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Showing papers in "IEEE Transactions on Power Systems in 2000"


Journal ArticleDOI
TL;DR: In this article, a particle swarm optimization (PSO) for reactive power and voltage control (volt/VAr control: VVC) considering voltage security assessment (VSA) is presented.
Abstract: Summary form only given, as follows. This paper presents a particle swarm optimization (PSO) for reactive power and voltage control (volt/VAr control: VVC) considering voltage security assessment (VSA). VVC can be formulated as a mixed-integer nonlinear optimization problem (MINLP). The proposed method expands the original PSO to handle a MINLP and determines an online VVC strategy with continuous and discrete control variables such as automatic voltage regulator (AVR) operating values of generators, tap positions of on-load tap changer (OLTC) of transformers, and the number of reactive power compensation equipment. The method considers voltage security using a continuation power now and a contingency analysis technique. The feasibility of the proposed method is demonstrated and compared with reactive tabu search (RTS) and the enumeration method on practical power system models with promising results.

1,340 citations


Journal ArticleDOI
TL;DR: In this article, a single-firm game model for analyzing power markets is presented, where each generating firm submits bids to an ISO, choosing its bids to maximize profits subject to anticipated reactions by rival firms.
Abstract: Transmission constraints and market concentration may prevent power markets from being fully competitive, allowing firms to exercise market power and raise prices above marginal cost. We present a strategic gaming model for analyzing such markets; it represents an oligopolistic market economy consisting of several dominant firms in an electric power network. Each generating firm submits bids to an ISO, choosing its bids to maximize profits subject to anticipated reactions by rival firms. The single-firm model is formulated as a mathematical program with equilibrium constraints (MPEC) with a parameter-dependent spatial price equilibrium problem as the inner problem. Power flows and pricing strategies are constrained by the ISO's linearized DC optimal power flow (OFF) model. A penalty interior point algorithm is used to compute a local optimal solution of the MPEC. Numerical examples based on a 30 bus network are presented, including multi-firm Nash equilibria in which each player solves an MPEC of the single-firm type.

840 citations


Journal ArticleDOI
TL;DR: In this paper, the main results of studies that have been carried out, during a period of more than a decade, at University of Pisa in co-operation with other technical Italian institutions, about models of electrochemical batteries suitable for the use of the electrical engineer, in particular for the analysis of electrical systems with batteries.
Abstract: This paper documents the main results of studies that have been carried out, during a period of more than a decade, at University of Pisa in co-operation with other technical Italian institutions, about models of electrochemical batteries suitable for the use of the electrical engineer, in particular for the analysis of electrical systems with batteries. The problem of simulating electrochemical batteries by means of equivalent electric circuits is defined in a general way; then particular attention is then devoted to the problem of modeling of lead-acid batteries. For this kind of battery, a general model structure is defined from which specific models can be inferred, having different degrees of complexity and simulation quality. In particular, the implementation of the third-order model, that shows a good compromise between complexity and precision, is developed in detail. The behavior of the proposed models is compared with results obtained with extensive lab tests on different types of lead-acid batteries.

592 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of the market structure on the elasticity of the demand for electricity is analyzed and the consumers' behavior can be modeled using a matrix of self-and cross-elasticities.
Abstract: As electricity markets are liberalized, consumers become exposed to more volatile electricity prices and may decide to modify the profile of their demand to reduce their electricity costs. This paper analyzes the effect that the market structure can have on the elasticity of the demand for electricity. It then describes how the consumers' behavior can be modeled using a matrix of self- and cross-elasticities. It is shown how these elasticities can be taken into consideration when scheduling generation and setting the price of electricity in a pool based electricity market. These concepts are illustrated using a 26-generator system.

591 citations


Journal ArticleDOI
TL;DR: In this paper, the optimal response of a thermal unit to an electricity spot market is addressed, where the objective is to maximize the unit profit from selling both energy and spinning reserve in the spot market.
Abstract: This paper addresses the optimal response of a thermal unit to an electricity spot market. The objective is to maximize the unit profit from selling both energy and spinning reserve in the spot market. The paper proposes a 0/1 mixed-integer linear programming approach that allows a rigorous modeling of (i) nonconvex and nondifferentiable operating costs, (ii) exponential start-up costs, (iii) available spinning reserve taking into account ramp rate restrictions, and (iv) minimum up and down time constraints. This approach overcomes the modeling limitations of dynamic programming approaches and is computationally efficient. Results from realistic case studies are reported.

