From 1929Thomas Parke Hughes Networks of power: electrification in Western society, 1880-1930 JHU Press, 1993 page 376 to the late 1960s, large alternating current power systems were modelled and studied on AC network analyzers (also called alternating current network calculators or AC calculating boards) or transient network analyzers. These special-purpose analog computers were an outgrowth of the DC calculating boards used in the very earliest power system analysis. By the middle of the 1950s, fifty network analyzers were in operation.Charles Eames, Ray Eames A Computer Perspective: Background to the Computer Age, Harvard University Press, 1990 0674156269, page 117 AC network analyzers were much used for power-flow studies, short circuit calculations, and system stability studies, but were ultimately replaced by numerical solutions running on digital computers. While the analyzers could provide real-time simulation of events, with no concerns about numeric stability of algorithms, the analyzers were costly, inflexible, and limited in the number of buses and lines that could be simulated.M.A. Laughton, D.F Warne (ed),Electrical Engineer's Reference Book (16th Edition), Elsevier, 2003 pages 368-369 Eventually powerful digital computers replaced analog network analyzers for practical calculations, but analog physical models for studying electrical transients are still in use.
Calculating methods As AC power systems became larger at the start of the 20th century, with more interconnected devices, the problem of calculating the expected behavior of the systems became more difficult. Manual methods were only practical for systems of a few sources and nodes. The complexity of practical problems made manual calculation techniques too laborious or inaccurate to be useful. Many mechanical aids to calculation were developed to solve problems relating to network power systems.
DC calculating boards used resistors and DC sources to represent an AC network. A resistor was used to model the inductive reactance of a circuit, while the actual series resistance of the circuit was neglected. The principle disadvantage was the inability to model complex impedances. However, for short-circuit fault studies, the effect of the resistance component was usually small. DC boards served to produce results accurate to around 20% error, sufficient for some purposes.
Artificial lines were used to analyze transmission lines. These carefully constructed replicas of the distributed inductance, capacitance and resistance of a full-size line were used to investigate propagation of impulses in lines and to validate theoretical calculations of transmission line properties. An artificial line was made by winding layers of wire around a glass cylinder, with interleaved sheets of tin foil, to give the model proportionally the same distributed inductance and capacitance as the full-size line. Later, lumped-element approximations of transmission lines were found to give adequate precision for many calculations.
Laboratory investigations of the stability of multiple-machine systems were constrained by the use of direct-operated indicating instruments (voltmeters, ammeters, and wattmeters). To ensure that the instruments negligibly loaded the model system, the machine power level used was substantial. Some workers in the 1920s used three-phase model generators rated up to 600 kVA and 2300 volts to represent a power system. General Electric developed model systems using generators rated at 3.75 kVA.H.P. Kuehni, R.G. Lorraine, A New A-C Network Analyzer, Transactions AIEE, February 1938 volume 57 page 67 It was difficult to keep multiple generators in synchronism, and the size and cost of the units was a constraint. While transmission lines and loads could be accurately scaled down to laboratory representations, rotating machines could not be accurately miniaturized and keep the same dynamic characteristics as full-sized prototypes; the ratio of machine inertia to machine frictional loss did not scale.David A. Mindell, Between Human and Machine: Feedback, Control and Computing Before Cybernetics, JHU Press, 2004 pp.149-150
Scale model A network analyzer system was essentially a scale model of the electrical properties of a specific power system. Generators, transmission lines, and loads were represented by miniature electrical components with scale values in proportion to the modeled system.Edward Wilson Kimbark, Power System Stability, Wiley-IEEE ,1948, page 64 and following Model components were interconnected with flexible cords to represent the schematic diagram of the modeled system.
Instead of using miniature rotating machines, accurately calibrated phase-shifting transformers were built to simulate electrical machines. These were all energized by the same source (at local power frequency or from a motor-generator set) and so inherently maintained synchronism. The phase angle and terminal voltage of each simulated generator could be set using rotary scales on each phase-shifting transformer unit. Using the per-unit system allowed values to be conveniently interpreted without additional calculation.
To reduce the size of the model components, the network analyzer often was energized at a higher frequency than the 50 Hz or 60 Hz utility frequency. The operating frequency was chosen to be high enough to allow high-quality inductors and capacitors to be made, and to be compatible with the available indicating instruments, but not so high that stray capacitance would affect results. Many systems used either 440 Hz, or 480 Hz, provided by a motor-generator set, to reduce size of model components. Some systems used 10 kHz, using capacitors and inductors similar to those used in radio electronics.
