08/16/04

Thomas Alva Edison


Video: The Edison Effect: The Electric Light, ISBN 1-56501-892-3.

Edison and the Maximum Power Transfer Theorem

Thomas Alva Edison is famous for inventing the electric light and is slightly less famous for inventing the phonograph and motion pictures. He is not at all famous for serving as one of the first Vice-Presidents of the American Institute of Electrical Engineers, a forerunner of the contemporary Institute of Electrical and Electronics Engineers (IEEE). But Edison's contributions to electrical engineering, and his personality, were considerably richer and more complex than this short list of notable achievements suggests.

It's a part of popular folklore that Edison had little formal schooling. He overcame that limitation quite successfully all his life by learning apart from schools. A less famous limitation must have been at least as difficult for him to overcome: he could not think abstractly. Edison thought in concrete physical terms. For example, Edison found it difficult to envision an electric current, which he could not see (and hence is an abstraction), flowing through a wire. At one point, Edison, together with many other inventors, worked on developing two-way telegraphy, a scheme for sending messages in both directions, simultaneously, over a single pair of telegraph wires. Two-way telegraphy was extremely important from an economic point of view because it would yield more monetary income doubling the number of messages that could be sent over an existing pair of wires. In other words, two-way telegraphy promised to generate much more profit from the capital invested in the telegraph lines that stretched across the country. Edison would seem to have been at something of a disadvantage in this work because, as we mentioned, he could not envision the currents flowing through the wires. He got around this limitation by exploiting the analogy of electricity flowing through wires and water flowing through pipes. He knew, for example, that water valves corresponded to electric switches, that differences in pressure in a system of pipes corresponded to differences in voltage in a circuit, and that water pumps corresponded to voltage generators (or batteries) in a circuit. So Edison would plumb up his ideas about multiplex telegraphy using water pipes and valves and then hire an electrical engineer to draw the corresponding electric circuit.

His difficulty in dealing with abstractions meant that he learned very little mathematics beyond arithmetic. Some of the electrical engineers of the day, on the other hand, had learned a little calculus and used it to demonstrate a remarkable result called the maximum power transfer theorem. Electric generators are built of wire, which exhibits some small resistance to current flow, despite all hopes and efforts to decrease the effect. The generator therefore exhibits a small, but non-zero, internal resistance to current flow. Suppose we call this internal electrical resistance Rgenerator. The content of the maximum power transfer theorem is that an electrical load (a bank of electric lights, for example) connected across the generator terminals draws the most power from the generator if the electrical resistance, Rload, of the load equals the internal resistance of the generator, Rgenerator. Electrical engineers were thrilled with the result because they were in the business of selling electric power and this remarkable little theorem told them how they could extract the very most power from their generators.

Edison couldn't understand the mathematics, but he smelled a rat. Who knows why. Perhaps it was just that the kind of keen intuition that we describe as genius. However it happened, I like to imagine the following conversation between Edison and the electrical engineers of the day:

EDISON: So all I need to do to get the most power out of this generator is to adjust the load resistance so that it equals the generator's internal resistance (Rload = Rgenerator)?

ELECTRICAL ENGINEERS: That's what the mathematics says. We can show you the proof, if you like.

EDISON: No, no. That's OK. But let me understand this a little better. Now the electric current flows out of the generator, then through the load, and then back through the generator, right?

ELECTRICAL ENGINEERS: Yep.

EDISON: That means that the same current, that is the same sized current, flows through both the generator and the load, correct?

ELECTRICAL ENGINEERS: True, just like water flowing through a pump and a closed loop of pipe.

EDISON: Now the current that flows through the load deposits an amount of power in the load that depends only on the size of the current and the resistance of the load (Rload), true?

ELECTRICAL ENGINEERS: Yes, and if the load is a bank of electric lights, it is this deposited power that heats the filaments so that they glow and give off light. The higher the current, the higher the power, the higher the temperature, and the brighter the light.

EDISON: I see. Let me summarize what I hear you saying. I believe I understand three things:

  1. The same sized current flows through both the generator and the load.
  2. When you operate at the conditions specified by your maximum power transfer theorem, the resistance of the load and the resistance of the generator are the same.
  3. The power deposited in a resistance depends only on its resistance and the size of the current flowing through it.

Am I correct?

ELECTRICAL ENGINEERS: Yes, now you seem to understand.

EDISON: Then you must be selling only half the electric power that you generate.

ELECTRICAL ENGINEERS: What?

EDISON: Well if the resistances of the generator and the load are the same and the current through them is the same size, then they both must absorb the same amount of power. But you sell only the power delivered to the load, right?

ELECTRICAL ENGINEERS: Yes, but ... .

EDISON: Do your generators run hot?

ELECTRICAL ENGINEERS: No. We're careful to build a large enough cooling system to keep that from happening.

EDISON: But if you didn't build a big cooling system, the generators would burn up, right?

ELECTRICAL ENGINEERS: Certainly.

EDISON: That's because half of the power you are generating ends up in the generator. That means not only that you cannot sell it, but that you must spend a lot of money on a cooling system trying to get rid of it.

ELECTRICAL ENGINEERS: But we have to operate this way because the maximum power transfer theorem says we should, and we can prove it using calculus.

EDISON: I don't know much about the maximum power transfer theorem, but it seems to me that if you are in the business of selling power, and you sell only half of what you generate and then pay a lot of money to get rid of the other half, you're doing something wrong.

ELECTRICAL ENGINEERS: Surely you can't do better than maximum power transfer!

