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The classical two-axis model of the synchronous machine governed by Park's equations is expanded by' viewing the magnetic-field couplings along each axis as multiports characterized by typical matrices whose elements are pertinent open-circuit, short-circuit, hybrid parameters and system functions associated with specific port constraints. Four equivalent state models are presented. A hybrid dynamical model that uses the "constants" of the machine and represents rotor currents and fluxes by equivalent voltages is developed in the forms of state equations and analog computer representations as well as phasor diagrams based upon ignoring armature dynamics.

This paper defines a mathematical model which simulates the growth of a power system and determines the least cost expansion plan for a system of distribution substations. A new approach employing linear and integer programming is used to optimize the system's substation capacities subject to the constraints of cost, load, voltage, and reserve requirements. The model has been successfully applied to a 1600 square mile urban area served by 70 distribution substations.

Security evaluation is becoming an important part of power system operation. This paper presents a feasible pattern recognition approach to security evaluation in power systems. The evaluation problem is defined in the framework of pattern recognition and methods to obtain security functions are outlined. Simulation results on steady state and transient securities of the CIGRE 225 kv system are included.

The analysis of power system performance has always been enhanced by close interaction between engineer and computation, and recent developments in high-speed displays, minicomputer capacity, and computational technology are encouraging major revisions of computing practices for power system analysis. A comprehensive power system analysis package, PSS/2, is described which has been developed specifically for use with dedicated computers. This dedicated computer approach allows load flow, short-circuit, and dynamic simulation work, data base maintenance, and printed report preparation to be handled in the interactive mode at lower cost than could be possible by alternative batch or time-shared computing methods. The subjects covered are data organization, computational techniques, user interface, and operational experience.

Important power system planning and operation problems have been formulated as mathematical optimization problems. Such problems as the economic dispatch, in many of its facets; var scheduling and allocation; pollution dispatch; maximum interchange; hydrothermal unit commitment and dispatch; generation, transmission, and distribution expansion planning; maintenance scheduling and substation switching, have been formulated and solved. Modern mathematical optimization techniques, such as nonlinear, quadratic, linear, integer and dynamic programming and their many combinations and extensions, have been exploited. Some of the formulations and solutions to these problems as presented in the recent literature within the power systems field are reviewed. The large number of papers available is a measure of the current immense activity in this area. Attempts are made to point out some specific areas where more work needs to be done.

Power system operation is outlined and system security is defined. The need for security evaluation in power system operation is discussed, and the evaluation is presented as a pattern recognition problem. A suitable straightforward and quick procedure is used to select a small number of variables as features from a large set of variables which are normally available in power systems. Comparison is made on the security classification performances of a number of different types ot classifiers. The training of classifiers is carried out by a search algorithm which seeks to minimize the number of classification errors. The procedure to determine the security functions (classifiers) is illustrated by an example, and simulation results on the steady-state security of the CIGRE 225-kV system show that the pattern recognition approach to security evaluation is encouraging. Some uses of security functions in the control and operation of power systems are outlined. The effect of many of these uses cannot be achieved as easily by other existing methods. Finally, some of the problems associated with the application of pattern recognition to power system security evaluation are discussed.

Switching operations, faults, and other disturbances produce surges on transmission lines and oscillations in transformer and generator windings. Such electromagnetic transients have primarily been studied with transient network analyzers since the late 1930's. In recent years, digital computer programs have been de-. veloped which make simulation by digital computer competitive. The solution techniques of such programs are described, and their usefulness is illustrated with practical examples. Possibilities for further improvements are mentioned.

A historical development of mechanical and electronic differential analyzers as well as the significant developments in simulation techniques are discussed. Present-day application of modern analog and hybrid computers to electric power systems are presented. Included are the simulation of electric machines, static converter drives, transmission lines, and dc power systems. Special-purpose analog and hybrid computers are also discussed briefly. The material presented in this paper should enable an informed evaluation of the capabilities of analog and hybrid computers in the analysis of power system problems.

An analog computer simulation is often a useful tool in optimizing the parameters in a complex system such as a practical cycloconverter power system consisting of a three-phase generator, an isolation network, a cycloconverter, and an output filter. The key component in the system is the SCR employed in the cycloconverter.

