ابزار جدید برای تجزیه و تحلیل سیستم های الکتریکی چندفازی بر اساس روش تزریق فعلی

This work presents a new methodology for steady state analysis of multiphase electrical systems, the N Conductor Current Injection Method – NCIM. It is based on the current injection method in rectangular coordinates that is defined directly in phase coordinates and applies the Newton–Raphson method in the solution process. The method can be used to analyze any electrical power system. NCIM has the capability to represent many features, such as unbalances, mutual couplings, multi-phase feeders and devices including neutral conductors and groundings, distributed generations and control actions, in such a way that the total dimension of the system of equations is the minimum required to obtain the solution. The method can be applied to analyze both balanced and unbalanced systems, radial or meshed, and can simulate the interconnected transmission, subtransmission and distribution networks, including large-scale systems. NCIM is shown to be very efficient and computationally robust.

In the last years, the power system researchers have become more interested in a more detailed kind of modeling of diverse aspects of the electrical power systems. They are looking for more general methods that give more precise results, and that permit advanced analysis [1]. The three-phase analysis, for example, has been growing stronger, especially for distribution systems. More detailed studies have been demanded due to the great increase of the distributed generation (DG) and they have shown that the simulation of distribution and subtransmission together might be necessary. Looking for improvements, many three-phase methodologies have been proposed for state-steady analysis in electrical power systems [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16] and [17]. Each methodology has its own main applications, being that, particular characteristics and simplified models adopted can restrict the correct and precise use for just some electrical systems. Among the new methodologies of analysis, there is one line of research based on the current injection method. The Three-Phase Current Injection Method – TCIM [7] has been proposed focusing on three-phase systems. New very efficient routines have been developed to perform matrix ordering and factorization and thus TCIM has become very robust computationally, especially for meshed DS, as well as in the presence of control devices [18]. In 2008 the Four-Conductor Current Injection Method – FCIM was conceived to include the explicit representation of neutral conductors and groundings [19]. Both TCIM and FCIM were constructed based on blocked structures. For example, in FCIM all components and controls have an 8 × 8 fixed dimension block for the Jacobian matrix, even when the equipment does not have the four nodes (related to the a, b and c phases and the neutral). And because of the blocked structure it was difficult to represent a component with more than four nodes in the same busbar. This blocked structure increased the system’s dimension to be solved. The objective of this work was to develop a new and improved methodology that could take advantage of all of the good characteristics of the FCIM, however it should be more flexible, without the fixed block structure, thus the N-Conductor Current Injection Method (NCIM) was developed. The key to such improvements was to extend the methodology to multiphase systems and to attain enhanced flexibility both on equipment modeling and on the structure of the Jacobian matrix. The NCIM is a multiphase method in which component models are built on an element by element basis. Thus the contribution of each element or phase of any equipment will reflect its physical construction, so that the final dimension of the Jacobian matrix will be the minimum required to represent the system. The fixed submatrix block structures used before are no longer necessary. Compared with many current methodologies, the following may be cited as some of the advantages of NCIM: i. Deals directly with multiphase models, without the need for fixed blocked matrix representations, or sequence networks, or any other transformations or simplifications. ii. The dimension of the system of equations to be solved is always kept to the minimum. iii. Allows direct modeling of components that have asymmetric representative matrix. iv. Allows the representation of all types of loads, including between phases and between phase and neutral, which are very common elements in distribution systems. v. Generator models do not use conventional busbar types, allowing the representation of neutral groundings as well as different models for positive and negative sequence circuits. vi. Controlled operation and loads characteristics of induction motors can be represented. vii. The transformer model implemented does not use pre-defined matrices for each type of connection. The transformers are modeled from their own windings connections, which allows the representation of more complex types of transformers, for example, the wye-delta with a central tap, or a physical connection between the primary and secondary of the transformer, etc. viii. The line model is general, allowing the representation of mutual couplings between phases or between lines even if different voltage levels are in the same right-of-way, communication cables, guard cables, neutral cables, groundings, etc. It is important to emphasize that all of these representations can be done in the NCIM directly, without the need for additional calculations or extra iterative processes, which are common in many current methodologies. The NCIM is a general methodology and can be used to simulate all kinds of systems; radial or meshed, from unbalanced multiphase systems that have equipments with n conductors, to the pure one-phase (or positive sequence) representations. All of this should be done with the same algorithm allowing the system to be solved, to have equipments with all these characteristics at the same time. In this work, the proposed methodology, some equipment models and controls developed or improved for NCIM will be presented, as well as potential analysis.

This paper proposes a method for the solution and analyses of any electrical system. The method was called the N Conductor Current Injection Method – NCIM. The systems components modeling are made from its elements. This new flexible structure makes the formation of models easier. Especially for equipments with more complex configurations, that in some previous methods needed tricks or simplifications to be represented or even could not be represented. Also, this method contributes to the improvement of the solution process, as the system of equations to be solved by the proposed method will only have the strictly necessary dimension. Besides this the voltages and the currents of all elements can be directly calculated with the NCIM. Improvements were made in the equipment modeling. Using NCIM we can consider the representation of very detailed characteristics. New controls and models were defined too. The IEEE DSASC distribution test feeders [22], with all its details were correctly represented and simulated by the NCIM, and matched all the available results by the subcommittee. Other systems were also tested, being that in almost all tests done, the NCIM presented much computational robustness, needing few iterations to get the solution and with low simulation times. The NCIM shows to be especially useful in the representation and simulation of unbalanced distribution systems, where the representation or not of the details make a great difference in results. With the NCIM, more detailed analysis can be carried out as the method does not have limitations presented by many published methods. The good characteristics of convergence, together with the possibility of great representation of details of the systems, suggest that the NCIM can be very useful in DG inclusion studies and the analysis of its impacts in the electrical systems, as well as for smart-grids studies. Concluding, NCIM can be considered as a general method that can be used in the analysis of: balanced or unbalanced systems, radial and meshed systems, systems with n-conductors components, with controls, with distributed generations, etc. NCIM also can be used in transmission, subtransmission and distribution systems, being efficient and computational robust, including for large scale systems.