Showing papers in "IEEE Transactions on Power Apparatus and Systems in 1968"

Optimal Power Flow Solutions

Abstract: A practical method is given for solving the power flow problem with control variables such as real and reactive power and transformer ratios automatically adjusted to minimize instantaneous costs or losses. The solution is feasible with respect to constraints on control variables and dependent variables such as load voltages, reactive sources, and tie line power angles. The method is based on power flow solution by Newton's method, a gradient adjustment algorithm for obtaining the minimum and penalty functions to account for dependent constraints. A test program solves problems of 500 nodes. Only a small extension of the power flow program is required to implement the method.

Computer representation of excitation systems

Abstract: The availability of large digital computers has permitted more extensive computation of power system stability, a subject of increasingly greater importance. This paper suggests a common nomenclature and control system representation of the various excitation systems now available. It can be used to define input data requirements for computer programs, and can provide a consistent format in which manufacturers can respond to requests for excitation system data to be used for system studies.

Field and Analytical Studies of Transmission Line Shielding: Part

Abstract: An analytical model for the shielding of transmission lines against lightning is extended to the case of partially effective shielding, including the effect of possible leader approach angle distributions. Results of the Pathfinder projects are brought up to date, and the data are shown to be consistent with the model. An index number is developed to aid in classifying line performance, and suggestions are made regarding the study of the backflash problem.

Optimum Number, Location, and Size of Shunt Capacitors in Radial Distribution Feeders A Dynamic Programming Approach

Abstract: A new method is described which determines the optimum number, location, and size of shunt capacitors in a radial distribution feeder with discrete lumped loads so as to maximize overall savings, including the cost of capacitors. The method also determines when capacitors are not economically justified. Dynamic programming techniques are used and several algorithms developed to obtain the optimal solution by regarding the optimization process as a multistage decision process with the desired Markovian property. Special cases are studied and solutions obtained when no capacitor cost, cost proportional to installed capacity, and cost proportional to installed capacity plus a fixed cost per installed bank are considered. The methods are suitable for efficient solution in a digital computer.

An Application of Mixed-Integer Programming Duality to Scheduling Thermal Generating Systems

Abstract: A decomposable mixed-integer programming model for simultaneous economic consideration of unit commitment and short-term dispatch of thermal power generating equipment is presented. An optimum solution procedure is described which takes advantage of the structure of the model and promises computational efficiency in practical applications. Characterizing the demand forecast as a discretized function permits a probabilistic forecast to be incorporated in the scheduling model. The model minimizes the total expected costs of start-up, shutdown, and unit operating costs subject to the demand, reserve, and unit commitment constraints. Extensions to multiple periods and to include additional constraints such as time dependent start-up costs and geographic constraints are given.

Polyphase Induction Motor Performance and Losses on Nonsinusoidal Voltage Sources

Abstract: Induction motors excited with static frequency converters almost invariably are subjected to nonsinusoidal voltage waveforms, and the presence of time harmonics in the applied voltage results in currents at the harmonic frequencies. These currents result in additional and sometimes rather large losses. A method for calculating these harmonic currents and losses is presented, and experimental data are included to substantiate it. The losses are separated into various components and it is shown that the largest loss is usually in the rotor bars as a result of deep bar effect. Harmonic losses are shown to be nearly independent of motor load and the fundamental magnetizing current is found to increase over that which would be present for the same rms fundamental voltage. These observations are explained on a theoretical basis. The encouraging correlation between test and calculated data confirms that the important elements which differ between motor performance on sinusoidal and nonsinusoidal waveforms have been identified and accounted for.

Sensitivity in Power Systems

Abstract: Sensitivity is defined as the ratio ?x/?y relating small changes ?x of some dependent variable to small changes ?y of some independent or controllable variable y. In power systems, two dominant types of sensitivity relations are defined, namely 1) sensitivity of one electrical variable, such as the voltage Vi at node i, with respect to another electrical variable, such as reactive production Qj at node j, and 2) sensitivity of the operating cost F with respect to such electrical variables as the consumption Ci at node i and the production Pj at node j.

Transmission System Reliability Evaluation Using Markov Processes

Abstract: The basic concepts of stationary Markov processes and particularly their application to transmission system reliability evaluation are discussed and illustrated. Transmission components are assumed to operate within a 2-state fluctuating environment described by normal and stormy weather conditions. Markov processes are used to determine the system failure rate and the probabilities of failure for simple configurations and to illustrate the bunching effect of storm associated failures on parallel facilities. The variation in the failure probabilities is shown as a function of the expected repair time and the degree of storm associated failures. The results are compared with those obtained using a previously published approximate method.

