Showing papers on "Power-flow study published in 1982"

Harmonic Power Flow Studies Part I - Formulation and Solution

Abstract: The conventional Newton-Raphson power flow study has been reformulated to permit the inclusion of nonlinear loads. These loads give rise to harmonic signals which propagate throughout the power system. The reformulation is based on the reduction to zero of the mismatch active power and reactive voltamperes, the imbalance current at harmonic frequencies, and the mismatch apparent Voltamperes. Conclusions on the existence of positive, negative, and zero sequence signals are made for harmonic frequencies. The harmonic power flow study formulation is illustrated for a three phase full wave bridge rectifier. A companion paper presents a discussion of the actual computer implementation and several practical examples.

Steady-State Security Regions of Power Systems

Abstract: A steady-state security region is a set of real and reactive power injections (load demands and power generations) for which the power flow equations and the security constraints imposed by equipment operating limits are satisfied. The problem of determining steady-state security regions is formulated as one of finding sufficient conditions for the existence of solutions to the power flow map within the security constraint set. Explicit limits on real and reactive power injections at each bus are obtained, such that if each injection lies within the corresponding limits, the system is guaranteed to operate with security constraints satisfied.

Interactive Transmission Network Planning Using a Least-Effort Criterion

Abstract: This paper describes an interactive software tool for long term transmission system expansion planning. All network synthesis is based on the DC power-flow model. The ranking of new additions is based on a "least-effort" criterion that takes into account the pattern of flow distribution in the network. An automatic network synthesis algorithm can be used for static studies. The reinforcement criterion is based on the cost/benefit analysis of "least-effort paths" in the network. Disconnected buses are conveniently handled by the superposition of a dummy network with very low transmission capacity over the actual network. Sensitivity analysis is extensively used. The program has been implemented in the transmission departmentof ELETROBRAS (the holding company of the Brazilian electric sector). Three case studies are presented and discussed.

Large Scale Optimal Power Flow

Abstract: A new optimization method is applied to optimal power flow analysis. The method is shown to be well suited to large scale (500 buses or more) power systems in that it is computationally efficient and is particularly effective with infeasible starting points. The optimization approach is based on transforming the original problem to that of solving a sequence of linearly constrained subproblems using an augmented Lagrangian type objective function. A fundamental feature of this algorithm (developed by Murtagh and Saunders) is that the solution converges quadratically on the nonlinear power flow constraints, rather than being forced to satisfy the constraints throughout the iterative process. To demonstrate the performance of this algorithm, a set of descent directions, which includes quasi-Newton (variable metric), conjugate directions, and steepest descent, are compared on the basis of convergence and computational effort for a 118 bus and a 600 bus power system.

Harmonic Power Flow Studies - Part II Implementation and Practical Application

Abstract: This is a companion paper to a paper of the same title, Part I, in which the eLectric power flow problem is reformulated to account for harmonic signals which arise from nonLinear loads. In this paper, implementation and practical applications are discussed. The problem of initialization of bus voltages (including harmonics) is considered and convergence of the algorithm is assessed from the theoretical viewpoint and from the results of actual studies. The principal content of this paper is two examples both containing nonlinear loads (rectifiers).

Geometric critical point analysis of lossless power system models

Abstract: Electric utility analysts today face an increasingly difficult task of formulating both long and short term operating plans which will provide at the same time efficient and economical operation while delivering reliable and uninterrupted service to electricity users. One of the key ingredients in this planning is a set of large scale simulations of the steady-state network performance under various anticipated operating conditions. Central to these analyses are the classical "load flow" equations which are the equilibrium equations for the "swing equations" which are a physically based model of the dynamic operation of an n -node power system. Despite the long standing and widespread use of these equations, there remain a number of very basic open questions: What are the number and nature of the equilibria of the swing equations? How many stable equilibrium operating points are there in an n -node electric power grid? In this paper some powerful analytical tools from topology and geometry are used to answer certain of these questions. It is well documented that the load flow equations comprise a formidable large scale system but what is interesting, and perhaps surprising, is that even for a small number of buses, these equations possess a rather rich and intricate qualitative behavior which has heretofor been only partially understood. Indeed, until now there was no complete statement in the literature concerning the number of load flows in a general three-bus network. In Theorem 2.7, we state that for the "generic" three-bus network there are, for sufficiently small power injections, either four or six real load flows and that, in either case, exactly one of those load flows is stable. This is a special case of the results we derive for a general n -bus powergrid. Our method consists in first transforming the load flow equations for a lossless electric power network by trigonometric substitutions into algebraic equations. This makes it possible to apply some deep and powerful results from algebraic geometry and intersection theory to study these equations. An obvious tool for determining the number of solutions is provided by the classical theorem of Bezout, but it is shown that for systems describing an n -machine network with n \geq 4 , this result cannot be directly applied because the solutions contain solution components of positive dimension "at infinity." A major result in this paper is a modified Bezout technique which allows us to compute the number of complex (and a fortiori an upper bound on the number of real) solutions to the load flow equations. Combining this with the classical Morse inequalities, we obtain very explicit results regarding the number of stable load flows for a given network topology and set of power injections. The cases of three and four machine networks are considered in detail.

