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Showing papers on "Power-flow study published in 1990"


Book
14 Dec 1990
TL;DR: This book describes the main computer modelling techniques that constitute the framework of modern power system analysis and covers load or power flow, AC system faults, and the electromechanical behavior of power systems.
Abstract: This book describes the main computer modelling techniques that constitute the framework of modern power system analysis. After describing the main computational and transmission system developments influencing power system analysis, the book covers load or power flow, AC system faults, and the electromechanical behavior of power systems. Dynamic models of power system plants and their use in multi-machine transient stability analysis are discussed, and chapters also cover the electromagnetic transients program, harmonic flow analysis, and power system security and optimization analysis. Recent advances in interactive power system analysis and developments in computer graphics are also presented.

232 citations


Journal ArticleDOI
01 Jul 1990
TL;DR: The authors present a new method for obtaining the PLF solution, by combining Monte Carlo simulation techniques and linearised power flow equations for different system load levels, through the IEEE 14-busbar test system and through its application in part of the Brazilian network.
Abstract: Load flow analysis is undoubtedly the most useful method of designing and operating power systems. The input data necessary for these studies are best described by random variables, considering the probabilistic nature of loads, generation and networks. The effects of uncertainties on the steady-state behaviour of power systems can be evaluated by a stochastic or probabilistic load flow (PLF) analysis. The authors present a new method for obtaining the PLF solution, by combining Monte Carlo simulation techniques and linearised power flow equations for different system load levels. The performance of the proposed algorithm is illustrated through the IEEE 14-busbar test system, and also through its application in part of the Brazilian network. >

164 citations


Journal ArticleDOI
TL;DR: In this article, a method for the simulation of the composite power system is proposed for the purpose of evaluating the probability distribution function of circuit flows and bus voltage magnitudes, which consists of two steps.
Abstract: A method for the simulation of the composite power system is proposed for the purpose of evaluating the probability distribution function of circuit flows and bus voltage magnitudes. The method consists of two steps. First, given the probabilistic electric load model, the probability distribution function of the total generation of generation buses is computed. Second, circuit flows and bus voltage magnitudes are expressed as linear combinations of power injections at generation buses. This relationship allows the computation of the distribution functions of circuit flows and bus voltage magnitudes. The method incorporates major operating practices such as economic dispatch and nonlinearities resulting from the power flow equations. Validation of the method is performed via Monte Carlo simulation. Typical results are presented, showing that the proposed method matches the results obtained with the Monte Carlo simulations very well. Potential applications of the proposed method are: composite power system reliability analysis and transmission loss evaluation. >

131 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a method and the mathematical formulation for large-scale optimal power flow sensitivity analysis, which has been implemented in a computer program (OPSENS) presently in use in the Pacific Gas and Electric Company.
Abstract: The authors present a method and the mathematical formulation for large-scale optimal power flow sensitivity analysis. The method has been implemented in a computer program (OPSENS) presently in use in the Pacific Gas and Electric Company. The results of using the OPSENS program for calculating the sensitivity of system losses for a 34 bus and a 1700 bus transmission network to bus load changes are reported and compared to the results of multiple OPF (optimal power flow) studies. The effectiveness of OPSENS in this application was demonstrated. >

76 citations


Proceedings ArticleDOI
11 Jun 1990
TL;DR: In this paper, the effect of a non-ideal source on system performance is determined using the impedance comparison technique, where the impedances at the interface bus provide all of the necessary information to determine the location of the integrated system eigenvalues.
Abstract: Aspects of integrating subsystems to form a high-performance distributed power system are addressed. Both intermediate bus and system input filters are designed for a two-stage conversion topology to minimize bus interaction and degradation of loop-gains. The effect of a nonideal source on system performance is determined. It is shown that the impedances at the interface bus provide all of the necessary information to determine the location of the integrated system eigenvalues. The system eigenvalues can be determined graphically using the impedance comparison technique. The technique is particularly useful for large-scale systems where analytical equations ar not available. >

63 citations


Journal ArticleDOI
29 Apr 1990
TL;DR: In this article, the authors considered the effect of harmonics on reactive power measurements, and presented a novel method for calculating active, reactive apparent, and residual power in nonsinusoidal conditions.
Abstract: The authors consider the effect of harmonics on reactive power measurements, and present a novel method for calculating active, reactive apparent, and residual power in nonsinusoidal conditions. The method considers common and uncommon harmonic components of voltage and current waveforms. It properly defines all power components at different harmonic frequencies, such as rotating real power, quadrature power, and the residual power (distortion). Each component is calculated correctly at different frequencies to define its physical meaning. A computer algorithm is developed to calculate all the power components for any distorted voltage and current waveforms. A numerical example is discussed. >