Techniques for damping power system swings have been studied by analog and digital simulation.

The numerical results presented in this paper, in Tables I through VI, apply only to the PSEG system. First presented is a summary of the forced-outage data collected; see Table I. Table II compares the actual distribution of up-period duration with an exponential distribution. Then, Tables III and IV give estimates of average up-period duration and the probabilities of an outage being a halfoutage for the four classes of units. Table V shows the component failure rates for mature units. Table VI gives the details of the durations and postponements of down periods. Comments on the numerical results are given in the section "Results" at the beginning of the paper.

Switching-surge overvoltages are a major concern in the establishment of insulation levels of modern EHV and UHV power systems. Transient Network Analyzer (TNA) and digital model simulations of these systems are the primary means of determining what the insulation levels should be before the actual systems are constructed.

Comparisons are made between the use of a large scale computer program, and a specialized simulation approach, when determining the value of damping forces present when large sources of generation are perturbed and angular swings develop between such sources, and persist for several seconds. In part I of this paper, the machine modelling and organization of machine-network interconnection equations are discussed.

The reinforcement of power-system interconnections intensifies the need for stability studies. The growing complexity of the networks tremendously increases the difficulties of performing these investigations. Present computers are not capable of representing a major system pool in detail and producing a study in reasonable time and at reasonable cost. One possible solution is to reduce the size of the system by the use of equivalents to represent portions of the network beyond the area of immediate interest. Stability equivalents are not perfect, but their use offers the possibility of reducing the problem to manageable proportions.

A direct method is introduced for minimizing the shift of generation required to meet temporary operating criteria, such as the elimination of overload lines or transformers, or fixed flows on inter-ties or critical lines. Also, a linear model for multiple contingencies is presented.

A simulation a roach suitable for non-linear analysis of the dynamic berformance of large power systems is developed. The problem of matching machine and network equations forms an important criterion in the development of the machine model. Among the major aspects treated is the influence of amortisseur circuits. Organization of system equations is evolved so as to permit rapid solution employing one level iteration of the resulting algebraic equations, which account for a very significant portion of the total computing time. In part II of this paper, network solution procedures and results of investigations carried out on typical systems are presented.

This paper describes the results of studies made to improve the dynamic response and damping torques of power systems incorporating synchronous machines with 2-axis excitation control. Dynamic optimization techniques have been used to determine the optimum controls subject to a quadratic integral performance index. The system has been simulated as a seventh order, closed loop, non-linear model incorporating speed governor and voltage and angle regulators. Modified quasilinearization and first order gradient methods have been utilized for solving the optimization problems for this non-linear system. The investigations indicate that optimal control of doubly excited synchronous machines is possible and that it yield, s improved transient performance. Incidentally, some possible limitations of the quasilinearization technique have also been brought out.

A linear programming model can be used to plan new generation and transmission systems. The instance described is a model for the Pacific Coast region of the United States for the years 1965 through 1980. The method allows simultaneous optimization, at a high level of aggregation, of all decision variables relevant to this geographic space and time period. The results include marginal cost estimates and analysis of the sensitivity of the solution to various given data and parameters, as well as a description of the optimal system. The strengths and limitations of linear programming in this use are discussed.

Since the development of sparsity techniques by Tinney, the power-flow program has become an extremely effective and often used tool for planning electric power networks. This program solves for the unknowns--voltages, phase angles, etc.--of a set of simultaneous nonlinear algebraic equations, the ac power-flow equations. The optimum power flow is likely to replace, in due time, the normal power flow in many important planning functions discussed in this paper. A number of mathematical programming techniques have recently been studied to solve the optimum power flow and several small-to-medium sized experimental programs have been written. The generalized reduced gradient (GRG), one of the most elegant nonlinear-programming techniques, is described and it is shown how it can be extended to solve optimum power flows of very high dimension (of the order of several thousand nodes). This extension consists mainly of using sparsity techniques in several of the solution steps of the GRG.