The Phase-Locked Oscillator - A New Control System for Controlled Static Convertors

Abstract: Static convertors for high-voltage direct-current transmission links, whether based on mercury-arc valves or thyristors, are controlled by accurately timed firing pulses from a control system. With conventional control systems it has not so far been practicable to operate a convertor on a very weak (high impedance) ac system; one principal reason is inherent harmonic instability caused by the direct dependence of the control system on ac line voltage and its distortion.

Dynamic Stability Calculations for an Arbitrary Number of Interconnected Synchronous Machines

Abstract: Describing the small signal performance of a multi- machine synchronous power system by a set of differential equations of the form [x] = [A] [x] allows standard multivariable control theory to be used in dynamic stability studies. The construction of the [A] matrix for a multimachine power system involves the application of Kron's rotational transformation to the transmission network admittance matrix, and a matrix analysis of the synchronous machines using internal flux linkages as state variables.

Application of Underfrequency Relays for Automatic Load Shedding

Abstract: During severe emergencies which result in insufficient generation to meet load, an automatic load shedding program throughout the affected area can prevent total area collapse. It also helps to achieve fast restoration of all affected loads. This paper describes the factors involved in applying underfrequency relays to achieve a desired "deficient generation" protection level and a calculating method to achieve optimum relay settings.

Modes of Corona Discharges in Air

Abstract: Corona discharges in air exist under several distinctive forms, either pulsative or stable. The properties of different corona modes are analyzed as they appear in a cylindrical distorted field. Differences between dc and ac excitations are emphasized. Corona discharges may produce energy loss without detectable radio noise or high noise at low energy loss, depending upon their form of appearance. The different withstands of asymmetric gaps under different polarities also find their explanation in corona mechanism.

Method of Multiple Reference Frames Applied to the Analysis of Symmetrical Induction Machinery

Abstract: A method of analyzing the constant-speed performance of a symmetrical induction machine with applied stator phase voltages of any periodic form is presented Symmetrical components are not used in this analysis Instead, it is shown that by employing a series of reference frames, dc circuit theory may be used to determine the performance of induction machines Since phasor and complex impedance concepts are not incorporated, the theory of multiple reference frames permits a convenient and simple method of analyzing steady-state modes of unbalanced or nonsinusoidal operation which have heretofore been limited to analysis by the method of symmetrical components Also, this method establishes a rigorous approach to the analysis of constant-speed electrical transients of induction machinery

Optimum Control of Reactive Power Flow

Abstract: The general problem of minimizing the operating cost of a power system by proper selection of the active and reactive productions is formulated as a nonlinear programming problem in accordance with previous work by Carpentier of Electricitede France. This general problem is particularized to the minimization of transmission line losses by suitable selection of the reactive productions and transformer tap settings. An efficient computational procedure based on the Newton-Raphson method for solving the power-flow equations and on the dual (Lagrangian) variables of the Kuhn and Tucker theorem is discussed. This minimization procedure has been applied successfully to a 500-node system studied by the Bonneville Power Administration for which an effective power-flow program had been developed previously. The dual variables associated with the primary (electrical) variables are obtained in the course of the computation, and their engineering significance for power system design and tariffication is emphasized. The procedure has been extended to the general case of combined active and reactive optimization.

Effect of High-Speed Rectifier Excitation Systems on Generator Stability Limits

Abstract: A device to provide a signal proportional to changes in generator speed has been developed by Ontario Hydro. Field tests have been performed to demonstrate that use of this signal with a high-speed rectifier excitation system results in dynamic stability limits which approximate those which can be obtained with a zero reactance generator. Transient stability limits are greater than those obtainable with high-response conventional excitation systems. Results from the field tests and a computer study are compared.

Representation of the Magnetization Characteristic of DC Machines for Computer Use

Abstract: The calculation of flux densities in dc machines using digital computers requires a representation of the magnetization curve of the materials either as H = f1(B) or B = f2(H). A figure of merit of the approximation is defined. The representation can be achieved by the use of simple algebraic or transcendental functions. For satisfactory fit, however, the B-H characteristic has to be subdivided into several parts. As a better alternative a numerical method is proposed in which the magnetization curve is subdivided into a large number of sections. A method of linear interpolation is then employed. A computer program to accomplish this task is described.