On-Line Load Forecasting for Energy Control Center Application

Abstract: An important component of a comprehensive real-time control center for power systems is a short-term internal system load forecast. Short-term forecasts are necessary for on-line commitment, maintenance scheduling, security analysis, and on-line load flow solutions. It enables the economic dispatch to coordinate forecasted load changes with rate-of- response of generating units.

Fast Linear Contingency Analysis

Abstract: This paper reports on a linear contingency analysis program that computes linearized real power flow changes resulting from branch outages and generation or load changes. A modern formulation has been adopted based on the relation ?P = ??rather than using current injections and the bus admittance matrix. For maximum speed in processing such a large number of contingencies, the explicit inverse (triangular portion) of H is computed by the back substitution method. Multiple branch contingencies require essentially the same time as would the same number computed individually. Multiple generation or load changes are handled most efficiently by a single repeat solution for ??using the sparse factors of H and a sparse ?P vector. Explicit branch distribution and generation shift factors are computed only for display to the operator.

Global analysis of swing dynamics

Abstract: The paper presents some asymptotic properties of the trajectories of an interconnected power system. Generators are described by their swing equations, loads are treated as PV buses. It is shown that' oscillations can never occur. Moreover, for small levels of injected power, all trajectories converge.

Optimal Long Range Transmission Planning with AC Load Flow

Abstract: This paper describes a new procedure for the optimal long range expansion planning of a transmission network. In addition to providing an optimal plan, a set of cost competitive expansion plans can be generated. System expansion is specified in terms of discrete transmission lines and two kV levels. Economic impact of factors such as cost escalation, economy of scale, right-of-way unavailability, external system interconnections, etc., are incorporated in the formulation. A dynamic optimization procedure based on a nonlinear branch and bound algorithm is employed. The resulting optimal plan specifies when, where, and what type of construction should occur. A unique feature of the method, which reduces considerably the computational burden, is an automatic generation of alternatives algorithm and associated procedures for elimination of infeasible and non-optimal alternatives early in the process. Computational speed can also be affected by the user option of employing either dc or ac load flow calculations.

Performance Evaluation of Parameter Estimation Algorithms for Economic Operation of Power Systems

Abstract: Four algorithms for estimation of the parameters of models used in optimal economic operation of electric power systems, are proposed. The details of the formulations for estimating the parameters of the fuel cost expression, the loss formula coefficients, and the active-reactive power loss models are highlighted. Critical performance evaluation of each of the proposed algorithms is carried out using some practical test systems. The first evaluation criterion is based on the familiar modeling error-comparison. Further evaluation is carried out on the basis of the optimal strategies resulting from the use of each estimated model. Optimal costs as well as overall network performance (based on load flow analysis) resulting from the implementation of each model, provide the basis for our comparisons.

A probabilistic model of power system disturbances

Abstract: Power system stability analysis involves the study of the state trajectories of a power system in response to a disturbance. The system is usually presumed to be in a static equilibrium state when the disturbance is initiated. The disturbance causes a dynamic motion of the system state variables to either a new equilibrium condition or an unstable condition, which we usually regard as a system failure in some sense. The disturbance that initiates system dynamic behavior is of primary interest here. Qualitatively, the system disturbance may be large or small, and may be a simple step change in some parameter or a complex sequence of changes. We are interested in describing the disturbance not just mathematically, but probabilistically. Thus we seek a definition that will permit us to associate probabilities with disturbance events, such that the probabilities conform to an axiomatic definition of probability.

Coherency identification for large electric power systems

Abstract: An important problem associated with contingency and reliability studies for large-scale electric power systems is the use of dynamic equivalent models to represent the behavior of aggregable parts of the system. Fundamental to the aggregation process associated with any coherency-based approach is an ability to identify groups of coherent generators or generators that swing together in response to a contingency. Coherency identification is thus a key step in the reduction process. In this paper, an analytical process is examined which permits identification of coherent groups based upon the closed-form solution of a linearized power system model and the use of the Cayley-Hamilton theorem. The result is an algebraic characterization of coherency. Computationally practical coherency indices are developed which do not require significant computer storage. A physical interpretation of this characterization is discussed which suggests that coherency depends not only of the electrical distances between generators but also on generator inertia constants. The method of coherency identification developed in this paper is evaluated on a detailed model of a 39-bus test system.