A field test program is described which was used to evaluate and then to adjust the 33 power system stabilizers installed on the Pacific Gas and Electric Company's system. Also included is a comparison of the results of these tests with those of a digital computer simulation.

A model of a single steam turbine generator is developed which includes the effects of random load fluctuations observed in interconnected power systems. This model is used in the design of an on-line state estimator for an individual generator. A digital simulation of the generator model and state estimator indicates the state estimation procedure is feasible and can be implemented on a small control computer.

In this paper the hybrid computer-is-used-to-study dc power system consieing-of a 2-wire transmission system and two 12-phase converters with ground return. This work is an extension of the hybrid computer study of a 6-phase, 2-wire dc system which was reported in Part I of this paper.[2] Several features of a dc power system are presented including a comparison of results obtained from the hybrid computer study and those obtained using the University of Wisconsin ac/dc system simulator for a line-to- ground fault. It appears that the hybrid computer may be used to advantage in studying the effects of ac or dc system disturbances as well as the feasibility of any type of converter control system. Moreover, the simulation techniques presented in this paper may be extended to include a 3-phase transmission system whereupon the hybrid computer may be used to study electrical transients in ac power systems.

The Bull Run supercritical unit was simulated by a linearized mathematical model based entirely on physical laws and design data, using an approach verified by comparison of an earlier simulation with field tests. A large set of differential and algebraic equations was solved to obtain transient responses. These responses were matched by transfer functions to obtain a process model which represented all significant plant inputs and outputs. In this study, appropriate use was made of a small digital computer, a large digital computer, and an analog computer. The process model of the Bull Run unit is believed to be the most detailed mathematical model which has been obtained for a supercritical electrical generation unit.

As systems have increased in size and complexity, and as the number of firm-power ties between systems have increased, the nature of the system stability problems has changed. Furthermore, there is also a demand for more accurate engineering analysis of these complex problems. Although much effort has been devoted to searching for alternate methods, the practical and effective method for large-scale studies is still the simulation of the system response, with time, following a prescribed disturbance. This emphasis on simulation necessarily requires system and equipment models which adequately represent their behavior over some time span, usually less than 20 seconds.

A study was made of the accuracy of utility power system stability simulations, as affected by the complexity of the synchronous generator models and the data used with the models. The investigation was performed by simulating the operation of a representative multimachine power system with many combinations of disturbance, initial load, system stiffness, model detail and model data. The findings from this study provide guidelines for the selection of the simplest computational machine models for use in large scale stability analyses, with the goal of minimizing the cost of computer usage while assuring sufficient accuracy of the results. Recommendations are made for selecting machine data more suitable for use in stability studies than the standard machine data.

In some studies of HVDC system design, ac system impedance is represented by its inductance at power frequency. However, for several studies better simulation of the impedance- frequency characteristic (from power frequency to a few kilohertz) of the ac system is important. This paper presents a simple approach to calculating an approximate equivalent network consisting of parallel LCR branches and having an impedance-frequency characteristic similar to that given for the ac system. For given typical ac system impedance diagrams (usually obtained from ac system models and simulators), simulation of an ac system by corresponding equivalent networks during studies of certain HVDC problems would provide a more accurate means of designing HVDC systems.

This paper presents a general, systematic formulation of the problem of dynamic analysis of multi-machine power systems for digital simulation. The analysis utilizes a generalized machine model which enables one to consider the affect of network response in more detail than described in the literature. The techniques of solution are discussed in order to indicate the structure of numerical computation.

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.

All the solutions for the determination of the stability of an electrical network by means of digital computers contain some approximation, because of the complexity of the system simulation. The simplifications adopted in the majority of these programs are not always justified and, therefore, the confidence in the results is not always well established. The choices made in making a new program are discussed. They are related to the network component simulation, to the numerical process, and to the program specifications.

A method is described for determining the most economical generating utiit commitment policy and loading schedule for a day's operation of an electric utility system while maintaining a desired level of system reliability.

This paper presents an analytical approch to the construction of power system dynamic equivalents for use in stability calculations and dynamic simulations. The method presented is capable of accurately representing the dynanlical effects of generator field and amortisseur windings, voltage regulators, and speed governors. Experimental evaluation of equivalents constructed by this method is reported in a companion paper.