Frequency and Duration Methods for Power System Reliability Calculations: I - Generation System Model

Abstract: As a goal, the evaluation and computation of electric power system reliability requires that a consistent technique be used for all portions?generation, transmission, and distribution. At present, a number of different methods are used for the generation system, while the frequency and duration of outages seems to be developing as a standard measure for the analysis of the distribution system. This paper and a subsequent one will present a reliability calculation method for the generation system that incorporates the frequency and duration of unit outages and includes consideration of the loads. This method leads to calculated generation reliability measures which are the availability, frequency of occurence, and mean duration of reserve states. These are cumulative states in that they specify system reserve conditions of a given magnitude or less. This paper is concerned with the procedure for calculating the availability, frequency, and outage duration for a number of generating units connected in parallel to form a single system. Numerical data are used to illustrate the technique and make comparisons with other methods.

Excitation Control to Improve Powerline Stability

Abstract: The influence of generator voltage regulators upon powerline stability is closely scrutinized by analog techniques. Contrary to common concepts, it is shown that high-speed control of excitation to maintain constant terminal voltage actually hampers rather than aids damping and powerline stability. It is further shown that damping and stability are greatly improved by supplementing excitation control with a specially derived function of frequency deviation. Results of the studies are verified in actual performance obtained in field tests.

Switching and Lightning Impulse Discharge Characteristics of Large Air Gaps and Long Insulator Strings

Abstract: Analysis of the influence of electrode shapes on the behavior of air gaps, both with and without insulator strings between the electrodes, is completed through the use of switching impulse tests. Results of a similar analysis for lightning impulse tests are also described. An attempt is made to correlate the behavior of air gaps in switching and lightning impulse tests to a factor k which characterizes the shape of the electrodes. Diagrams are given that express discharge voltages for switching and lightning impulse tests as a function of k.

A Technical Assessment of Artificial Commutation of HVDC Converters with Series Capacitors

Abstract: Artificial commutation with series capacitors, to extend the operation of mercury tube or solid-state converters beyond the normally attainable control angles, is analyzed in detail, and performance assessed for application to HVDC transmission. Operating characteristics are presented, including details of tube voltage stress and attainable range of control for particular capacitor values and system quantities. The repercussions of arc-back and commutation failure are discussed, and control requirements outlined.

Induction Motor Speed Control by Stator Voltage Control

Abstract: This paper establishes the fundamental laws relating to the speed control of induction motors by simple voltage control and emphasizes the problems that may be caused by excessive input currents which cause stator overheating. Eight different thyristor voltage control circuits have been tested to determine a best control circuit for three-phase motors and test results are given. A practical speed control for a 4-hp motor is described and the way in which a special rotor design can minimize the problem of excessive stator losses is convincingly demonstrated.

Optimum Load-Shedding Policy for Power Systems

Abstract: The now classical problem of optimlum dispatching miimizes the cost of production and transmission of electrical power to meet a specified demand under normal operating conditions. It appears logical and desirable to utilize and extend the methodology of optimum dispatching to problems encountered during abnormal operating conditions. This paper, as a first step in that direction, discusses a systematic approach toward minimizing the curtailment of service in a power system after a severe fault. The problem of minimizing load curtailment under a given set of emergency conditions is formulated as a problem of static optimization, subject to operational and equipment constraints. First, a feasible steady-state solution is obtained for the postfault network configuration. Starting from this initial feasible solution, the optinum (minimum curtailment) is approached by a gradient technique. An efficient computational procedure is based on the Newton-Raphson technique for solving the power flow equations, and the Kuhn-Tucker theorem for the optimization. The analytical results are verified on a 26-node example problem. Two typical emergency situations are considered: the loss of generation and the loss of an interconnection tie line. The same optimization procedure and the computed dual (Lagrangian) variables can be utilized for computer programs involving optimum service restoration, generation reserve scheduling, and system expansion studies.

Digital Simulation of Multimachine Power Systems for Stability Studies

Abstract: A digital simulation technique suitable for detailed analysis of both large and small disturbances on extensive power systems is presented. The analysis employs a hybrid reference frame for statement of the problem and for its solution. The equations of the interconnecting network are expressed with regard to a synchronously rotating common reference frame and are treated with the aid of matrix methods. Synchronous machine equations and equations of the voltage regulator and of the speed governor are solved in Park's reference frame fixed to the field of each individual machine. Provision is made for representing different machines in different degrees of detail. An efficient numerical technique for solution of the resulting complex nonlinear equations describing the behavior of the complete power system is introduced.

