Solution Of Power Flow Equations Research Articles

Compressed Newton-Raphson Method for Power Flow Analysis in DC Traction Network

In this letter, a compressed Newton-Raphson (CNR) method is presented to achieve a high efficient and fast convergent result of power flow analysis of general DC traction network (DCTN). Due to CNR method, the higher-order Jacobian matrix of power flow equation is compressed as a 2-by-2 matrix, which can be calculated by the automatic differentiation technique. As a result, the proposed method has a quadratic convergent speed and a linear computational complexity of every iteration simultaneously. Under ill condition, a high precision solution of power flow equation also can be obtained by CNR method. Finally, the numerical simulation shows the effectiveness and advantages of the proposed method.

Locating all real solutions of power flow equations: a convex optimisation‐based method

This paper proposes a convex optimization based method that either locates all real roots of a set of power flow equations or declares no real solution exists in the given area. In the proposed method, solving the power flow equations is reformulated as a global optimization problem (GPF for short) that minimizes the sum of slack variables. All the global minima of GPF with a zero objective value have a one-to-one correspondence to the real roots of power flow equations. By solving a relaxed version of GPF over a hypercube, if the optimal value is strictly positive, there is no solution in this area and the hypercube is discarded. Otherwise the hypercube is further divided into smaller ones. This procedure repeats recursively until all the real roots are located in small enough hypercubes through the successive refinement of the feasible region embedded in a bisection paradigm. This method is desired in a number of power system security assessment applications, for instance, the transient stability analysis as well as voltage stability analysis, where the closest unstable equilibrium and all Type-I unstable equilibrium is required, respectively. The effectiveness of the proposed method is verified by analyzing several test systems.

Transversality enforced Newton–Raphson algorithm for fast calculation of maximum loadability

The authors propose a novel modification of the conventional Newton–Raphson load flow solver for characterisation of the maximal system loadability. Within the proposed approach, the standard power flow equations are extended with (i) an algebraic representation of maximal and minimal voltage level conditions and (ii) with the so-called transversality condition restricting the set of solutions to the boundary of the solvability region. Solutions to this extended system of equation characterise the maximal load levels for which the solution of power flow equations exists and satisfies the standard feasibility constraints on voltage levels. The resulting system of equations is non-singular and can be solved with just a few standard Newton–Raphson type iterations. Different possible choices of transversality conditions are discussed together with fast algorithms for evaluating the transversality conditions and their gradients. Implementation of the algorithm is described in detail, and its performance is validated on several IEEE cases.

Control of a Detailed Model of Microgrids from a Hamiltonian Approach

Using a well-known Passivity-based controller, in this paper is considered a stabilization scheme that explicitly includes the structure of the network and the dynamics of the power converters, features that are not usually found in the reported results. In addition, a procedure that does not rely on the solution of power flow equations is presented, guaranteeing satisfaction of load power demand with a limited capacity of some of the sources. The usefulness of the proposed control strategy is illustrated via a numerical evaluation although it is also recognized that further work is required in order to fully formalize their properties.

Numerical polynomial homotopy continuation method to locate all the power flow solutions

The manuscript addresses the problem of finding all solutions of power flow equations or other similar non-linear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly the direct methods for transient stability analysis and voltage stability assessment. Here, the authors introduce a novel form of homotopy continuation method called the numerical polynomial homotopy continuation method that is mathematically guaranteed to find all the solutions without ever encountering a bifurcation. Since finding real solutions is much more challenging, first the authors embed the real form of power flow equation in complex space, and then track the generally unphysical solutions with complex values of real and imaginary parts of the voltages. The solutions converge to physical real form in the end of the homotopy. The so-called gamma-trick mathematically rigorously ensures that all the paths are well-behaved along the paths, so unlike other continuation approaches, no special handling of bifurcations is necessary. The method is embarrassingly parallelisable. The authors demonstrate the technique performance by solving several test cases up to the 14 buses. Finally, they discuss possible strategies for scaling the method to large size systems, and propose several applications for security assessments.

Derivation of Distributed Generation Impact Factor in a Networked System in Case of Simultaneous Outputs of Multiple Generation Sites

A new measure, the distributed generation impact factor (DGIF), is used for evaluating the impact of newly introduced distributed generators on a networked distribution or a transmission system. Distribution systems are normally operated in a radial structure. But the introduction of distributed generation needs load flow calculation to analyze the networked system. In the developed framework, the potential share of every generation bus in each line flow of a networked system can be directly evaluated. The developed index does not require the solution of power flow equations to evaluate the effect of the distributed generation. The main advantage of the developed method lies in its capability of considering simultaneous outputs of multiple generation sites.

Numerical solution of the power flow equation in step-index plastic optical fibers

The numerical solution of the complete power flow equation is reported and employed to investigate the state of mode coupling along a step-index plastic optical fiber. This solution is based on the explicit finite-difference method and, in contrast to earlier solutions, does not neglect absorption and scattering loss. It is the only solution that can accommodate any input condition throughout the entire range of feasible input angles without the need for restriction to those angles that are sufficiently far away from critical. Our results for the field patterns at different locations along one type of fiber are in agreement with reported measurements earlier. Furthermore, the length of fiber required for achieving a steady-state mode distribution matches the analytical solution that is available for such distribution as a special case. Mode coupling in plastic fibers is known to affect fiber-optic power delivery, data transmission, and sensing systems.

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.

Practical complex solution of power flow equations

This paper applies and illustrates the compact, complex notation introduced by Bandler and El-Kady to the practical solution of the power flow equations. The solution of the complex linearized power flow equations, which is required by the Newton-Raphson method, is obtained by a direct method. The method, fully and exactly, incorporates generator buses as well as dummy load buses.

A New Method for Computerized Solution of Power Flow Equations

We employ an adjoint network concept based on an augmented form of Tellegen's theorem to describe a novel method for solving the load flow problem. The method incorporates successive adjoint network simulations with a sparse, mostly constant matrix of coefficients, the majority of its elements representing basic data of the problem already stored in computer memory. Nevertheless, the exact version of the method enjoys the same rate of convergence as the Newton-Raphson method. Moreover, it automatically supplies the sensitivities of all system states with respect to adjustable variables at the load flow solution without any additional adjoint simulation. An approximate version of the method is also presented. It partly employs very fast repeat forward and backward substitutions with constant LU factors of a reduced matrix of coefficients and is applicable to both the rectangular and the polar formulations of the power flow equations. Numerical examples are presented for illustration and comparison.

A New Method for Computerized Solution of Power Flow Equations

A New Method for Computerized Solution of Power Flow Equations