63 citations


Journal ArticleDOI
01 Jan 1990
TL;DR: In this article, the authors present a physical interpretation of active, reactive, distortion, and apparent power for nonsinusoidal and sinusoidal systems with sinusoid and/or nonsinoidal voltage and current.
Abstract: Currently accepted definitions of power components are reviewed, and their disadvantages are analysed. New definitions of active, reactive, distortion, and apparent power are discussed. It is attempted to find a clear physical interpretation, and to formulate this for each power component in systems with sinusoidal and/or nonsinusoidal voltage and current. Formulas for the straightforward calculation of each power component are obtained. It is shown that (a) distortion power, as defined here consists of both active and reactive terms (b) apparent power in a nonsinusoidal system must be represented as a many-dimensional vector, and not as a vector of three dimensions as is generally accepted today. Examples are given to illustrate the application of the developed theory.

57 citations


Journal ArticleDOI
01 Jan 1990
TL;DR: In this paper, a new formulation of the OLF problem has been attempted to minimise both the cost of generation and transmission loss simultaneously through a multiple objective programming technique (priority goal programming technique).
Abstract: In the past a great deal of work has been reported on optimal load flow (OLF). However, in most of the works only one aspect of the power system has been optimised. The OLF problem (optimal real and reactive power dispatch) has been attempted sequentially, rather than simultaneously. In this paper a new formulation of the OLF problem has been attempted to minimise both the cost of generation and transmission loss simultaneously through a multiple objective programming technique (priority goal programming technique).

29 citations


Journal ArticleDOI
TL;DR: A review of the existing techniques for the reactive power allocation in large power systems is presented in this article, where the authors describe the problem with its significance to the operation and planning of power systems.
Abstract: This paper reviews of the existing techniques for the reactive power allocation in large power systems. The description of the problem with its significance to the operation and planning of power systems is presented. Merits of the corresponding techniques are reviewed according to their types of formulation.

23 citations


Proceedings ArticleDOI
05 Dec 1990
TL;DR: In this article, the authors used algebraic geometry techniques to determine the number of solutions of the full-fledged load flow of power systems and then developed an imbedding-based continuation method to reduce the computational complexity in finding all or some of the solutions.
Abstract: Powerful analytical tools and modern techniques from algebraic geometry are used to determine the number of solutions of the full-fledged load flow of power systems. Sufficient conditions are provided which guarantee the precise number of solutions to the load flow. The sufficient conditions are cast in terms of properties of the physical admittance matrix of the power grid. When the sufficient conditions are not satisfied, the cluster method is used to provide a 'tighter' upper bound on the load flow solutions for special power grid structures. The authors then develop an imbedding-based continuation method to reduce the computational complexity in finding all (or some of) the solutions of the so-called class of deficient systems. The authors specialize some of the results to example models and illustrate the computational efficiency of the proposed procedures by numerically finding all of the load flow solutions of the examples. >

20 citations


Journal ArticleDOI
01 Sep 1990
TL;DR: A review of three-phase power metering is given in this paper, and the effects of harmonics on power measurement are analyzed, and it is noted that applying digital microprocessor technology to power meters permits the precise measurement of power.
Abstract: Energy (kWh) measurement has become critically important in determining industrial power flow. With the proliferation of nonlinear loads, there are significant amounts of harmonics in the power distribution system. The effects of nonlinear loads on devices such as circuit breakers have been studied in detail. A review of three-phase power (kW) metering is given, and the effects of harmonics on power measurement are analyzed. It is noted that applying digital microprocessor technology to power metering permits the precise measurement of power. With sample data techniques, it is possible to determine true real power or kWh consumed by the power distribution system or resolve poor power factor questions. >

