Optimal Reactive Power Flow Research Articles

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

Este artigo apresenta uma nova abordagem para a resolução do problema de Fluxo de Potência Ótimo Reativo. Nesta abordagem, as restrições de desigualdade são tratadas pela associação dos métodos de Barreira Modificada e Primal-Dual Barreira Logarítmica (PDBL). As restrições de desigualdade são transformadas em igualdades introduzindo variáveis de folga positivas e são relaxadas através do parâmetro de barreira. Uma função Lagrangiana é associada ao problema modificado. As condições necessárias de primeira ordem são aplicadas à função Lagrangiana, gerando um sistema de equações não-lineares, o qual é linearizado pelo método de Newton. A relaxação das variáveis de folga resulta na expansão da região factível do problema original, permitindo que os limites das restrições de desigualdade sejam atingidos. Testes numéricos utilizando os sistemas CESP-440kV e SUL-SUDESTE BRASILEIRO e um teste comparativo com o método PDBL indicam que a nova abordagem é eficiente na resolução do problema Fluxo de Potência Ótimo Reativo.

An Unfixed Piecewise-Optimal Reactive Power-Flow Model and its Algorithm for AC-DC Systems

A novel AC-DC optimal reactive power flow (ORPF) model with the generator capability limits is proposed. The objective is to minimize the total cost of generator reactive and active power outputs paid by an independent transmission company. In the model, the generator operation area is divided into four parts with each one having a different reactive output cost function. The boundaries between the four parts change with operation states of generators and are unfixed. The model is an unfixed piecewise mixed-integer nonlinear programming problem. A heuristic approach is introduced into the interior point method to solve the unfixed piecewise problem. The numerical results of six test systems that range in size from 14 to 2572 buses demonstrate the effectiveness of the proposed method.

Multi-objective optimal reactive power flow including voltage security and demand profile classification

This paper proposes a method to optimize reactive power flow (ORPF) with regard to multiple objectives while maintaining system voltage security across a time-domain. Compromise programming is employed in the ORPF formulation, which is designed to minimize both losses and payment for the reactive power service in the framework of the UK daily balancing market. In coordination with ORPF, continuation power flow (CPF) is applied to evaluate and maintain the voltage security margin of the system. Prior to the optimisation procedure, the related control parameters can be grouped with the aid of a load classification method in order to simplify the control actions. During the optimisation, through the application of both ORPF and CPF, multi-objective optimisation can be achieved with voltage security at an acceptable level. The Ward and Hale 6-bus system and a 60-bus UK test system are presented to illustrate the application of the proposed modeling framework.

Interior‐point methods applied to the AC active‐reactive optimal power‐flow problem using cartesian coordinates

AbstractThe primal dual interior point methods are developed to the AC active and reactive optimal power flow problem. The representation of the tensions through cartesian coordinates is adopted, once the Hessian is constant and the Taylor expansion is accurate for the second order term. The advantage of working with polar coordinates, that easily model the tension magnitudes, lose importance due to the efficient treatment of inequalities proportionated by the interior point methods. Before the application of the method, the number of variables of the problem is reduced through the elimination of free dual variables. This elimination does not modify the sparse pattern of the problem. The linear system obtained can be further reduced to the dimension of twice the number of buses also with minor changes in the sparse structure of the matrices involved. Moreover, the final matrix is symmetric in structure. This feature can be exploited reducing the computational effort per iteration. Computational experiments for IEEE system problems are presented for several starting point strategies showing the advantages of the proposed approach. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimal reactive power flow incorporating static voltage stability based on multi-objective adaptive immune algorithm

People have paid more attention to enhancing voltage stability margin since voltage collapses happened in some power systems recently. This paper proposes an optimal reactive power flow (ORPF) incorporating static voltage stability based on a multi-objective adaptive immune algorithm (MOAIA). The main idea of the proposed algorithm is to add two parts to an existing immune algorithm. The first part defines both partial affinity and global affinity to evaluate the antibody affinity to the multi-objective functions. The second part uses adaptive crossover, mutation and clone rates for antibodies to maintain the antibodies diversity. Hence, the proposed algorithm can achieve a dynamic balance between individual diversity and population convergence. The paper describes ORPF’s multi-objective functional mathematical model and the constraint conditions. The problems associated with the antibody are also discussed in detail. The proposed method has been tested in the IEEE-30 system and compared with IGA (immune genetic algorithm). The results show that the proposed algorithm has improved performance over the IGA.