550 citations


Journal ArticleDOI
TL;DR: Numerical results show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the proposed Lagrangian relaxation and genetic algorithms (LRGA).
Abstract: This paper presents an application of a combined genetic algorithms (GAs) and Lagrangian relaxation (LR) method for the unit commitment (UC) problem. Genetic algorithms (GAs) are a general purpose optimization technique based on principle of natural selection and natural genetics. The Lagrangian relaxation (LR) method provides a fast solution but it may suffer from numerical convergence and solution quality problems. The proposed Lagrangian relaxation and genetic algorithms (LRGA) incorporates genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers and improve the performance of Lagrangian relaxation method in solving combinatorial optimization problems such as the UC problem. Numerical results on two cases including a system of 100 units and comparisons with results obtained using Lagrangian relaxation (LR) and genetic algorithms (GAs), show that the feature of easy implementation, better convergence, and highly near-optimal solution to the UC problem can be achieved by the LRGA.

488 citations


Journal ArticleDOI
TL;DR: A new methodology that eliminates the need for repeated simulation to determine a transiently secure operating point is presented, and dynamic equations are converted to numerically equivalent algebraic equations and integrated into the standard OPF formulation.
Abstract: Stability is an important constraint in power system operation. Often trial and error heuristics are used that can be costly and imprecise. A new methodology that eliminates the need for repeated simulation to determine a transiently secure operating point is presented. The theoretical development is straight-forward: dynamic equations are converted to numerically equivalent algebraic equations and then integrated into the standard OPF formulation. Implementation issues and simulation results are discussed in the context of a 162-bus system.

445 citations


Journal ArticleDOI
TL;DR: In this paper, a sparse formulation for the solution of unbalanced three-phase power systems using the Newton-Raphson method is presented, where the Jacobian matrix is composed of 6/spl times/6 block matrices and retains the same structure as the nodal admittance matrix.
Abstract: This paper presents a new sparse formulation for the solution of unbalanced three-phase power systems using the Newton-Raphson method. The three-phase current injection equations are written in rectangular coordinates resulting in an order 6n system of equations. The Jacobian matrix is composed of 6/spl times/6 block matrices and retains the same structure as the nodal admittance matrix. Practical distribution systems were used to test the method and to compare its robustness with that of the backward/forward sweep method.

411 citations


Journal ArticleDOI
TL;DR: An approach to parallelizing optimal power flow (OPF) that is suitable for coarse-grained distributed implementation and is applicable to very large interconnected power systems is presented.
Abstract: We present an approach to parallelizing optimal power flow (OPF) that is suitable for coarse-grained distributed implementation and is applicable to very large interconnected power systems. The proposed distributed scheme can be used to coordinate a heterogeneous collection of utilities. Three mathematical decomposition coordination methods are introduced to implement the proposed distributed scheme: the auxiliary problem principle (APP), the predictor-corrector proximal multiplier method (PCPM), and the alternating direction method (ADM). We demonstrate the approach on several medium size systems, including IEEE Test Systems and parts of the ERCOT (Electric Reliability Council of Texas) system.

373 citations


Journal ArticleDOI
TL;DR: In this paper, two methods are proposed for the simulation of wind farms with asynchronous generators in the load flow analysis, which are based on the steady-state model of the induction machine.
Abstract: Two methods are proposed, for the simulation of wind farms with asynchronous generators in the load flow analysis. Both methods are based on the steady-state model of the induction machine. The first involves improving the conventional PQ bus, and the second involves modeling the generators in steady-state in the bus where the wind farm is located. The two sets of results are then compared.

354 citations


Journal ArticleDOI
TL;DR: In this paper, a fuzzy logic technique is used to diagnose multiple faults in a transformer and quantitatively indicate the likelihood/severity of each fault, which is important for a transformer in critical situation.
Abstract: Dissolved gas analysis (DGA) of transformer oil has been one of the most useful techniques to detect the incipient faults. Various methods, such as the IEC codes, have been developed to interpret DGA results directly obtained from a chromatographer. Although these methods are widely used in the world, they sometimes fail to diagnose, especially when more than one fault exists in a transformer. This paper presents a fuzzy logic technique which can diagnose multiple faults in a transformer and quantitatively indicates the likelihood/severity of each fault. Insulation deterioration at each fault location can then be monitored closely according to its trend, which is important for a transformer in critical situation. Tests using this technique on a number of transformers have given promising results.