Model circuits were energized at relatively low voltages to allow for safe measurement with adequate precision. The model base quantities varied by manufacturer and date of design; as amplified indicating instruments became more common, lower base quantities were feasible. Model voltages and currents started off around 200 volts and 0.5 amperes in the MIT analyzer, which still allowed directly driven (but especially sensitive) instruments to be used to measure model parameters. The later machines used as little as 50 volts and 50 mA, used with amplified indicating instruments. By use of the per-unit system, model quantities could be readily transformed into the actual system quantities of voltage, current, power or impedance. A watt measured in the model might correspond to hundreds of kilowatts or megawatts in the modeled system. One hundred volts measured on the model might correspond to one per-unit, which could represent, say, 230,000 volts on a transmission line or 11,000 volts in a distribution system. Typically, results accurate to around 2% of measurement could be obtained.Institution of Engineering and Technology, Power System Protection, Volumes 1-4, 1995 pages 216-220 Model components were single-phase devices, but using the symmetrical components method, unbalanced three-phase systems could be studied as well.
A complete network analyzer was a system that filled a large room; one model was described as four bays of equipment, spanning a U-shaped arrangement 26 feet (8 metres) across. Companies such as General Electric and Westinghouse could provide consulting services based on their analyzers; but some large electrical utilities operated their own analyzers. The use of network analyzers allowed quick solutions to difficult calculation problems, and allowed problems to be analyzed that would otherwise be uneconomic to compute using manual calculations. Although expensive to build and operate, network analyzers often repaid their costs in reduced calculation time and expedited project schedules.Aad Blok, Greg Downey (ed) Uncovering Labour in Information Revolutions, 1750-2000, Cambridge University Press, 2003 , pp. 76-80 For example, a stability study might indicate if a transmission line should have larger or differently spaced conductors to preserve stability margin during system faults; potentially saving many miles of cable and thousands of insulators.
Network analyzers did not directly simulate the dynamic effects of load application to machine dynamics (torque angle, and others). Instead, the analyzer would be used to solve dynamic problems in a stepwise fashion, first calculating a load flow, then adjusting the phase angle of the machine in response to its power flow, and re-calculating the power flow.
In use, the system to be modelled would be represented as a single line diagram and all the impedances of lines and machines would be scaled to model values on the analyzer. A plugging diagram would be prepared to show the interconnections to be made between the model elements. The circuit elements would be interconnected by patch cables. The model system would be energized, and measurements taken at the points of interest in the model; these could be scaled up to the values in the full-scale system.http://www.ieeeghn.org/wiki/images/e/ec/Chapter_6-Calculating_Power_(Edwin_L._Harder).pdf Calculating Power, retrieved 2013 Feb 26
The MIT network analyzer The network analyzer installed at Massachusetts Institute of Technology (MIT) grew out of a 1924 thesis project by Hugh H. Spencer and Harold Locke Hazen, investigating a power system modelling concept proposed by Vannevar Bush. Instead of miniature rotating machines, each generator was represented by a transformer with adjustable voltage and phase, all fed from a common source. This eliminated a significant source of the poor accuracy of models with miniature rotating machines. The 1925 publication of this thesis attracted the attention at General Electric, where Robert Doherty was interested in modelling problems of system stability. He asked Hazen to verify that the model could accurately reproduce the behavior of machines during load changes.
Design and construction was carried out jointly by General Electric and MIT. When first demonstrated in June 1929, the system had eight phase-shifting transformers to represent synchronous machines. Other elements included 100 variable line resistors, 100 variable reactors, 32 fixed capacitors, and 40 adjustable load units. The analyzer was described in a 1930 paper by H.L Hazen, O.R. Schurig and M.F. Gardner. The base quantities for the analyzer were 200 volts, and 0.5 amperes. Sensitive portable thermocouple-type instruments were used for measurement.H.L Hazen, O.R. Schurig and M.F. Gardner. The M.I.T. Network Analyzer Design and Application to Power System Problems, Transactions AIEEE, July 1930 pp.1102-1113 The analyzer occupied four large panels, arranged in a U-shape, with tables in front of each section to hold measuring instruments. While primarily conceived as an educational tool, the analyzer saw considerable use by outside firms, who would pay to use the device. American Gas and Electric Company, the Tennessee Valley Authority, and many other organizations studied problems on the MIT analyzer in its first decade of operation. In 1940 the system was moved and expanded to handle more complex systems.
By 1953 the MIT analyzer was beginning to fall behind the state of the art. Digital computers were first used on power system problems as early as "Whirlwind" in 1949. Unlike most of the forty other analyzers in service by that point, the MIT instrument was energized at 60 Hz, not 440 or 480 Hz, making its components large, and expansion to new types of problems difficult. Many utility customers had bought their own network analyzers. The MIT system was dismantled and sold to the Puerto Rico Water Resources Authority in 1954.Karl L. Wildes, Nilo A. Lindgren A Century of Electrical Engineering and Computer Science at MIT, 1882-1982 MIT Press 1985 , pp. 100-104
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