton's method. The auxiliary variables perturbation result in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reach. Numeric tests with the systems CESP 53 buses and the south-southeast Brazilian and the comparative test with the primal-dual logarithmic barrier method indicate that presented method is efficient in the resolution of optimal reactive dispatch problem.

Transmission network expansion planning considering uncertainty in generation and demand

This paper presents a mathematical model and a methodology to solve a transmission network expansion planning problem considering uncertainty in demand and generation. The methodology used to solve the problem, finds the optimal transmission network expansion plan that allows the power system to operate adequately in an environment with uncertainty. The model presented results in an optimization problem that is solved using a specialized genetic algorithm. The results obtained for known systems from the literature show that cheaper plans can be found satisfying the uncertainty in demand and generation. ©2008 IEEE.