Mathematical Modelling and Analysis of Multi Phase Systems

Abstract: Recently, the multi phase transmission systems are being considered as a viable transmission alternative to achieve efficient utilization of rights of way and increased transmission capability to meet growing power supply demands. However, detailed modelling and analysis of multi phase systems and associated transformers have not been carried out to substantiate the preliminary findinge. This paper is an attempt in this direction by presenting the various representations of multi phase components; transmission lines, transformers and loads suitable for balanced as well as unbalanced network analysis. Employing one of the proposed modelling schemes, the impact of addition of multi phase lines in existing three phase network is investigated for the load flow analysis. The results of a sample system are presented and discussed.

AC to AC power converter with a controllable power factor

Abstract: The input power factor of an AC to AC static- power converter Is continuously adjustable between a maximum leading or lagging phase angle, determined by the load power factor, through rapidly transferring between conventional and complementary unrestricted frequency changer operation with the proportion of each sub generator cycle interval dedicated to each mode of operation being selected to produce the desired input power factor. Since the input power factor affects generator excitation, the input power factor control can be used in a closed loop feedback control system to regulate generator voltage.

Load Management Assessment Methodology at PSE&G

Abstract: Recognizing the need for a procedure which can effectively analyze all of the variables involved in conducting an evaluation of end-use alternatives in power system planning, PSE&G developed a comprehensive methodology. This methodology encompasses all elements of corporate planning and establishes the financial impacts of specific load management and/or conservation activities or combinations thereof. This paper describes that methodology and uses one sample analysis to demonstrate its application

Bulk Power Area Reliability Evaluation Considering Propabilistic Transfer Capability

Abstract: This paper describes a method proposed for use in the PJM pool to evaluate the adequacy of inter-area transfer capability. The method considers the generating capacity deficiency of an area and transfer capability into that area as random variables to determine the area loss of load expectation. Loss of load in an area may result from two conditions: (1) available generating capacity is less than load coupled with inadequate transfer capability into the area, or (2) additional generating capacity is not started promptly when economy imports are curtailed due to tripping of key transmission lines. The proposed method considers both these conditions. The method is applied to the IEEE Reliability Test System for illustration.

A complex Lagrangian approach with applications to power network sensitivity analysis

Abstract: The well-known Lagrangian approach, traditionally described in real form, for calculating first-order changes and gradients of functions of interest subject to equality constraints is generalized and applied in a compact complex form. Hence, general complex functions and constraints can be handled directly while maintaining the original complex mode of formulation. The theoretical foundations of the approach are stated. An application to power network sensitivity analysis and gradient evaluation is presented.

Parallel Optimization with Applications to Power Systems

Abstract: A new pseudo-conjugate direction algorithm for the solution of the unconstrained optimization problem on a parallel computer is presented. At each iteration, n one-dimensional searches along n directions are performed simultaneously on n processors. These directions are so chosen that they progressively become more nearly conjugate as a minimum is approached. The algorithm does not require the evaluation or computation of any derivatives and it is suitable for execution on an existing multiprocessor computer (Siemens SMS 201). To assess the effectiveness of the proposed algorithm in solving optimization problems that occur in power systems analysis, (i.e. load flow, state estimation and optimal load flow type), its implemenation on the SMS-201 (128-processor system) is analyzed.

Application of minimum loss property of resistive networks to power scheduling

Abstract: The load flow equations of a loss less transmission system has the same structure that of a nonlinear resistive network. By utilizing the minimum loss property of nonlinear resistive networks [9], the solution to the load flow equation can be characterized as the minimum of a suitably defined function. This characterization is utilized in solving the problem of scheduling power for economic operation of power systems, while taking account the transient stability margin of the resulting operating point. For the model used in this paper it is shown that the solution is essentially a load flow problem of a suitably modified system.

The analysis of high-phase-order power transmission systems

Abstract: In this letter the analysis of power systems with more than three phases is discussed. It is shown that the six-phase elements can be replaced by equivalent three-phase elements. The load-flow algorithms and the techniques for the computation of short-circuit currents, which are available for three-phase power systems, can hence be used for six-phase and other high-phase-order power systems.

Practical complex solution of power flow equations

Abstract: This paper applies and illustrates the compact, complex notation introduced by Bandler and El-Kady to the practical solution of the power flow equations. The solution of the complex linearized power flow equations, which is required by the Newton-Raphson method, is obtained by a direct method. The method, fully and exactly, incorporates generator buses as well as dummy load buses.

Computer techniques for power system design analysis

Abstract: A method of industrial and commercial power systems design, planning, and analysis by computer is described. The use of modular computer programs operating from a common data base is used for evaluation of connected, demand, and design load conditions; feeder and transformer size selections; voltage drop and load flow analysis; three phase bolted fault analysis; and unbalanced fault analysis. Each program module may be executed separately or modules may be executed as a group. One program module solution may be used to generate data for the following module. The program uses a design library which may be user-modified to meet individual design specifications.