Proceedings ArticleDOI
11 Jun 1990
TL;DR: In this article, a DC model for a computer backplane power distribution system with multiple sources and loads is proposed, and criteria are derived to determine the allowable range of variation in DC output voltage for a power module operating in a multiple source, multiple load system with a backplane interconnect.
Abstract: A DC model for a computer backplane power distribution system with multiple sources and loads is proposed. Criteria are derived to determine the allowable range of variation in DC output voltage for a power module operating in a multiple-source, multiple-load system with a backplane interconnect. These criteria impose constraints on output voltage as a consequence of load voltage specifications, and of current-sharing accuracy required of the sources. An algorithm for implementing the solution of these criteria is presented. Computational results for two examples of power distribution systems using this algorithm are presented. The advantage of the system model is that a complete description is provided for a generalized power bus system, which may include ground and power planes of arbitrary geometry. The advantages of the algorithm are that the constraints determined for source voltage are valid under all combinations of load variation and source voltage variation. >

Journal ArticleDOI
TL;DR: A Jacobian matrix of the fast decoupled power flow algorithm is modified to account for the voltage-dependent reactive power consumption of AC/DC converters to find a power flow solution for weak AC systems where the standard sequential algorithm fails.

Journal ArticleDOI
K.F. Chan1, J. Ding1
TL;DR: POSCODAM (power system computation and data management) is an integrated package of three program systems, namely, POSDAM, POSCO, and POSGRAPH, for graphical input and output of network topologies and computed results.
Abstract: Features of POSCODAM, a power system planning and analysis software package, are described. POSCODAM (power system computation and data management) is an integrated package of three program systems, namely, POSDAM (power system data management), POSCO (power system computation), which consists of load-flow and short-circuit analysis modules, and POSGRAPH (power system graph), for graphical input and output of network topologies and computed results. During the past six years, this package has been used for applications such as optimization of energy transmission in regional electric networks, determination of reactive power compensation, investigation of system and equipment overloads, determination of system short-circuit power levels, dimensioning of switchgear and protection coordination, and grounding of power system neutrals. >

Proceedings ArticleDOI
11 Jun 1990
TL;DR: In this paper, a method for efficiently analyzing distributed power systems during the design process is presented, where individual DC-DC power converters are modeled by using averaged or device-level representations.
Abstract: A method for efficiently analyzing distributed power systems during the design process is presented. Individual DC-DC power converters are modeled by using averaged or device-level representations. The averaged models for basic power converter topologies are combined with behavioral models for the control loop. Simulation accuracies close to those for a full component-level model can be achieved with more than an order-of-magnitude reduction of the simulation time. The newly developed models are used for system-level simulation. System stability for fully distributed loads is readily determined for a number of power systems configurations. >

Proceedings ArticleDOI
31 Aug 1990
TL;DR: The authors present a comparison of three phase load flow algorithms for distribution power systems and studies of two Chilean distribution networks are made with an algorithm based on the power summation method.
Abstract: The authors present a comparison of three phase load flow algorithms for distribution power systems. Reference is made to traditional single-phase load flow methods used in transmission systems and the main three-phase load flow methods used in distribution. Studies of two Chilean distribution networks are made with an algorithm based on the power summation method, and a comparison of errors and the influence of modeling are reported. >

Journal ArticleDOI
TL;DR: The authors discuss the development of applications software called the System Reconfiguration Analysis Program (SYSRAP) for modeling distribution automation operations on the Athens Utilities Board (AUB) and the database techniques that SYSRAP uses to speed up database access and computation time and the data requirements for modeling the real-time operation of an electric distribution system.
Abstract: The authors discuss the development of applications software called the System Reconfiguration Analysis Program (SYSRAP) for modeling distribution automation operations on the Athens Utilities Board (AUB). The first phase of development involved the testing of algorithms that combine a radial power flow analysis, short-circuit analysis, and database structuring of input and calculated values in a database management program. In the second phase, the algorithms were written in a Pascal program and feeder data were dynamically allocated to system memory to speed computation and access times. During the last phase of development, the program was linked with the real-time data monitored by the distribution automation system at AUB so that SYSRAP could model the real-time behavior of the distribution system as closely as possible. The authors discuss the database techniques that SYSRAP uses to speed up database access and computation time and the data requirements for modeling the real-time operation of an electric distribution system. >

