Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

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.

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.

Real power losses reduction and loading margin improvement via continuation method

This letter presents an alternative approach for reducing the total real power losses by using a continuation method. Results for two simple test systems and for the IEEE 57-bus system show that this procedure results in larger voltage stability margin. Besides, the reduction of real power losses obtained with this procedure leads to significant money savings and, simultaneously, to voltage profile improvement. Comparison between the solution of an optimal power flow and the proposed method shows that the latter can provide near optimal results and so, it can be a reasonable alternative to power system voltage stability enhancement.

An Improved Parameterization Technique for the Continuation Power Flow

Continuation methods have been long used in P-V curve tracing due to their efficiency in the resolution of ill-conditioned cases, with close to singular Jacobian matrices, such as the maximum loading point of power systems. Several parameterization techniques have been proposed to avoid matrix singularity and successfully solve those cases. This paper presents a simple geometric parameterization technique to overcome the singularity of the Jacobian matrix by the addition of a line equations located at the plane determined by a bus voltage magnitude and the loading factor. This technique enlarges the set of voltage variables that can be used to whole P-V curve tracing, without ill-conditioning problems and no need of parameter changes. Simulation results, obtained for large realistic Brazilian and American power systems, show that the robustness and efficiency of the conventional power flow are not only preserved but also improved.

Improved geometric parameterisation techniques for continuation power flow

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Parameterization Technique for the Continuation Power Flow Developed from the Analysis of Power Flow Curves

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Study of alternative schemes for the parameterization step of the continuation power flow method based on physical parameters, part II: Performance evaluation

New parameterization schemes have been proposed by the authors in Part I of this paper. In this part these new options for the parameterization of power flow equations are tested, namely, the total power losses (real and reactive), the power at the slack bus (real or reactive), the reactive power at generation buses, and the transmission line power losses (real and reactive). These different parameterization schemes can be used to obtain the maximum loading point without ill-conditioning problems, once the singularity of Jacobian matrix is avoided. The results obtained with the new approach for the IEEE test systems (14, 30, 57, and 118 buses) show that the characteristics of the conventional method are not only preserved but also improved. In addition, it is shown that the proposed method and the conventional one can be switched during the tracing of PV curves to determine, with few iterations, all points of the PV curve. Several tests were also carried out to compare the performance of the proposed parameterization schemes for the continuation power flow method with the use of both the secant and tangent predictors.

An efficient geometric parameterization technique for the continuation power flow

Continuation methods have been shown as efficient tools for solving ill-conditioned cases, with close to singular Jacobian matrices, such as the maximum loading point of power systems. Some parameterization techniques have been proposed to avoid matrix singularity and successfully solve those cases. This paper presents a new geometric parameterization scheme that allows the complete tracing of the P-V curves without ill-conditioning problems. The proposed technique associates robustness to simplicity and, it is of easy understanding. The Jacobian matrix singularity is avoided by the addition of a line equation, which passes through a point in the plane determined by the total real power losses and loading factor. These two parameters have clear physical meaning. The application of this new technique to the IEEE systems (14, 30, 57, 118 and 300 buses) shows that the best characteristics of the conventional Newton's method are not only preserved but also improved. (C) 2006 Elsevier B.V. All rights reserved.

Power flow in distribution networks with earth return

The problems of wave propagation and power flow in the distribution network composed of an overhead wire parallel to the surface of the ground have not been satisfactorily solved. While a complete solution of the actual problem is impossible, as it is explained in the famous Carson's paper (1926), the solution of the problem, where the actual earth is replaced by a plane homogenous semi-infinite solid, is of considerable interest. In this paper, a power flow algorithm in distribution networks with earth return, based on backward-forward technique, is discussed. In this novel use of the technique, the ground is explicitly represented. In addition, an iterative method for determining impedance for modelling ground effect in the extended power flow algorithm is suggested. Results obtained from single-wire and three-wire studies using IEEE test networks are presented and discussed. (C) 2003 Elsevier Ltd. All rights reserved.

Power flow in four-wire distribution networks - General approach

The neutral wire in most power flow software is usually merged into phase wires using Kron's reduction. Since the neutral wire and the ground are not explicitly represented, neutral wire and ground currents and voltages remain unknown. In some applications, like power quality and safety analyses, loss analysis, etc., knowing the neutral wire and ground currents and voltages could be of special interest. In this paper, a general power flow algorithm for three-phase four-wire radial distribution networks, considering neutral grounding, based on backward-forward technique, is proposed. In this novel use of the technique, both the neutral wire and ground are explicitly represented. A problem of three-phase distribution system with earth return, as a special case of a four-wire network, is also elucidated. Results obtained from several case studies using medium- and low-voltage test feeders with unbalanced load, are presented and discussed.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.