Journal ArticleDOI
TL;DR: In this paper, a short historical overview of the symmetrical component transformation and the application of unitary and orthogonal transformations are presented and logic choices for base quantities necessary in per unit calculations are derived.
Abstract: Although the symmetrical component transformation has existed for 80 years, its application in the time-dependent form is practically restricted to the electric-machine theory. In the power systems field one uses the transformation applied to steady-state sinusoidal phasors in a nonunitary form for fault calculations. For time-domain calculations the real equivalent, 0, /spl alpha/, /spl beta/, is preferred, usually extended to 0, d, q-components. In network calculations, however, the application of time-dependent symmetrical components makes sense, since many net-component parameters are already available in this form. In this paper a short historical overview of the symmetrical-component transformation and the application of unitary and orthogonal transformations are presented. From these general transformations logic choices for base quantities necessary in per unit calculations are derived. The relations between real and complex transformations, steady-state phasors and well-known sequence networks are given and illustrated through the use of some examples with asymmetrical faults.

Journal ArticleDOI
TL;DR: In this paper, a method that simultaneously tune multiple power system damping controllers using genetic algorithms (GAs) is presented for global PSS tuning to the well-known New England system and coordinated tuning of 22 PSSs in a 1762-bus modified equivalent South-Southeastern Brazilian system.
Abstract: This paper presents a method that simultaneously tune multiple power system damping controllers using genetic algorithms (GAs). Damping controller structures are assumed to be fixed consisting basically of lead-lag filters. The tuning method takes robustness into consideration as it guarantees system stabilization over a prespecified set of operating conditions. Modified GA operators are used in the simultaneous optimization of both phase compensations and gain settings for the stabilizers. The method is applied for global PSS tuning to the well-known New England system and to the coordinated tuning of 22 PSSs in a 1762-bus modified equivalent South-Southeastern Brazilian system.

Journal ArticleDOI
TL;DR: In this article, an advanced load flow model for the static VAr compensator (SVC) is presented, which uses the firing angle as the state variable to provide key information for cases when the load flow solution is used to initialize other power system applications.
Abstract: Advanced load flow models for the static VAr compensator (SVC) are presented in this paper. The models are incorporated into existing load flow (LF) and optimal power flow (OPF) Newton algorithms. Unlike SVC models available in open literature the new models depart from the generator representation of the SVC and are based instead on the variable shunt susceptance concept. In particular, a SVC model which uses the firing angle as the state variable provides key information for cases when the load flow solution is used to initialize other power system applications, e.g., harmonic analysis. The SVC state variables are combined with the nodal voltage magnitudes and angles of the network in a single frame-of-reference for a unified, iterative solution through Newton methods. Both algorithms, the LF and the OPF exhibit very strong convergence characteristics, regardless of network size and the number of controllable devices. Results are presented which demonstrate the prowess of the new SVC models.

Journal ArticleDOI
TL;DR: In this article, the revelation principle is adopted from game theory and applied to the interaction between a utility and its customers to design an incentive structure that encourages customers to sign up for the right contract and reveal their true value of power.
Abstract: Demand relief from customers can help a utility (or any "load serving entity") solve a variety of problems. There exist all sorts of different demand management programs that utilities use. A critical issue is the incentive paid to the customer to participate in demand management programs and provide load relief. The utility has to design cost effective yet attractive demand management contracts. The main goal is to get load relief when needed, and to do so in a cost effective way. Customers sign up for programs when the benefits they derive in the form of up front payments, demand discounts and interruption payments exceed their cost of interruption. In order to design such contracts, mechanism design with the revelation principle is adopted from game theory and applied to the interaction between a utility and its customers. The idea behind mechanism design is to design an incentive structure that encourages customers to sign up for the right contract and reveal their true value of power (and thus, the value of power interruptibility).