Quadratic models of AC–DC power flow and optimal reactive power flow with HVDC and UPFC controls

Quadratic models of power flow (PF) and optimal reactive power flow (ORPF) for AC–DC power systems are proposed in the paper. Voltage magnitudes at the two sides of ideal converter transformers are used as additional state variables to build the quadratic models. Effects of converter controls on equality constraints are considered. The quadratic expression of unified power flow controller (UPFC) is also developed and incorporated into the proposed models. The proposed PF model retaining nonlinearity has a better convergence feature and requires less CPU time compared to traditional PF models. The Hessian matrices in the quadratic AC–DC ORPF model are constant and need to be calculated only once in the entire optimization process, which speeds up the calculation greatly. Results obtained from the four IEEE test systems and an actual utility system indicate that the proposed quadratic models achieve a superior performance than conventional models.

Parallel Optimal Reactive Power Flow Based on Cooperative Co-Evolutionary Differential Evolution and Power System Decomposition

Differential evolution (DE) is a promising evolutionary algorithm for solving optimal reactive power flow problems, but it requires relatively large population to avoid premature convergence. In order to overcome this disadvantage, a novel decomposition and coordination method based on the cooperative co-evolutionary architecture and the voltage-var sensitivity-based power system decomposition technique is proposed and incorporated with DE in this paper. It is implemented with a three-level parallel computing topology on a PC-cluster. Based on the IEEE 118-bus system test case, the effectiveness of the proposed method has been verified by comparison with the parallel basic DE not using the decomposition and coordination technique

Study of differential evolution for optimal reactive power flow

Differential evolution (DE) is studied in detail for optimal reactive power flow (ORPF) problems. The concept, mechanism, and parameter setting of DE are discussed. Based on the IEEE 14-, 30- and 57-bus system test cases, DE is compared with some basic or improved evolutionary algorithms that have been applied to ORPF. It is found that DE is generally a good algorithm for ORPF and worthy of more attention. However, it is also found that DE requires relatively large populations to avoid premature convergence. The impact of this shortcoming is made clear in the IEEE 118-bus system test case. The effectiveness of parallel computing technology for speeding up the computation of DE-based ORPF is also analysed.

A Hybrid Genetic Algorithm–Interior Point Method for Optimal Reactive Power Flow

By integrating a genetic algorithm (GA) with a nonlinear interior point method (IPM), a novel hybrid method for the optimal reactive power flow (ORPF) problem is proposed in this paper. The proposed method can be mainly divided into two parts. The first part is to solve the ORPF with the IPM by relaxing the discrete variables. The second part is to decompose the original ORPF into two sub-problems: continuous optimization and discrete optimization. The GA is used to solve the discrete optimization with the continuous variables being fixed, whereas the IPM solves the continuous optimization with the discrete variables being constant. The optimal solution can be obtained by solving the two sub-problems alternately. A dynamic adjustment strategy is also proposed to make the GA and the IPM to complement each other and to enhance the efficiency of the hybrid proposed method. Numerical simulations on the IEEE 30-bus, IEEE 118-bus and Chongqing 161-bus test systems illustrate that the proposed hybrid method is efficient for the ORPF problem

A new optimal reactive power flow model in rectangular form and its solution by predictor corrector primal dual interior point method

A new optimal reactive power flow (ORPF) model in rectangular form is proposed in this paper. In this model, the load tap changing (LTC) transformer branch is represented by an ideal transformer and its series impedance with a dummy node located between them. The voltages of the two sides of the ideal transformer are then used to replace the turn ratio of the LTC so that the ORPF model becomes quadratic. The Hessian matrices in this model are constants and need to be calculated only once in the entire optimal process, which speed up the calculation greatly. The solution of the ORPF problem by the predictor corrector primal dual interior point method is described in this paper. Two separate prototypes for the new and the conventional methods are developed in MATLAB in order to compare the performances. The results obtained from the implemented seven test systems ranging from 14 to 1338 buses indicate that the proposed method achieves a superior performance than the conventional rectangular coordinate-based ORPF.

Comparison and improvement of evolutionary programming techniques for power system optimal reactive power flow

Some recently developed evolutionary programming (EP) techniques for the optimal reactive power flow (ORPF) problem are investigated. By comparing the performances of four control schemes of the strategy parameter (CSSPs), two principles for designing effective CSSPs are identified and are further used to develop two improved CSSPs. The effectiveness of the Levy distribution based technique of adaptive fast EP is also studied. The investigations are conducted with simulations on the ORPF problems of the IEEE 14-, 30- and 118-bus standard test systems.

Optimal Reactive Power Flow ( Orpf ) Program for Voltage Profile Enhancement and Loss Minimization

Optimal Reactive Power Flow ( Orpf ) Program for Voltage Profile Enhancement and Loss Minimization

Reactive optimal power flow incorporating margin enhancement constraints with nonlinear interior point method

A reactive optimal power flow incorporating margin enhancement constraints is described. Margin sensitivity at a steady-state voltage instability point is calculated using invariant space parametric sensitivity, and can provide valuable information for selection of effective control parameters. However, weakest buses in neighbouring regions have high margin sensitivities in a certain range, so control determination using only the sensitivity information might cause violation of operational limits of the base operating point, at which the control is applied to enhance voltage stability margin in the direction of parameter increase. A nonlinear interior point method (NIPM) is applied to solve the optimal power flow formulation with margin enhancement constraints, and shunt capacitances are mainly considered as control variables. In the case study, an example applying the proposed method to the IEEE 118-bus test system is shown, and experiences with margin enhancement constraints are also included.

