Large-scale Unbalanced Distribution Systems Research Articles

Machine Learning Based Method for Estimating Energy Losses in Large-Scale Unbalanced Distribution Systems with Photovoltaics

Machine Learning Based Method for Estimating Energy Losses in Large-Scale Unbalanced Distribution Systems with Photovoltaics

Capacitor placement and real time control in large-scale unbalanced distribution systems: numerical studies

A novel solution algorithm for capacitor placement and real-time control in real large-scale unbalanced distribution systems is evaluated and implemented to determine the number, locations, sizes, types and control schemes of capacitors to be placed on large-scale unbalanced distribution systems. A detailed numerical study regarding the solution algorithm in large scale unbalanced distribution systems is undertaken. Promising numerical results on both 292 bus and 394 bus real unbalanced distribution systems containing unbalanced loads and phasing and various types of transformers are presented, The computational performance for the capacitor control problem under load variations is encouraging.

Capacitor placement and real time control in large-scale unbalanced distribution systems: loss reduction formula, problem formulation, solution methodology and mathematical justification

A comprehensive study of capacitor placement and real-time control in general unbalanced distribution systems is undertaken. New developments in a loss reduction formula, problem formulations, solution methodology and mathematical justification are presented. The problem is decoupled into two subproblems: the capacitor placement subproblem; and the real-time control subproblem. An effective solution algorithm for placing capacitors and determining their real-time control schemes for general unbalanced distribution systems is proposed. To meet the need for efficient implementation in real-time environments, a fast pseudo gradient-type mechanism for deriving capacitor control settings is incorporated into the solution algorithms. A quadratic integer programming based approach is proposed to determine the number, locations and sizing of capacitors to be placed in the distribution systems. The subproblem of determining capacitor control settings under varying loading conditions is formulated as another quadratic integer programming problem. Mathematical justification is provided to show that the proposed algorithms are guaranteed to yield local optimal solutions.

Explicit loss formula, voltage formula and current flow formula for large-scale unbalanced distribution systems

Explicit formulas for determining system loss, current flows and voltages in terms of system and network data are developed for large-scale unbalanced distribution systems. The three-phase formulas consider multi-phase grounded or ungrounded loads and lines, cogenerators, multi-phase shunt elements and transformers of different connections all of which exist in large-scale unbalanced distribution systems. Test results on a number of distribution systems, including an actual 394-bus distribution network, are included to illustrate the accuracy and speed of the proposed formula for real-time analysis and control of distribution systems. It is shown numerically that the results given by these closed-form formulas are very close to those obtained by rigorous three-phase power flow methods. Applications of the explicit expressions to real-time control of distribution systems are also identified. Also, some features of the explicit formulas which are not possible with traditional power flow studies are discussed.

An efficient algorithm for real-time network reconfiguration in large scale unbalanced distribution systems

Real-time applications demand fast computation, this paper proposes an efficient algorithm for real-time network reconfiguration on large unbalanced distribution networks. A novel formulation of the network reconfiguration to achieve loss minimization and load balancing is given. To reduce computational requirements for the solution algorithm, well justified power flow and loss reduction formulas in terms of the on/off status of network switches are proposed for efficient system updating. The algorithm relies only on a few full power flow studies based on system states attained by explicit expressions using backward-forward sweeps for efficient computation of the system's states at the critical system operating points. The solution algorithm runs in an amount of time linearly proportional to the number of the switches and the number of sectionalizing switches in the system. The solution algorithm has been implemented into a software package and tested on unbalanced distribution systems including a system with 292-buses, 76-laterals, 7 transformers, 45 switches and 255 line sections under diverse system conditions.

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>

Three-phase modeling for transient stability of large scale unbalanced distribution systems

The authors propose a generalized method to analyze the transient stability by using the three-phase bus admittance matrix algorithm for any network configuration. The method takes into account the unbalance created by large single-phase loads, untransposed feeders, conductor bundles, and cables. Consequently, the effects of unsymmetrical shunt and/or series faults, as well as the addition or removal of single-phase feeders, can be simulated anywhere in the network. Also presented is a novel, general systematic technique of studying transient stability of unbalanced distribution systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Three-Phase Modeling for Transient Stability of Large Scale Unbalanced Distribution Systems

The transient stability of a distribution system containing rotating machines is usually evaluated by considering a symmetrical disturbance applied to a balanced network. Hence, most, if not all, available algorithms and stability programs use the bus admittance matrix for the positive sequence only. However, a typical distribution system may contain untransposed feeders, single-and/or three-phase unbalanced static shunt loads, single-and/or three-phase dynamic loads (such as induction motors), co-generators, transformers and capacitor banks. Furthermore, even if the network is balanced, unsymmetrical faults introduce unbalance. The effects of unbalances on the transient behavior of a single induction motor in a two-bus system using simultaneous nodal voltage equations has been recently investigated. It was concluded that a significant error may occur by replacing an unbalanced shunt load by an averaged balanced load and by assuming an unbalanced feeder to be an equivalent balanced feeder. This paper extends the previous investigation to large scale networks using a generalized three-phase bus admittance matrix [Ybus] method which takes care of the unbalances referred to above. Developing the three-phase [Ybus] itself is not new, but the novelty of the proposed method lies in the combination of the three-phase [Ybus] with the dynamics of rotating machines in transient stability studies of large networks using step-by-step integration of nonlinear differential equations. The method utilizes phase frame representation of network and machine elements. In order to be general, the computer program allows the user to include synchronous generators, induction motors, transformers, feeders and static loads.