Journal ArticleDOI
TL;DR: In this paper, an approach to very short-time load forecasting by the application of artificial neural networks to model load dynamics has been presented, which is more robust as compared to the traditional approach when actual loads are forecasted and used as input variables.
Abstract: In a deregulated, competitive power market, utilities tend to maintain their generation reserve close to the minimum required by an independent system operator This creates a need for an accurate instantaneous-load forecast for the next several dozen minutes This paper presents a novel approach to very short-time load forecasting by the application of artificial neural networks to model load dynamics The proposed algorithm is more robust as compared to the traditional approach when actual loads are forecasted and used as input variables It provides more reliable forecasts, especially when the weather conditions are different from those represented in the training data The proposed method has been successfully implemented and used for online load forecasting in a power utility in the United States To assure robust performance and training times acceptable for online use, the forecasting system was implemented as a set of parsimoniously designed neural networks Each network was assigned a task of forecasting load for a particular time lead and for a certain period of day with a unique pattern in load dynamics Some details of this are presented in the paper

Journal ArticleDOI
TL;DR: This paper presents a study of the simplified homogeneous and self-dual (SHSD) linear programming (LP) interior point algorithm applied to the security constrained economic dispatch (SCED) problem, which considers both (N-1) and ( N-2) network security conditions.
Abstract: This paper presents a study of the simplified homogeneous and self-dual (SHSD) linear programming (LP) interior point algorithm applied to the security constrained economic dispatch (SCED) problem. Unlike other interior point SCED applications that consider only the N security problem, this paper considers both (N-1) and (N-2) network security conditions. An important feature of the optimizing interior point LP algorithm is that it can detect infeasibility of the SCED problem reliably. This feature is particularly important in SCED applications since line overloading following a contingency often results in an infeasible schedule. The proposed method is demonstrated on the IEEE 24 bus test system and a practical 175 bus network. A comparison is carried out with the predictor-corrector interior point algorithm for the SCED problem presented previously (see ibid., vol. 12, no.2, p.803-10, 1997).

Journal ArticleDOI
TL;DR: In this article, several compensation strategies are examined, in terms of satisfying custom power while taking into consideration the capacity of the energy-storage device and the voltage injection constraint of the dynamic voltage restorer.
Abstract: Summary form only given, as follows. Voltage sags are one of the most important power quality problems challenging the utility industry. Voltage sags can be compensated for by voltage and power injection into the distribution system. By injecting voltage with a phase advance with respect to the sustained source-side voltage, reactive power can be utilized to help voltage restoration. Hence, the consumption of real power, from the perspective of the energy supply device, can be reduced. This energy-saving voltage injection comes at the expense of an increased voltage injection magnitude, load power swing phase shift and discontinuity of voltage wave-shape. For this reason, several proposed compensation strategies are examined, in term of satisfying custom power while taking into consideration the capacity of the energy-storage device and the voltage injection constraint of the dynamic voltage restorer. Numerical examples are included to illustrate the efficacy of the proposed control strategies.

Journal ArticleDOI
TL;DR: In this paper, a new Hopfield model based approach for the economic dispatch problem of power systems is presented, where an energy function composing power mismatch, total fuel cost and the transmission line losses is defined.
Abstract: This paper presents a new Hopfield model based approach for the economic dispatch problem of power systems. To solve the economic dispatch problem using the Hopfield model, an energy function composing power mismatch, total fuel cost and the transmission line losses is defined. The weighting factors associated with the terms of the energy function can be either appropriately selected or directly estimated in the proposed model. Which, however, are determined by trial and error in the conventional Hopfield method. To minimize the value of the energy function, the computational procedures including a series of adjusting the weighting factor associated with the transmission line losses and updating the unit generations and power losses are carried out. Because the weighting factors are governed by some relationships developed, adjustment of the weighting factor is much simpler and more effective in steadily achieving solutions than adjustment of the /spl lambda/-multiplier in the lambda-iteration method for economic dispatch problems. Computational results reveal that this approach can find accurate solutions more simply and fast compared with the conventional lambda-iteration method.

Journal ArticleDOI
TL;DR: Based on AC load flow solution a novel method is suggested which can decide downstream and upstream power flow tracing paths very fast and can calculate the contribution factors of generations and loads to the line flows efficiently.
Abstract: In this paper, graph theory is used to calculate the contributions of individual generators and loads to line flows and the real power transfer between individual generators and loads that are significant to transmission open access. Related lemmas are proved which present necessary conditions required by the method. Based on AC load flow solution a novel method is suggested which can decide downstream and upstream power flow tracing paths very fast and can calculate the contribution factors of generations and loads to the line flows efficiently. The power transfer between generators and loads can also be determined. The suggested method is suitable for both active and reactive power tracings of real power systems.

