Three-phase Unbalanced Distribution Systems Research Articles

Distributed Generator Placement And Sizing in Unbalanced Radial Distribution System

ABSTRACT To minimize power losses, it is important to determine the location and size of local generators to be placed in unbalanced power distribution systems. Because of some inherent features of unbalanced distribution systems, such as radial structure, large number of nodes, and a wide range of X/R ratios, the conventional techniques developed for the transmission systems generally fail to determine optimum size and location for distributed generation (DG). This article presents a simple method for investigating the problem of contemporaneously choosing the best location and capacity of DG in three-phase unbalanced radial distribution systems (URDS) for power loss minimization and to improve the voltage profile of the system. The best DG location is determined by using voltage index analysis, and capacity of DG is computed by a variational technique algorithm according to the available standard capacity of DG. This article presents the results of simulations for 25-bus and IEEE 37-bus unbalanced radial distribution system.

A Probability Method for Very Short-Term Steady State Analysis of a Distribution System with Wind Farms

In this paper, a probabilistic method is proposed to analyze the very short-term steady-state performance of an unbalanced distribution electrical system characterized by the presence of wind farms. This method, which can take into account the uncertainties of loads and wind productions, is based on a Monte Carlo simulation procedure applied to the non-linear three-phase load flow equations, including wind farm models. Bayesian time series models are used to predict the next hour's wind speed probability density functions, making possible a predictive evaluation of the very short-term system steady-state behavior. Numerical applications are presented and discussed with reference to the three-phase unbalanced IEEE 34-bus test distribution system in the presence of wind farms connected at different busbars.

Loss Partitioning and Loss Allocation in Three-Phase Radial Distribution Systems With Distributed Generation

In this paper, the concepts related to loss partitioning among the phase currents in three-phase distribution systems are revisited in the light of new findings identified by the authors. In particular, the presence of a paradox in the classical loss partitioning approach, based on the use of the phase-by-phase difference between the input and output complex power, is highlighted. The conditions for performing effective loss partitioning without the occurrence of the paradox are thus established. The corresponding results are then used to extend the branch current decomposition loss allocation method for enabling its application to three-phase unbalanced distribution systems with distributed generation. Several numerical examples on a three-phase line with grounded neutral and on the modified IEEE 13-node test system are provided to assist the illustration and discussion of the novel conceptual framework.

Probabilistic three-phase load flow for unbalanced electrical distribution systems with wind farms

A probabilistic method is proposed to take into account the uncertainties of loads and wind production in electrical unbalanced distribution systems. The proposed method is based on Monte-Carlo simulation applied to the nonlinear three-phase load flow equations including wind farms, thereby taking into account all load and line unbalances that can characterise the distribution systems. The method allows the evaluation of phase-voltage and unbalance factor probability functions and in particular the maximum values and 95th percentiles, being the statistical measures of greatest interest in many international standards for power quality. Numerical applications are presented and discussed with reference to the three-phase unbalanced IEEE 34-bus test distribution system in presence of wind farms connected at different busbars.

Voltage Regulators and Capacitor Placement in Three-phase Distribution Systems with Non-linear and Unbalanced Loads

This paper investigates the problem of contemporaneously choosing optimal locations and sizes for both shunt capacitors and series voltage regulators in three-phase unbalanced distribution systems. The sizing and placement procedure not only minimizes the power losses along distribution feeders but also makes sure that both capacitors and series regulators will have the minimum possible impact on the harmonic distortion of bus voltages in the system. The fact that distribution systems can operate under unbalanced loading conditions means that the optimization will have to account for any unbalances in the system. A genetic algorithm, which successfully solves the above-described problem, is developed and tested. This paper presents the results of simulations for a 34-bus IEEE distribution test system.

Consideration of Input Parameter Uncertainties in Load Flow Solution of Three-Phase Unbalanced Radial Distribution System

In this paper, a technique based on interval arithmetic is presented for considering the uncertainties of the input parameters in the power flow solution of three-phase unbalanced radial distribution systems. The uncertainties in both the load demand and the feeder parameters have been considered. The results obtained from an interval arithmetic-based power flow solution have been compared with those obtained from repeated load flow simulations

Modeling and analysis of unbalanced distribution system using object-oriented methodology

An object-oriented (OO) model for three-phase unbalanced distribution system is proposed and implemented. Single-phase system components are initially modeled using object-oriented methodology. Later, it is extended to unbalanced three-phase distribution system using the “composition” technique of object-oriented design. The main features of object-oriented methodology such as “inheritance”, “aggregation”, “association” and “polymorphism” have been exploited to obtain a better software model. Three-phase distribution load flow analysis and short circuit analysis modules have been developed using the proposed object model. The performance of the developed software has been tested on IEEE 13-Node, IEEE 34-Node and IEEE 123-Node distribution systems.