Journal ArticleDOI
TL;DR: A microcomputer-based power network control simulator designed to be used as a teaching aid for students in power engineering courses is introduced, an offline version of control systems actually used in power utilities.
Abstract: A microcomputer-based power network control simulator designed to be used as a teaching aid for students in power engineering courses is introduced. The system is an offline version of control systems actually used in power utilities. It includes functions such as steady-state security analysis and security monitoring, online load flow, and contingency analysis. Using a special feature implemented in the system called perturbation scheduling, different events can be set up to occur at different times before the simulation takes place. Also available to the user are other functions, such as short-circuit study and transient stability analysis, that are normally used for planning or study purposes. Following a detailed description of the system, software integration in an undergraduate power system operation course is illustrated, and students responses are discussed. >

Journal ArticleDOI
01 Nov 1990
TL;DR: In this paper, the gradient projection method (GPM) is applied to optimal power flow (OPF) problems and four objectives are chosen to illustrate the flexibility of the method with respect to the analytical formulation: active power dispatch, active power transmission loss minimisation, the minimisation of the weighted reactive power injection and the complete active-reactive power dispatch.
Abstract: For pt.I see ibid., vol.137, pt.C, no.6, p.424 (1990). The authors look at the application of nonlinear programming particularly the gradient projection method (GPM), to optimal power flow (OPF) problems. Four objectives are chosen to illustrate the flexibility of the method with respect to the analytical formulation: the active power dispatch; the active power transmission loss minimisation; the minimisation of the weighted reactive power injection; and the complete active-reactive power dispatch. Results from the application of the proposed technique to five power systems, including a practical network, are used to assess its performance. These demonstrate that this approach is quite competitive with other methods, and is superior in many ways.< >

Journal ArticleDOI
01 May 1990
TL;DR: In this article, a technique that deals with the power system hydro-thermal optimal power dispatch problem accounting for the effects of uncertainty in predicting active power demand is presented, which relates the probability distribution of the uncertain factors in the system active power generation, bus voltages, and phase angles to the probability distributions of the errors resulting from the forecast of the active power consumption.
Abstract: A technique that deals with the power system hydro-thermal optimal power dispatch problem accounting for the effects of uncertainty in predicting active power demand is presented. The method relates the probability distribution of the uncertain factors in the system active power generation, bus voltages, and phase angles to the probability distribution of the errors resulting from the forecast of the active power demand. The equality constraints considered are the power flow equations in the polar co-ordinates, using the nodal admittance matrix formulation. A comparison of stochastic results with the conventional dispatch is offered for the 14-bus system. The differences in voltage profiles are minimal, but the corresponding differences in power, and energy losses can be noticeable. The authors also discuss the potential for using the proposed technique to supplement spinning reserve allocation as a tool for catering to uncertainty in demand.

Proceedings ArticleDOI
15 Oct 1990
TL;DR: In this article, a bus voltage performance index (VPI) is proposed for optimal reactive power planning, which is equal to the root mean square value of the corresponding column of the sensitivity matrix.
Abstract: A systematic procedure is developed to locate and minimize the number of reactive power devices in power systems based on a set of indices and the sensitivity matrix. A definition of the bus voltage performance index (VPI) is proposed for optimal reactive power planning. It is equal to the root mean square value of the corresponding column of the sensitivity matrix. The VPIs in previous work depend on the norms which can be defined in nonunique ways. In the proposed technique, the three indices are given different weights depending on their values. The load buses are also ordered on the basis of their values depending on the total weights at each bus for the three indices. This ordering of load buses as well as the sensitivity matrix is then used to determine the optimal location and number of reactive power devices required in the system. >

Journal ArticleDOI
L. Wang, Niande Xiang1, Shuxiao Wang1, Bingqing Zhang1, Minlie Huang1 
01 Jan 1990
TL;DR: In this paper, a decoupled power flow method based on a novel decoupling form was developed for the purpose of obtaining best convergence, which is referred to as the best in the novel decoding form.
Abstract: A novel decoupled power flow method is reported, based on a novel decoupling form, and is developed for the purpose of obtaining best convergence. It is therefore referred to as the best in the novel decoupling form. The proposed method converges well not only on normal r/x ratio systems, but also on systems with high r/x ratio lines; the difficulties in convergence of decoupled power flow methods caused by high r/x ratio lines are overcome by the method proposed. Numerical results are presented to demonstrate the efficiency of the proposed method.