A two-step optimization method for increasing post-contingency loadability limits

In this paper, we propose a combined control strategy which is designed to improve the post-contingency loadability limits in the system. In the first step, the operating point is determined using a contingency constrained optimal reactive power flow, in which the cost function reflects the proximity of the reactive power generation to its limits at critical PV buses, both in the base case and for selected contingencies. This operating point is then used to design robust decentralized turbine/governor control, in the framework of linear matrix inequalities. Results obtained for the IEEE 39 bus system are provided to demonstrate the effectiveness of the proposed method.

Fuzzy OPF incorporating UPFC

A new optimal reactive power flow (ORPF) method is proposed which considers the inclusion of unified power flow controllers (UPFC). The modelling and inclusion of UPFC in the solution of power flow equations is presented. The ORPF problem is formulated as a fuzzy optimisation problem considering the objectives of minimising system transmission loss and obtaining the best voltage profile. The fuzzy formulation of the ORPF problem is solved using an EP algorithm. The proposed method is applied on the 6-bus and 57-bus IEEE test systems and on a 191-bus Indian electric power system. The results demonstrate the applicability of the method.

Real-time implementation of optimal reactive power flow

The application of optimal reactive power flow (ORPF) to the New Brunswick (NB) power system is presented. The potential benefits and the real-time implementation problems of ORPF are discussed. Some important issues of real-time implementation on ORPF, such as frequency of running, the number of activated control variables, and the order of adjustment of different controls, are discussed. The application of ORPF on the NB power network has shown two major benefits: (1) an improvement in the voltage profile and voltage stability, and (2) a saving in active power loss. The improvement in the voltage profile can cause fewer violations and a more stable system from the voltage point of view. A reduction in active power loss gained from ORPF can save a significant amount of money. The total ideal savings for the year 1997 predicted in the study was in excess of $900000, however, only 10 to 30% of this amount is realistically obtainable due to operational and other constraints. These savings can be gained simultaneously with the improvement of the voltage profiles.

A method for simulation and analysis of reactive power market

This paper presents a method for the simulation and analysis of alternative reactive power market arrangements based on combined reactive power capacity and energy payments. The value of reactive power support, in terms of both capability and utilisation, of each particular generator is quantified using a developed security constrained reactive optimal power flow. The relative competitiveness of participating generators is also assessed for a spectrum of arrangements between a reactive capacity and a reactive utilisation based market. Also, the conflicting objectives of the system operator, as a purchaser of reactive power service, and generators, as suppliers of the services, are analysed.

Contingency constrained optimal reactive power flow procedures for voltage control in planning and operation

The paper presents a preventive secure contingency constrained approach to power system voltage profile optimization suitable both for VAr planning and for short term reactive scheduling. The solution of the problems is based upon the implementation of two optimal reactive power flow (ORPF) programs: the first relevant to determining a workable state (security aspect); and the second relevant to attaining the optimal and secure point (global target). The first ORPF is solved by recursively employing a linear programming algorithm, whilst the second is based on the Han-Powell algorithm. In the paper, emphasis is given to the introduction of the contingency constraints in the ORPF models. The N-1 security constraints are explicitly introduced in the programs in order to obtain an operating point preventive-secure with respect to a selected contingency set. The performances of the procedures are shown by presenting the numerical results obtained from their applications to a small test network and to the large ENEL transmission system. >

Optimal power flow emulation of interchange brokerage systems using linear programming

The authors propose an interchange brokerage system based on an optimal power flow (OPF) solution using linear programming (LP). Interchange brokering schedules power imports and exports between interconnected electric utilities to maximize profits for all participating parties and enhances the security of power systems. The data required for interchange brokerage systems are the amount of power available for trading and the system incremental cost. An LP software package called STORM was used to solve the active and reactive OPF subproblems and the interchange brokerage systems. The steps required for the implementation and problems involved in loss minimization are considered. The development of LP theory for OPF and interchange brokerage systems and its limitations are discussed. The experimental results are included. >

System voltage and reactive power control: A computer-assisted manual/automatic concept

The paper describes a new computerassisted software concept for hierarchic control of voltages and reactive powers in the real-time operation of power systems. The concept uses the local and centralised control levels. The local level employs existing automatic or manually operated control devices on regulating resources. The centralised level applies a superimposed computerassisted manual control, based on reactive optimal power flow, with a dedicated criterion function dealing with system economy and security. An adaptive system zoning is incorporated in the concept, aimed at the matching, inherently local, character of voltage/reactive power control.