Influence of Excitation and Speed Control Parameters in Stabilizing Intersystem Oscillations

Abstract: Intersystem power oscillations have occurred between the interconnected utility systems of Saskatchewan, Manitoba, and Ontario (West System). Such power swings have been most evident when the power transmission angles on the interconnections or on certain internal 138-kV and 115-kV transmission have been of relatively great magnitude. The oscillations have been controlled or reduced by adjustment of the excitation of speed control parameters on various groups of machines throughout the three inter- connected systems. The analytical techniques utilized to determine the adjustments will be of considerable benefit in planning future exrtensions to the interconnections and facilities within the power systems in the three provinces.

The Analysis of Induction Machines Controlled by Series Connected Semiconductor Switches

Abstract: The widespread interest in applying semiconductor switching elements to induction motor speed control has created. a need for a fast and accurate means of predicting motor performance under the unconventional excitation inherent in these systems. In many cases this excitation takes the form of alternate periods of normal sine-wave excitation and periods of open-circuit operation. This paper presents an analytic means of determining steady-state performance under these conditions. Use of the techniques presented permits direct computer solution without iteration. Solution time is thus much shorter than can be achieved by iterative solution of the system differential equations and the necessarily long computation times required to allow the solution to reach steady state from arbitrary initial conditions. Computer results for a single-phase motor and for a capacitor run motor are presented. Results include average torque, motor losses, and efficiencies, and instantaneous torque, current, and voltage as a function of speed. Run time on an IBM 1620 Model II is approximately 100 seconds for each of the desired speeds. The method is thus well suited to evaluation of proposed motor designs and subsequent design optimization.

The Accurate Calculation of Skin Effect in Conductors of Complicated Shape

Abstract: Skin-effect behavior of long straight conductors of complicated cross-sectional shape may be predicted using the recently developed modal theory of current flow. Practical use of this method presupposes that suitable numerical techniques can be found to allow adequate accuracy to be attained without excessive use of computer time. A digital computer program is described that achieves this purpose satisfactorily, using very fast numerical techniques and making automatic compensation for truncation error. The program does not require the conductor description to be furnished in analytical form and may easily be employed to study a wide variety of conductor shapes. Some typical results are shown and comparisons with experimental data made.

Digital Simulation of Synchronous Machine Transients

Abstract: When synchronous machine transients in an extensive system are to be accurately calculated, many problems arise for which the information required to resolve them is not available. The resulting accuracy will depend upon the assumptions used not only in the development of the machine model but also in the way in which the incomplete model is solved. The primary problems involve the manner in which the machine terminal relations are related to those of the system and in the handling of the various torques produced in the transient operation. The state of the art of machine analysis is now such that synchronous machine transients are fairly well understood and calculations may be reasonably comprehensive. The system representation is, however, not capable of accepting the information available from the machine with the result that a satisfactory marriage is difficult. Some of the inadequacies of large scale stability analysis as it now exists and some of the precautions and planning that should be observed before embarking upon extensive studies or in drawing conclusions from such studies are covered here, in a philosophic and general manner.

Unusual Current Harmonics Arising from High-Voltage DC Transmission

Abstract: Unbalance in the operation of high-voltage dc convertors gives rise to unusual or uncharacteristic harmonics in the ac waveform not expected from the existing theory relating to balanced operation. Analysis of the effect of unbalances in the altemating voltages and the valve firing angles is provided together with selected characteristics illustrating the variations in the harmonics with unbalance as determined by a comprehensive digital computer program. Six-pulse and 12-pulse operation is considered.

Dynamic Simulation of HVDC Power Transmission Systems on Digital Computers - Generalized Mesh Analysis Approach

Abstract: This paper introduces and develops a new generalized approach to the dynamic simulation of an HVDC power transmission system. The approach involved is a generalized method of mesh analysis applied to the HVDC network. The simulation of HVDC convertors is characterized by the fact that the network to be solved changes with each discontinuity, such as valve firing and end of commutation. To facilitate such an analysis, topology is used and a technique is developed for the automatic selection of the appropriate network by recognizing the state of conducting and nonconducting valves. The method is inherently suitable for following the natural process of convertor operation which may culminate in various faults. To illustrate this method a simple HVDC system consisting of one convertor at each end is considered. Essential features of the program are shown by deriving waveforms of normal operation, commutation failure, four-valve conduction, bypass valve operation, and backfire.