Proceedings ArticleDOI
23 May 1990
TL;DR: In this article, the authors examined the relationship between small-magnitude load fluctuations and their relative intensities to the voltage collapse in a power system and derived an indicator to determine the system's relative time to collapse at various buses.
Abstract: The aim of this paper is to examine the relationship between small-magnitude load fluctuations and their relative intensities to the voltage collapse in a power system. Based on this examination, an indicator is derived to determine the system's relative time to collapse at various buses. This indicator is represented by the mean first passage time of a power system which is perturbed by small load fluctuations, from the domain of attraction of its stable operating point at the incidence of the voltage collapse. This time is indicative of the often on-field reported relatively long period of uncertainty, before the voltage collapse occurs. A relatively simple power system model is used in this study because the main idea is to test the viability of the proposed indicator in system dynamics representation. Since voltage collapse is a local problem, imminent critical buses or areas within the power system will be identified by this method. Computationally, the method will provide various means for its eventual on-line implementation in a large-scale power system environment. Among the many questions that this project will answer are how the size of the region of attraction, the structure of the system dynamics, and properties of various disturbances would influence the voltage collapse indicator.

Proceedings ArticleDOI
17 Sep 1990
TL;DR: In this article, a split level bus (SLB) is proposed to operate at full differential mode at all times so the receiver never detects an indeterminate state, allowing full common mode range.
Abstract: A low-power differential bus utilizing a novel split level bus (SLB) technique is described. There are several inherent advantages with the SLB. The bus operates at full differential mode at all times so the receiver never detects an indeterminate state. There are no reference levels on the bus, allowing full common mode range. Making D and DB both passive or active at the same time can make the SLB appear similar to single-ended operation. This makes any present single-ended bus technique, such as future-bus arbitration, directly applicable to the SLB. The reduced power dissipated by the internal circuitry, and reduction in power supply pins, allow wider parts in the same package. The losses on the bus are reduced and the bus power remains constant for any number of drivers. >

Proceedings ArticleDOI
21 May 1990
TL;DR: In this paper, the authors discussed the desirability of no-break power transfer, optimal no break power transfer and the reason for minimizing circulating watts and VARs, power flow control, other factors affecting circulating power, synchronization control, and means of no break transfer.
Abstract: No break power transfer can be accomplished from ground power to an aircraft or between multiple sources on an aircraft with 400-Hz electrical power using a frequency reference autoparallel unit (FRAPU). The no-break function can also be included in the control functions of the feedback control system of the electrical power generating system. The parameters that are controlled to achieve this successful electric power generator system approach to no-break transfer, allowing the airframe manufacturer and operator to take advantage of this normal operating function for commercial and military mission activities are discussed. The following topics are discussed: desirability of no-break power transfer, optimal no-break power transfer, the reason for minimizing circulating watts and VARs, power flow control, other factors affecting circulating power, synchronization control, and means of no-break transfer. >

Journal ArticleDOI
TL;DR: The application of artificial intelligence for knowledge-based systems (KBSs) is reviewed and applied to the basic power system network analysis problem and a frame-based KBS has been developed to assist students in preparing data for power flow analysis.
Abstract: The application of artificial intelligence for knowledge-based systems (KBSs) is reviewed and applied to the basic power system network analysis problem. A frame-based KBS has been developed to assist students in preparing data for power flow analysis. The prototype for a power flow knowledge-based system (PFKBS) is an example of a shallow knowledge system. The details of an implementation for a simple power system are used to highlight the difference between a frame-based approach and a conventional FORTRAN approach. The data structures used within the developed frame-based KBS are presented in sufficient detail for anyone to regenerate the database. The user interface is illustrated for a small power system. The method of preparing data for the power flow as a sequence of knowledge bases is discussed for the example system. >