Journal ArticleDOI
TL;DR: In this article, the bidding decision making problem is studied from a supplier's viewpoint in a spot market environment, and the optimal strategy is calculated to maximize the expected reward over a planning horizon.
Abstract: The bidding decision making problem is studied from a supplier's viewpoint in a spot market environment. The decision-making problem is formulated as a Markov decision process-a discrete stochastic optimization method. All other suppliers are modeled by their bidding parameters with corresponding probabilities. A systematic method is developed to calculate transition probabilities and rewards. A simplified market clearing system is also included in the implementation. A risk-neutral decision-maker is assumed, the optimal strategy is calculated to maximize the expected reward over a planning horizon. Simulation cases are used to illustrate the proposed method.

Journal ArticleDOI
TL;DR: The purpose of this paper is to propose a new short-term load forecasting method for special days in anomalous load conditions, which uses a hybrid approach of ANN based technique and fuzzy inference method to forecast the hourly loads of special days.
Abstract: Conventional artificial neural network (ANN) based short-term load forecasting techniques have limitations in their use on holidays. This is due to dissimilar load behaviors of holidays compared with those of ordinary weekdays during the year and to insufficiency of training patterns. The purpose of this paper is to propose a new short-term load forecasting method for special days in anomalous load conditions. These days include public holidays, consecutive holidays, and days preceding and following holidays. The proposed method uses a hybrid approach of ANN based technique and fuzzy inference method to forecast the hourly loads of special days. In this method, special days are classified into five different day-types. Five ANN models for each day-type are used to forecast the scaled load curves of special days, and two fuzzy inference models are used to forecast the maximum and the minimum loads of special days. Finally, the results of the ANN and the fuzzy inference models are combined to forecast the 24 hourly loads of special days. The proposed method was tested with actual load data of special days for the years of 1996-1997. The test results showed very accurate forecasting with the average percentage relative error of 1.78%.

Journal ArticleDOI
TL;DR: In this article, an improved genetic algorithm incorporating a stochastic crossover technique and an artificial initial population scheme is developed to provide a faster search mechanism for the least-cost generation expansion planning problem.
Abstract: This paper presents a development of an improved genetic algorithm (IGA) and its application to a least-cost generation expansion planning (GEP) problem. Least-cost GEP problem is concerned with a highly constrained nonlinear dynamic optimization problem that can only be fully solved by complete enumeration, a process which is computationally impossible in a real-world GEP problem. In this paper, an improved genetic algorithm incorporating a stochastic crossover technique and an artificial initial population scheme is developed to provide a faster search mechanism. The main advantage of the IGA approach is that the "curse of dimensionality" and a local optimal trap inherent in mathematical programming methods can be simultaneously overcome. The IGA approach is applied to two test systems, one with 15 existing power plants, 5 types of candidate plants and a 14-year planning period, and the other, a practical long-term system with a 24-year planning period.

Journal ArticleDOI
TL;DR: In this paper, a new power frequency model for unified power flow controller (UPFC) is suggested with its DC link capacitor dynamics included, and four principal control strategies for UPFC series element main control and their impacts on system stability are discussed.
Abstract: In this paper, a new power frequency model for unified power flow controller (UPFC) is suggested with its DC link capacitor dynamics included. Four principal control strategies for UPFC series element main control and their impacts on system stability are discussed. The main control of UPFC series element can be realized as a combination of the four control functions. The supplementary control of UPFC is added for damping power oscillation. The integrated UPFC model has then been incorporated into the conventional transient and small signal stability programs with a novel UPFC-network interface. Computer tests on a 4-generator interconnected power system show that the suggested UPFC power frequency model and the UPFC-network interface method work very well. The results also show that the suggested UPFC control strategy can realize power flow control fairly well and improve system dynamic performance significantly.

Journal ArticleDOI
TL;DR: In this article, the authors present an overview of usage-based methods of transmission cost allocation under open access and provide a summary of techniques used for designing fair and equitable access fees for the recovery of fixed transmission costs.
Abstract: This paper presents an overview of usage-based methods of transmission cost allocation under open access. Allocation of transmission costs involves both technical and regulatory issues, and as a result, the methods available in the literature differ in their definition and measure of the "extent of use" of transmission resources. The primary objective of this paper is to provide a summary of techniques used for designing fair and equitable access fees for the recovery of fixed transmission costs. The discussion is thus organized under two major subtopics: algorithms for transmission usage evaluation and alternative pricing strategies. Numerical examples are provided to show the results using different methods.