A new production-testing facility utilizing an analog computer to help test voltage regulators and excitation systems and, thereby, reduce installation time is described. Field tests and factory tests are indicated to show the accuracy of the computer simulation. An Appendix thoroughly discusses theory of analog computers.

Overall critical evaluation of the dynamics of EHV dc-power transmission requires that a variety of system conditions and effects of many parameters be studied. Problems can be strictly electrical or electromechanical. In general, those that fall in the former category are of short time duration, while those in the latter may be either of intermediate duration, on the order of 1 second, or of long duration, from 2 to 40 seconds. The approach used, whether it be 1) a physical model such as a transient network analyzer; 2) an analog computer, sometimes called an electronic differential analyzer, or 3) a digital computer, will depend upon the specific problem at hand. The capabilities and limitations of the analog computer in providing solutions to electromechanical problems are outlined in this paper, and the results reported give insight into the dynamic performance characteristics of a dc link under constant current or power control, with or without a parallel ac line.

A composite model for multireservoir hydroelectric power systems is constructed for studying the monthly decision conceming total hydrogeneration. This is an important decision when the inflows are uncertain and when hydro, with zero marginal cost, can be used not only to satisfy firm load commitments but also to displace other firm resources or to serve secondary loads. In such a case, the tradeoff between savings at the present and expected benefits in the future is determined mainly by the total hydrogeneration. The construction of a composite representation for the multireservoir hydroelectric power system in the Pacific Northwest is described. The composite model is based on a single measure "potential energy" which is indicative of the system's generating capability. This results in a one-dam representation of the multireservoir system which, in effect, receives, stores, and releases potential energy, in a statistical model for the potential energy inflow and in a generation function which relates potential energy released to actual electric power generated. It has applications in the study of different operating policies, market structures, and investment programs through simulation or optimization. As an example, it is used to obtain the net operating revenues as a function of the excess thermal in the system.

Outline of a group of methods that will permit calculation of all the common changes on power-system networks by superposition methods having as a basis the representation of loads as fixed currents. Investigation of the errors involved, and comparison with results obtained by assuming constant-impedance loads, when applied to the average power-system networks in operation today.

A complete and comprehensive mathematical model of phase shifting components is developed using a delta-wye transformer bank as an example of a typical phase shifting component. Linear graph theory techniques are used to form the model which is called a V-equivalent. The V-equivalent is incorporated into the network matrix called ZBUS which is then used in the short circuit equations for a line-to-ground fault. In this paper, a numerical example utilizing a sample power system is used to illustrate the method by which the V-equivalent of a delta-wye transformer bank is incorporated into a digital computer program for short circuit studies. The results of the digital computer program demonstrate that, by the use of the V- equivalent, phase shifting components such as delta-wye transformers can be made an integral part of the power system model. A single line-to-ground fault can occur on either side of the delta-wye transformer bank, and the correct values of the currents and voltages at the fault and throughout the system can be obtained directly from the solution of the system model. No subsequent calculations are necessary to correct for the effect of the phase shift.

Switching of series capacitors to improve system stability is of current interest. Investigations indicate that modern control theory might be applied to determine switching of a combination of series capacitors so that the system may be transferred from one state to another in minimum time and in a nonoscillatory manner. In these studies, a simplified voltage-reactance equivalent of the one-machine infinite bus system was used. The material presented in this paper shows that this simplified model does not predict the performance of a one-machine infinite bus system with the accuracy necessary to determine the capacitor switching times so as to achieve the control objectives. However, it is shown that computation accuracy may be improved by including system losses. It appears that in order to apply optimal control techniques it will be necessary to develop more accurate models of the power system components. Also, faster than real time iterative, on-line, computation techniques as simulatedc in this paper should be implemented and used to calculate the switching times. Until these obstacles are overcome, optimal control theory will have little impact upon the power industry.

Simulation programs for electromagnetic transients must provide models for lightning arresters, transformer saturation, circuit breakers and other nonlinear and time-varying effects. This paper describes techniques for keeping the solution time in networks with such elements as low as possible, by using the compensation method or network equivalents.

