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Object-Oriented Load Flow for Radial and Weakly Meshed Distribution Networks Arturo Losi, Member, IEEE, and Mario Russo, Member, IEEE

Abstract—Object-oriented load flow modeling is presented for both radial and weakly meshed distribution systems. An OO algorithm based on the Newton–Raphson technique is proposed. In the object oriented formulation, some approximations to the full Jacobian matrix are introduced. Consequently, a detailed study of the convergence characteristics of the proposed object oriented algorithm is presented and some sufficient conditions for convergence are derived. Particular attention is paid to the relationship between the electrical parameters of the distribution system and the mathematical parameters that influence the convergence properties of the algorithm. The numerical results obtained in the case of some test systems give evidence of the features of the algorithm. Index Terms—Convergence of numerical methods, load flow analysis, Newton–Raphson method, object-oriented methods, object oriented programming, power distribution.

I. INTRODUCTION OAD flow analysis is a basic function in modern distribution management systems (DMSs) [1]. In literature, many methods and solving algorithms have been proposed for distribution load flow analysis. They can be essentially classified into three categories: direct methods, backward/forward sweep methods, and Newton–Raphson (NR)-based methods. Direct methods [2], [3] require the construction of an impedance matrix and the direct solution of some equations . These methods usually present a heavy in the form computational burden and require an accurate numbering of nodes and branches. On the other hand, these methods prove to converge also in the case of unbalanced systems and weakly meshed topologies. Backward/forward sweep methods are based on a Gauss-Seidel iterative technique. The basic method has been presented in [4]. The case of weakly meshed topologies is treated by breaking the loops and by applying the equivalent current injection (ECI) method to the break points. The approach in [4] has been extended to account for load dependency on the voltage amplitude in [5] and for unbalanced systems in [6]. Improvements of the computational efficiency of the algorithms have been proposed in [7]–[9]. The convergence characteristics of such methods have been studied in [10]. Backward/forward sweep methods usually present a slow convergence rate but each iteration is computationally efficient. The NR-based methods use the distribution load flow equations to derive voltage drop and power propagation along Manuscript received November 15, 2002. This work was supported by Ministero dell’ Istruzione, Universita e Ricérca (MIUR). The authors are with the Dipartimento di Ingegneria Industriale, Università degli Studi di Cassino, Cassino 03043, Italy (e-mail: russo@unicas.it). Digital Object Identifier 10.1109/TPWRS.2003.818600

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a radial distribution system [11]. The values of the active and reactive powers that are injected into the main section and into the laterals are corrected using the Jacobian matrix and the power errors at the terminal nodes. In [12], the convergence characteristics of the NR-based method have been studied in the case of radial networks. The method has been extended to unbalanced systems in [13] and improvements of the computational efficiency of the solving algorithms have been proposed in [14]–[16]. A hybrid NR-ECI approach has been proposed in [17] to cope with weakly meshed topologies. The NR-based method is applied to a radial network which is obtained by breaking the loops and applying the ECI method to the break points. Such hybrid method has been extended to unbalanced systems in [18]. Generally speaking, the NR-based methods present a high convergence rate but each iteration requires matrix computations. In conclusion, it can be stated that research...