Optimal reactive power flow via the modified barrier Lagrangian function approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of the supply of reactive power in the calculation of the transfer capability

This paper presents some initial concepts for including reactive power in linear methods for computing Available Transfer Capability (ATC). It is proposed an approximation for the reactive power flows computation that uses the exact circle equations for the transmission line complex flow, and then it is determined the ATC using active power distribution factors. The transfer capability can be increased using the sensitivities of flow that show the best group of buses which can have their reactive power injection modified in order to remove the overload in the transmission lines. The results of the ATC computation and of the use of the sensitivities of flow are presented using the Cigré 32-bus system. © 2004 IEEE.

An unequivocal normalization-based paradigm to solve dynamic economic and emission active-reactive OPF (optimal power flow)

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

Despacho ótimo de potências ativa e reativa de sistema elétricos multi-áreas considerando restrições físicas, econômicas e ambientais =: Envronmentally constrained active-reactive optimal power flow-a compromising strategy for economic-emission dispatch and a multi-area paradigm

Pós-graduação em Engenharia Elétrica - FEIS

Interior-exterior point method with global convergence strategy for solving the reactive optimal power flow problem

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q-theta decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either theta or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus (Q(PV)) as continuation parameter (mu) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used in predictor step. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approach for the IEEE test systems (14, 30, 57 and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. (C) 2003 Elsevier B.V. All rights reserved.

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part II. Performance evaluation

The parameterized fast decoupled power flow (PFDPF), versions XB and BX, using either theta or V as a parameter have been proposed by the authors in Part I of this paper. The use of reactive power injection of a selected PVbus (Q(PV)) as the continuation parameter for the computation of the maximum loading point (MLP) was also investigated. In this paper, the proposed versions obtained only with small modifications of the conventional one are used for the computation of the MLP of IEEE test systems (14, 30, 57 and 118 buses). These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approaches are presented and discussed. The results show that the characteristics of the conventional FDPF method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that these versions can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. A trivial secant predictor, the modified zero-order polynomial, which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used for the predictor step. (C) 2003 Elsevier B.V. All rights reserved.

Continuation fast decoupled power flow with secant predictor

The conventional Newton and fast decoupled power flow methods are considered inadequate for obtaining the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. At this point, the Jacobian matrix of the Newton method becomes singular. In addition, it is widely accepted that the P-V and Q-theta decoupling assumptions made for the fast decoupled power flow formulation no longer hold. However, in this paper, it is presented a new fast decoupled power flow that becomes adequate for the computation of the maximum loading point by simply using the reactive power injection of a selected PV bus as a continuation parameter. Besides, fast decoupled methods using V and 0 as parameters and a secant predictor are also presented. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained for the IEEE systems (14 and 118 buses) show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged.

Alternative parameters for the continuation power flow method

The conventional Newton's method has been considered inadequate to obtain the maximum loading point (MLP) of power systems. It is due to the Jacobian matrix singularity at this point. However, the MLP can be efficiently computed through parameterization techniques of continuation methods. This paper presents and tests new parameterization schemes, namely the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, the reactive power at shunts (capacitor or reactor), the transmission lines power losses (real and reactive), and transmission lines power (real and reactive). Besides their clear physical meaning, which makes easier the development and application of continuation methods for power systems analysis, the main advantage of some of the proposed parameters is that its not necessary to change the parameter in the vicinity of the MLP. Studies on the new parameterization schemes performed on the IEEE 118 buses system show that the ill-conditioning problems at and near the MLP are eliminated. So, the characteristics of the conventional Newton's method are not only preserved but also improved. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Power flow for primary distribution networks considering uncertainty in demand and user connection

This paper presents a method for calculating the power flow in distribution networks considering uncertainties in the distribution system. Active and reactive power are used as uncertain variables and probabilistically modeled through probability distribution functions. Uncertainty about the connection of the users with the different feeders is also considered. A Monte Carlo simulation is used to generate the possible load scenarios of the users. The results of the power flow considering uncertainty are the mean values and standard deviations of the variables of interest (voltages in all nodes, active and reactive power flows, etc.), giving the user valuable information about how the network will behave under uncertainty rather than the traditional fixed values at one point in time. The method is tested using real data from a primary feeder system, and results are presented considering uncertainty in demand and also in the connection. To demonstrate the usefulness of the approach, the results are then used in a probabilistic risk analysis to identify potential problems of undervoltage in distribution systems. (C) 2012 Elsevier Ltd. All rights reserved.

Study of alternative schemes for the parameterization step of the continuation power flow method based on physical parameters, part I: Mathematical modeling

The conventional power flow method is considered to be inadequate to obtain the maximum loading point because of the singularity of Jacobian matrix. Continuation methods are efficient tools for solving this kind of problem since different parameterization schemes can be used to avoid such ill-conditioning problems. This paper presents the details of new schemes for the parameterization step of the continuation power flow method. The new parameterization options are based on physical parameters, namely, the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, and transmission line power losses (real and reactive). The simulation results obtained with the new approach for the IEEE test systems (14, 30, 57, and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are not only preserved but also improved.