Nonlinear Primal-dual Interior Point Research Articles

Performance analysis of Newton-Raphson Power flow computations based on Power and Current Mismatches

This work studies the performance of single-phase power flow computations implemented using vector-based Python scripting language. Two approaches are considered, namely the current mismatch and power mismatch based on Newton-Raphson method. Both approaches are developed using rectangular coordinates and tested through a variety of IEEE test systems modelling high voltage transmission networks. The computational burden and accuracy of both implementations are duly discussed. This work will be later incorporated into our vector-based Non-linear Primal-Dual Interior Point Method as constraints.

Multi-area Generation Dispatching Distributed Coordination and Optimization Algorithm

As the fast expansion and interconnection of power system, it makes higher requirements for Optimal Power Flow (OPF) calculation in modern power grid. A distributed coordination and optimization method is presented in this paper. Injection power equivalent of sub-system boundary bus is utilized to solve multi-area dispatching problem. Based on regional decomposition model, it decouples the integrated optimization and avoids complex computation of system parameters equivalent in conventional methods. Besides, it reduces the communication between different regions. The nonlinear primal-dual interior point method is used for optimization in each sub-system, outer coordination of boundary bus’s voltage correction is conducted to compute the optimized dispatching in the whole interconnected power system. Numerical simulations are taken in IEEE test systems. The results show that the proposed method is validated, effective and suitable for online application.

Decomposition–coordination interior point method and its application to multi-area optimal reactive power flow

A decomposition–coordination interior point method (DIPM) is presented and applied to the multi-area optimal reactive power flow (ORPF) problem in this paper. In the method, the area distributed ORPF problem is first formed by introducing duplicated border variables. Then the nonlinear primal dual interior point method (IPM) is directly applied to the distributed ORPF problem in which a Newton system with border-matrix-blocks is formulated. Finally the overall ORPF problem is solved in decomposition iterations with the Newton system being decoupled. The proposed DIPM inherits the good performance of the traditional IPM with a feature appropriate for distributed calculations among multiple areas. It can be easily extended to other distributed optimization problems of power systems. Numeric results of five IEEE Test Systems are demonstrated and comparisons are made with those obtained using the traditional auxiliary problem principle (APP) method. The results show that the DIPM for the multi-area OPRF problem requires less iterations and CPU time, has better stability in convergence, and reaches better optimality compared to the traditional auxiliary problem principle method.

Optimal wind-thermal coordination dispatch based on risk reserve constraints

This paper presents a dynamic economic dispatch (DED) model with large-scale wind power penetration. The uncertainties induced by generation forced outages, wind speed and load forecast errors are taken into consideration. In order to cater for any possible unexpected generation deficit, the spinning reserve constraints based on system risk are introduced. The study is aimed to schedule wind-powered and thermal generation under the condition of satisfying risk threshold and other technical constraints. With the assumption of normal distributions of wind speed and load forecast errors, the probabilistic constraints will be converted into deterministic inequality constraints. The DED issue modeled in the paper is solved by a nonlinear primal-dual interior-point (IP) method. A 10-generator system with one wind farm is tested to validate the effectiveness of the proposed model and method; analysis is also conducted to investigate the effect factors of the DED problem. Copyright © 2010 John Wiley & Sons, Ltd.

Wheeling cost influence in hydrothermal dispatch and series compensation allocation

This paper presents a methodology for optimizing both the transmission tariff and the thermal generation costs, considering the series compensation (SC) allocation problem in a multiperiod dispatch. The inclusion of the tariff cost in the objective function of the hydrothermal coordination problem can change the dispatch of remote hydro plants, especially if the SC is considered. The proposed methodology is important because the transmission cost tariff can affect the network users in a competitive environment. The OPF problem is based on the nonlinear primal-dual interior point technique associated with the Benders decomposition approach. The algorithm is tested using an equivalent of the southern system of Brazil and compared with existing techniques.

Optimal power flow solutions under variable load conditions

This work presents a methodology to calculate a sequence of optimal power flow (OPF) solutions under variable load conditions. The aim is to obtain a set of optimal operating points in the neighborhood of the bounds of the region defined by the load flow equations and a set of operational limits. For this, an algorithm based on the continuation method and on a primal-dual interior point optimization method is proposed. Such an algorithm consists of two main steps: the predictor step, which uses a linear approximation of the Karush-Kuhn-Tucker (KKT) conditions to estimate a new operating point for an increment in the system load; and the corrector step, which calculates the optimum corresponding to the new load level via a nonlinear primal-dual interior point method. Indices for critical buses and inequality constraints are a byproduct of the methodology. In addition, sensitivity analysis is performed to calculate the amount of reactive compensation which allows for a pre-specified increase in the system load. Results for realistic test systems are presented.