Dissertation
01 Jan 1990
TL;DR: In this article, a voltage collapse proximity indicator based on the optimal impedance solution of a two bus system has been generalised to an actual system and the performance of this indicator has been investigated over the whole range (stable and unstable region) to see how useful this indicator can be for an operator at any operating point.
Abstract: With the increased loading and exploitation of the power transmission system and also due to improved optimised operation, the problem of voltage stability and voltage collapse attracts more and more attention . A voltage collapse can take place in systems or subsystems and can appear quite abruptly. Continuous monitoring of the system state is therefore required. The cause of the 1977 New York black out has been proved to be the reactive power problem. The 1987 Tokyo black out was believed to be due to reactive power shortage and to a voltage collapse at summer peak load. These facts have strongly indicated that reactive power planning and dispatching play an important role in the security of modern power systems. A proper compensation of system voltage profiles will enhance the system securities in the operation and will reduce system losses. In this thesis, some aspects of reactive power dispatch and voltage control problem have been investigated. The research has focused on the following three issues: Firstly, the steady-state stability problem has been tackled where, a voltage collapse proximity indicator based on the optimal impedance solution of a two bus system has been generalised to an actual system and the performance of this indicator has been investigated over the whole range (stable and unstable region) to see how useful this indicator can be for an operator at any operating point. Then we went further to implement a linear reactive power dispatch algorithm in which this indicator was used for the first time to attempt to prevent a voltage collapse in the system. Secondly, a new efficient technique for N-1 security has been incorporated aiming at either maximising the reactive power reserve margin for the generators or minimising active power losses during normal as well as outage conditions (single line outage) .The reactive power redistribution after an outage is based on the S-E graph adopted by Phadke and Spong[72].Thirdly, the dispatch (N-1 security excluded) has been incorporated on line in the O.C.E.P.S. control package to improve the quality of the service and system security by optimally controlling the generator voltages (potentially the reactive control system is able to control transformers, switchable capacitors and reactors). A new function called load voltage control (similar to the load frequency control function) has been introduced to allow smooth variation of the reactive control signals towards their targets.

Proceedings ArticleDOI
05 Sep 1990
TL;DR: The development of a prototype expert system for developing strategic operating guidelines and for advising electric power system operators of control action required to ensure security with respect to line overloads is described, and an overview of the expert-system structure is provided.
Abstract: The development of a prototype expert system for developing strategic operating guidelines and for advising electric power system operators of control action required to ensure security with respect to line overloads is described. The heuristics of the problem map into an object-oriented architecture wherein the properties of the objects define security constraints. These properties are defined/updated through power-flow analysis. The reasoning involved in security assessment and the determination of control action is modeled by rules. The key point is that expert systems used in security analysis must necessarily be flexible and able to reorganize knowledge bases as system structure changes. Security assessment and control aspects of power-system operation are explored, and an overview of the expert-system structure is provided. The operation and use of the system are discussed, and the need for and possibility of making the system even more autonomous are considered. >

Proceedings ArticleDOI
22 Jan 1990
TL;DR: An analytical method to decompose a power system into a number of weakly interconnected areas and further to identify the coherent machine groups in each area is presented in this paper.
Abstract: An analytical method to decompose a power system into a number of weakly interconnected areas and further to identify the coherent machine groups in each area is presented in this paper The proposed method is based on a technique of grouping related elements of the network The system decomposition and coherency groupings obtained is independent of the location of the faults to be simulated in the system The first part of the algorithm of decomposing the system into weakly coupled areas uses only the information about the transfer admittances between the generator internal nodes For the subsequent part of identifying the coherent groups of machines in each area, transfer admittances and moments of inertias of the machines are used

Journal ArticleDOI
TL;DR: For example, transient network analyzers (TNAs) as mentioned in this paper can be used to simulate a portion of a power system in miniature, complete with voltage sources representing generators and various kinds of capacitive or inductive loads.
Abstract: Electromagnetic transients are the tidal waves of electric power systems. These momentary voltage surges generally lasting only fractions of a second can be powerful enough to disrupt normal operations and even cause serious damage to major pieces of equipment, such as transformers. Created by lightning, line faults, substation switching functions, and other sudden events along a utility network, transients must be taken into account both in choosing equipment ratings for a power system and in setting its operating parameters. Like the builders of a seawall that must withstand the highest expected waves from the ocean, engineers trying to guard against damage from transients face an extraordinary design task. Most of the huge computer simulation codes related to power systems either model steady-state conditions or deal with system stability problems. The analysis of electromagnetic transients, on the other hand, requires a much more detailed examination of how some critical portion of a power system will react to conditions that can change greatly in microseconds. For many years, simulation of transient effects was performed by special-purpose analog computers called transient network analyzers (TNAs). These machines, which are still in use, recreate a portion of the power system in miniature, complete with voltage sources representing generators and various kinds of capacitive or inductive loads. TNAs are generally adequate but relatively inflexible, tedious to set up, and cumbersome to use. Once a system configuration is modeled, many simulations can be performed. Given the need to manually reconfigure TNA circuits to represent changes in a system, however, the analyzers can also be quite expensive to use. During the late 1960s, Herman Dommel of the Bonneville