This paper presents the results of an Anacom study which investigated the performance of modern lightning arresters during switching surge operation. A description of the variable characteristic arrester model used to simulate the lightning arrester is presented as are the results of the study using the model on a representative 345-kV system. Particular emphasis is placed on the parameters effecting the discharge current, voltages and energy with attention given to the protective characteristic of the arrester.

Reliability measures how well a system can be expected to perform its intended purpose; it is expressed as a probability function with time and environment as variables. This paper discusses the mechanics of component failure and repair and shows that power system behavior follows a Markov process. The reliability of simple system configurations is evaluated analytically by solving the Markov equations. The reliability of complex systems is more easily evaluated by the use of digital computer simulation. The simulation method is described.

This paper summarizes the results of an investigation into the use of hybrid computer systems for the solution of problems associated with the generation and transmission of electrical power. In particular the study was conducted to determine if hybrid computing techniques could result in the capability of real time, or faster, transient stability studies. It was determined that a special purpose hybrid system could provide simulations of power system transient disturbances 100 times faster than real time.

A gas-turbine package power plant was used to provide startup power for a 250-MW steam-generating unit. Performance of the excitation system during startup of large power-station auxiliary motors closely matched that previously calculated by a digital-computer program. Results of the computer study and full- scale verification tests are presented. These results verified that the digital-computer program used accurately simulated the dynamic characteristics of the excitation system, generator, and motor. Based on this verification, it was concluded that further computer studies could be utilized with confidence to predict voltage dips at critical locations in the power system.

After mentioning different methods of testing the ability of an arrester to discharge long-duration switching surges, the artificial line discharge test with applied power frequency voltage is discussed. Oscillograms show that voltage transients during such tests may be influenced by the series gap of the test circuit. Test results agree fairly well with curves obtained from digital computations. Hence it appears justifiable to investigate by digital computations alone how test results are influenced by varying certain test- circuit parameters and the rate of rise of the arrester arc voltage. Computations were made for a 525-kV line and a modem 80 percent arrester. Particular mention is made of the disadvantage that could arise from too high a rate of rise of the arc voltage and of the fact that short lines can, in certain cases, impose a heavier duty on an arrester than longer lines.

Test and adjustment of hydraulic turbine governors has been an unfortunately complicated process involving the optimization of several interrelated variables. In earlier years stable performance was achieved by empirical adjustments in the field on isolated load, but optimum was seldom achieved. In more recent years the interconnection of systems has denied the opportunity for testing of units on isolated load. Nevertheless, the interconnection of systems actually places a higher premium on good coordination. Optimization by test and adjustment of individual parameters has yielded improvement but it is limited in dealing with nonlinearities.

During the last few years, there has been expanded effort throughout the country to install frequency actuated load shedding programs for the purpose of providing means to safeguard a power system should a condition of declining frequency occur. Hand in hand with a load shedding program a convenient means must be provided for restoring load after the system returns to a normal state. In this series of papers, the authors will present some of the basic principles which should be considered in the application of a load shedding and load restoration program and will describe the philosophy which led to the frequency actuated load shedding and load restoration program being implemented on the American Electric Power System. As part of this presentation, the various analytical studies which were carried out to determine the load management programs for the AEP system will be described in detail. In addition, the method of program implementation and management is presented in a companion paper.

A survey is made of the present status of technology of solar photovoltaic, photoemissive, thermoelectric and thermionic power systems for spacecraft. The subjects of radiation damage to solar cells, power-system design, and solar simulation are reviewed. Various types of solar power systems are discussed and compared with respect to weight, availability, environmental tolerance, and cost. It is concluded that solar photovoltaic and solar thermionic systems are most desirable for power levels up to 3 kw. However, the life capability of thermionic converters has not yet been established. Solar thermoelectric and photoemissive systems will be less desirable because of their lower efficiency and, therefore, larger area per unit power output, except for missions where radiation resistance or economy are paramount considerations.

In considering the problem of quantitative evaluation of the reliability of a power system for planning purposes, the authors show the advisability of making use of a couple of risk indices in terms of curtailed energy and abruptly disconnected power.