Journal ArticleDOI
P. Zarco1, A.G. Exposito
TL;DR: A classification of the techniques proposed in the literature to estimate parameter errors is then suggested, followed by a description of the main ideas behind each method and a discussion is included on the possibilities and limitations of every class of methods.
Abstract: This paper deals with the problem of network parameter errors in state estimation. First of all, some experimental results are presented showing the influence of these errors on the performance of weighted least squares state estimators. Secondly, the preliminary step of identifying suspicious network parameters is briefly discussed. A classification of the techniques proposed in the literature to estimate parameter errors is then suggested, followed by a description of the main ideas behind each method. Finally, a discussion is included on the possibilities and limitations of every class of methods.

Journal ArticleDOI
TL;DR: In this paper, a pseudo-chronological simulation approach is proposed to evaluate loss of load indices, with particular emphasis on LOLC (loss of load cost) assessment, for composite generation and transmission systems considering time varying loads for different areas or buses.
Abstract: This paper presents a new methodology to evaluate loss of load indices, with particular emphasis on LOLC (loss of load cost) assessment, for composite generation and transmission systems considering time varying loads for different areas or buses. The proposed approach, named pseudo-chronological simulation, retains the computational efficiency of nonsequential Monte Carlo simulation and the ability to model chronological load curves in sequential simulation. It considers the actual blocks of unsupplied energy per consumer class, per bus, and the respective duration, to accurately characterize the interruption process. Case studies on the IEEE-MRTS (Modified Reliability Test System) and the BSS (Brazilian South-Southeastern System) are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, an optimal reactive power scheduling method is sought which minimizes real power transmission loss and maximizes voltage stability margin (VSM) subject to the utmost satisfaction of all the violated load bus voltage constraints.
Abstract: Insufficient reactive power support in a power grid results in under voltages at load centres and also limits the real power transfer capacities of the transmission systems leading to voltage collapse. An optimal reactive power scheduling method is sought which minimizes real power transmission loss and maximizes voltage stability margin (VSM) subject to the utmost satisfaction of all the violated load bus voltage constraints. A multi-objective fuzzy LP (MFLP) method of solution in the successive LP (SLP) framework is proposed to solve the problem. A set of least singular values of the load flow Jacobian is used as VSM indicator. This set is expressed in terms of the control vector and is maximized in the proposed formulation to maximize VSM. Results of the tests of the proposed method on modified IEEE 6 bus and 57 bus systems are presented. The changes in the load flow Jacobian singular values during scheduling are studied.

Journal ArticleDOI
TL;DR: A new and comprehensive load flow model for the unified power flow controller (UPFC) is presented, incorporated into an existing Newton-Raphson load flow algorithm, which exhibits quadratic or near-quadratic convergence characteristics.
Abstract: A new and comprehensive load flow model for the unified power flow controller (UPFC) is presented in this paper. The model is incorporated into an existing Newton-Raphson load flow algorithm. Unlike existing UPFC models available in open literature, it can be set to control active and reactive powers and voltage magnitude in any combination or to control none of them. A set of analytical equations has been derived to provide good UPFC initial conditions. Hence, the algorithm exhibits quadratic or near-quadratic convergence characteristics. Suitable guidelines are suggested for an effective control coordination of two or more UPFCs operating in series or parallel arrangements. Test results are presented which demonstrate the effectiveness of the new model.

Journal ArticleDOI
G. A. Hamoud1
TL;DR: In this paper, a method for determining the available transfer capability (ATC) between any two locations in a transmission system (single-area or multi-area) under a given set of system operating conditions is described.
Abstract: The available transfer capability (ATC) of a transmission system is a measure of unutilized capability of the system at a given time and depends on a number of factors such as the system generation dispatch, system load level, load distribution in the network, power transfers between areas, network topology, and the limits imposed on the transmission network due to thermal, voltage and stability considerations. This paper describes a method for determining the ATC between any two locations in a transmission system (single-area or multiarea) under a given set of system operating conditions. The method also provides ATCs for selected transmission paths between the two locations in the system and identifies the most limiting facilities in determining the network's ATC. In addition, the method can be used to compute multiple ATCs between more than one pair of locations. The proposed method is illustrated using the IEEE reliability test system (RTS).