This paper presents a new algorithm of accurate bus-wise transmission loss allocation based on path-integrals. With rigorous theoretical analysis, a new path-integral method is developed by integrating the partial differential of the system loss along a path reflecting the transaction strategy. This path-integral enables us to remarkably enhance the accuracy in loss allocation with full consideration of nonlinearity. The accuracy has been further improved by using the ac power flow. Determining the integral path is discussed to reflect various situations of the power market. Given an integral path, the proposed algorithm provides a unique and accurate solution to the loss allocation.

Transmission Loss Allocation Algorithm Using Path-Integral Based on Transaction Strategy

This paper explains the concept of dynamic line rating (DLR) and suggests the method to forecast the thermal rating. The weather parameters are modeled corresponding to each transmission line, and thermal overload probability (TOP) is estimated using the predicted weather models and the present DLR value. In particular, a statistical wind speed model is developed using time series with compensation. In the case study, it is confirmed that the predicted TOP should be utilized as the criterion that decides forecast rating (FR) in order to operate the transmission line reasonably. The proposed method would be useful to enhance security and reliability of the transmission line. Moreover, this study could provide a better insight into the system operation and control, especially now a days when deregulation and liberalization of transmission systems are introduced. Copyright © 2009 John Wiley & Sons, Ltd.

Prediction of transmission-line rating based on thermal overload probability using weather models

In the modern power system, transmission losses play an increasingly important role in determining the costs of transmission system operators, in particular in cross-border energy exchange. A variety of transmission losses calculation methods are present in scientific literature in recent years, but regularly neglecting the measurement uncertainty, which is an important contribution in calculating the final cost of exchanged energy. Due to the significant cost of transmission losses in total costs, all transmission system operators are interested in discovering the probabilistic nature of transmission losses as a fundamental requirement for finding the fair method for transmission losses allocation. In this paper, transmission losses are simulated on 110-kV cross-border transmission line using an adaptive Monte Carlo method. The probability density estimation procedure is performed by the non-linear least-squares method, using the Levenberg–Marquardt algorithm. The Gaussian, log-normal, Rayleigh, four-parameter beta, generalized trapezoidal, and the sum of uniform and normal distribution are fitted and the quality of the distribution estimates is compared according to the corresponding values of the Kolmogorov–Smirnov statistic. Furthermore, an additional example presents a distribution fitting procedure on the zero-impedance data of the same transmission line.

Non-Linear Least Squares and Maximum Likelihood Estimation of Probability Density Function of Cross-Border Transmission Losses

Economic dispatch (ED) is an optimisation tool that is used to allocate active load demands to the generating units through optimising the fuel generation cost function subject to the different operational constraints. The high non-linearity of the power system imposes mathematical challenges in formulating the generation cost function models, which makes the ED problem hard to solve. This study introduces two ideas to solve issues related to the ED problem. First, a dynamic formulation technique is developed to optimally allocate the change in the total active load demand to the generating units. This technique is shown to be insensitive to the optimality of the initial active load distribution unlike the base point and participation factor method. Moreover, it guarantees an optimal distribution among the generating units due the change in the active load demand. Second, a novel approximation of the non-convex generation cost function is developed to solve non-convex ED problem with the transmission losses. This approximation enables the use of gradient and Newton techniques to solve the non-convex ED problem with valve point loading effect and transmission losses in an analytic approach. This approximation is compared with some heuristic optimisation techniques.

Dynamic formulation and approximation methods to solve economic dispatch problems

For original article by A. M. Leite da Silva and J. G. de Carvalho Costa see ibid., vol.18, p.1389-94, Nov. 2003.

Discussion of &#8220 Transmission Loss Allocation: Part I&#8212 Single Energy Market&#8221

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the λ-P table method is used to calculate ED for the fitness function of GA. The λ-P table method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with three kinds of ED problems, namely ED considering valve-point effects (EDVP), ED with multiple fuel units (EDMF), and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all three ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

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An Economic Dispatch Algorithm as Combinatorial Optimization Problems

The deregulation problem has recently attracted attentions in a competitive electric power market, where the cost must be earmarked fairly and precisely for the customers and the Independent Power Producers (IPPs) as well. Transmission loss is an one of several important factors that determines power transmission cost. Because the cost caused by transmission losses is about 3-5%, it is important to allocate transmission losses into each bus in a power system. This paper presents the new algorithm to allocate transmission losses based on an integration method using the loss sensitivity. It provides the buswise incremental transmission losses through the calculation of load ratios considering the transaction strategy of an overall system. The performance of the proposed algorithm is evaluated by the case studies carried out on the WSCC 9-bus and IEEE 14-bus systems.

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Allocation of Transmission Loss for Determination of Locational Spot pricing

This paper presents a new algorithm to determine accurate bus-wise transmission loss allocation utilizing path-integrals dictated by the transaction strategy. For any transaction strategy, the total sum of the allocated transmission losses of all buses is equal to the actual loss given by the AC powerflow calculation considering the distributed slack. In this paper, the bus-wise allocation of the transmission loss is calculated by integrating the differential loss along a path determined by the transaction strategy. The proposed algorithm is also compared with Galiana’s method, which is the well-known transmission loss allocation algorithm based on integration. The performance of the proposed algorithm is evaluated by case studies carried out on the WSCC 9-bus, IEEE 14-bus, New England 39-bus, and IEEE 118-bus systems. The simulation results show that the proposed algorithm is fast and accurate with a large step size.

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Accurate Transmission Loss Allocation Algorithm Based on the Virtual Transaction Strategy: Comparison of Path-integral with Discrete Integral Methods

In this paper, current limiter using a magnetic switching which is based on magnetic flux change in the case of fault is proposed. This current limiter consists of iron-core and three parts of coils. One is the primary coil connected to the power system. Another is the secondary coil wound to the opposite direction of the primary coil's winding. The other is the secondary of the secondary coil which is a movable copper plate winding and located below the secondary coil. In the normal state, the magnetic flux produced in the primary and secondary coils flows to the opposite directions each other and becomes to be canceled out. Therefore the voltages induced between the coils are zero. In the case of a fault, at the moment of a fault occurrence recognition, the switch connected to a secondary coil is opened and the secondary of the secondary coil is pulled out to the outside of the iron-core. Then, magnetic flux becomes to flow through the iron-core. Accordingly, the voltage is induced between the both ends of the primary coil and makes the current reduced. Therefore it is possible to cut off the circuit breaker easily with the proposed current limiter. This paper analyzes the current limiting effects and the detailed results are given.

Kyung-Il Min

Papers

An Economic Dispatch Algorithm as Combinatorial Optimization Problems

Allocation of Transmission Loss for Determination of Locational Spot pricing

Accurate Transmission Loss Allocation Algorithm Based on the Virtual Transaction Strategy: Comparison of Path-integral with Discrete Integral Methods

The Research for a Structure of Current Limiter using a Phasic Similitude of Magnetic Circuit

Emm-Based Voltage Stability Analysis in Consideration of Load Power Factor