Transformer and load modeling in short circuit analysis for distribution systems

Accuracy of short circuit analysis depends on the modeling of transformers and loads. This paper addresses implementation of various transformer and load models in a short-circuit analysis for three-phase unbalanced distribution systems. Detailed transformer models are derived and incorporated into a production grade short circuit program with three different load models. Our studies show that different transformer connections, load models, and loading conditions may have significant impact on post-fault currents and voltages. Some test results on PG&E distribution feeders are presented.

State estimation for distribution systems with zero-injection constraints

In this paper, a new fast decoupled state estimator with equality constraints is proposed for the three-phase distribution systems. The Lagrange multipliers were utilized to deal with the zero injections. The proposed method is based on the equivalent-current-measurement and rectangular coordinates. The method uses a compact constant-symmetric gain matrix which can be decoupled into two "identical" sub-gain matrices. The update and factorization of the gain matrix needs to be done only once. Tests have shown that the proposed low-storage method is efficient, accurate and robust in solving the unbalanced three-phase distribution systems.

Optimal capacitor placement, replacement and control in large-scale unbalanced distribution systems: system solution algorithms and numerical studies

This paper develops an effective and, yet, practical solution methodology for optimal capacitor placement, replacement and control in large-scale unbalanced, general radial or loop distribution systems. The solution methodology can optimally determine: (i) the locations to install (or replace, or remove) capacitors; (ii) the types and sizes of capacitors to be installed (or replaced); and (iii) during each load level, the control schemes for each capacitor in the nodes of a general three-phase unbalanced distribution system such that a desired objective function is minimized while the load constraints, network constraints and operational constraints at different load levels are satisfied. The solution methodology is based on a combination of the simulated annealing technique and the greedy search technique in order to achieve computational speed and high-quality of solutions. Both the numerical and implementational aspects of the solution methodology are detailed. Analysis of the computational complexity of the solution algorithm indicates that the algorithm is also effective for large-scale distribution systems in terms of computational efforts. Test results on a realistic, unbalanced distribution network, a 291-bus with 77 laterals, 305 distribution lines and 6 transformers, with varying loading conditions, are presented with promising results. The robustness of the solution methodology under varying loading conditions is also investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal capacitor placement, replacement and control in large-scale unbalanced distribution systems: modeling and a new formulation

This paper undertakes the problem of optimal capacitor placement, replacement and control in large-scale unbalanced, radial or loop distribution networks. The problem is how to optimally determine the locations to install (or replace, or remove) capacitors, the types and sizes of capacitors to be installed (or replaced) and, during each load level, the control schemes for each capacitor in the nodes of a general three-phase unbalanced distribution system such that a desired objective function is minimized while the load constraints, network constraints and operational constraints (e.g. the voltage profile) at different load levels are satisfied. The objective function considered consists of two terms: cost for energy loss; and cost related to capacitor purchase, capacitor installation, capacitor replacement and capacitor removal. Comprehensive modelings of different components are presented which include primary power networks, three-phase transformers (different winding connections, off-nominal tap ratio, core and copper losses), cogenerators, voltage sensitive load models for single-phase, two-phase and three-phase loads, shunt capacitors and reactors. The new problem is formulated as a combinatorial optimization problem with a nondifferentiable objective function. The configuration space essential in the design of a annealing-based solution methodology for the new problem is derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A fault-induced transient analysis of unbalanced distribution systems with harmonic distortion

Abstract This paper presents a new method to calculate a fault-induced transient in an unbalanced three-phase distribution system, subjected to a shunt fault and/or a series fault, using the three-phase bus impendance matrix. The method is also applicable to multiple faults which involve a shunt fault and an open conductor. The imbalance caused by large single-phase loads, untransposed feeders, conductor bundles, etc., is reflected in the polyphase bus impedance matrix. Consequently, line removals, additions, impedance changes, conductor and phase openings can be simulated by modifying the base-case impedance matrix in the complex frequency domain. Thus, the proposed method makes it possible to analyze any type of single or multiple fault-induced transient occurring anywhere in the system.

Three-phase modeling of unbalanced distribution systems during open conductors and/or shunt fault conditions using the bus impedance matrix

Abstract This paper presents a digital simulation technique for unbalanced three-phase distribution systems subjected to a shunt or a series fault. The method is also applicable to multiple faults which involve a shunt fault at one location and blown fuses or open conductors at another. The method utilizes the phase frame representation of network elements. The imbalance conditioned by large single-phase loads, untransposed feeders, conductor bundles, etc., is reflected in the polyphase impedance matrix. Consequently, line removals, additions, impedance changes, conductor and phase openings can be simulated by modifying the base-case impedance matrix. Thus, the proposed method makes it possible to analyze any type of single or multiple fault occurring anywhere in the system.