EDISON: I think we can. Although it seems to me that we're stuck with having the same amount of current flow through the generator as through the load, we can make the resistance of the load much higher than the resistance of the generator, at least if we disregard the maximum power transfer theorem. Since, as I understand it, the power deposited in a resistance for a certain current increases in proportion to the resistance, a large load resistance should result in more power being delivered to the load (sold) and less power devoted to overheating the generator. Not only could we sell more of the power by operating this way, we could save money by building smaller coolers for the generator.

ELECTRICAL ENGINEERS: We still don't see how you can do better than the maximum power transfer theorem.

Maybe Edison couldn't prove it, but he did turn out to be right. Indeed, some argue that Edison's idea of using a high resistance load and a low resistance generator was a far more important contribution to the electric utility industry than his invention of the electric lamp. After all, several other people came up with electric lamps almost simultaneously with Edison. All the others, however, were working on low resistance lamps. Ultimately, it was the high resistance of his lamps that permitted Edison's power systems to be successful commercially.

But where had the electrical engineers messed up? Was the maximum power transfer theorem wrong? Not at all. The electrical engineers assumed that just because you can maximize something that you think is good, that you should maximize it. Simply put, they maximized one thing, power transferred to the load, when another thing, efficiency with which power is transferred to the load, was more important.

Why, for an electric utility, does maximizing efficiency turn out to be more important than maximizing the amount of power transferred? The answer is basically economic, not electrical. In the utility industry, the cost of fuel is a large fraction of the total cost of generating electric power. Capital costs, largely the cost of "renting" the money necessary to build the generating plant, also constitute a large component of the total cost of generating electric power, but not a large enough part to make the fuel costs negligible in comparison. By delivering a larger fraction of the generated power to the load, Edison's approach improved the efficiency with which fuel was utilized and hence lowered the total cost of generating electric power. Edison's approach lowered capital (and hence total) costs, as well, by reducing the cooling required for the generator.

The electrical engineers simply fell into a type of trap that still snares engineers, even though we have the benefit of more than 100 years additional hindsight. Just because you know how to optimize something doesn't mean that it's what you should optimize. It gets even more complicated. If a process depends on two or more quantities, which individually are good, and you maximize only one of these good things, then the other good things may suffer so much that the process operates far from overall optimum. The moral to the story is this: be sure that you really want to optimize something before you take the plunge and do it. Otherwise, you may end up doing much worse than if you'd never encountered the concept of optimization at all, and realizing your mistake only much later. The electrical engineers who worked for Edison later described their feelings upon finally understanding his point as a mixture of exhilaration from the beauty of the concept and of disappointment and embarrassment from their folly.

OK, so the maximum power transfer theorem is correct in theory and useless in practice. Not true at all. In fact, when you hook an 8 Ohm speaker to an 8 Ohm output terminal on your stereo system, you are employing the maximum power transfer theorem, in practice, to transfer as much power as possible from your stereo to your speakers. So what makes this circumstance different from the utility industry? Different economics. Basically, the economics of stereo systems means that maximum power transfer is more important than efficiency. Question: do you worry about how much it costs for the electricity required to operate your stereo system? Probably not: it's a negligible part of your utility bill. The negligible cost of powering the stereo means that the efficiency with which power is delivered to your speakers is not a very pressing concern to you. Most of the cost for your stereo system is capital cost, the cost of purchasing the system. Thus, you want to get as much sound as you can out of your investment, regardless of the efficiency. Therefore, you match the load (speaker) resistance to the generator (stereo amplifier) effective internal resistance to extract as much power as possible to run the speakers. That way, you get the most bang for your buck.

Edison and AC Power

Edison's intuition, as good as it was, failed him when it came to the choice between direct current (DC) and alternating current (AC) in electric power systems. In DC systems, those in contemporary automobiles for example, the current flows steadily in one direction. In AC systems, contemporary electric utility systems for example, the current reverses its direction of flow typically 60 times each second. Perhaps because it was harder to visualize, but probably just because it was something new that he did not understand, Edison hated AC. The fact that AC requires more sophisticated mathematics to work with in practice doubtless also influenced his feelings. For whatever reasons, Edison was a DC chauvinist. When George Westinghouse and Nikola Tesla began to promote AC in the electric utility industry, Edison sneakily set up some companies that looked innocent enough that Westinghouse, not realizing their connection to Edison, granted patent licenses to them for making electric chairs powered by AC. These companies then vigorously promoted AC electric chairs to the states as an allegedly more humane alternative to execution by hanging. After successful executions with the chairs occurred, Edison supported a widespread publicity campaign that admonished the public not to let AC into their homes -- AC, after all, was what the government used to kill people. Use only good ol' safe DC, Edison said. To be sure, DC just happened to be the only kind of electricity offered by Edison's companies. His argument, of course, was self-serving hog wash. Both AC and DC can kill, neither more especially effective than the other.

In the electric utility industry, AC power eventually won out over DC power for two main reasons. First, transformers make it easy to adjust AC power to a higher or lower voltage very efficiently. Transformers do not work for DC, however, so adjusting DC voltages requires converting the DC to AC, adjusting the resulting AC voltage with a transformer, and then converting the adjusted AC voltage to a corresponding DC voltage. Clearly, adjusting DC voltages is more complicated, and not surprisingly more expensive, than adjusting AC voltages.

Why is the ability to adjust the voltage of electric power up and down so important in the electric utility industry? To see, we begin by noting that when we send power over wires, the amount of power transported increases as the product of the current through the wires and the voltage between them. To transport a particular amount of power, therefore, we can choose a high voltage and a low current, a low voltage and a high current, or, obviously, something in between. In principle, each choice could deliver the required amount of power. If we want to send large amounts of power over some distance, say from Niagara Falls to Buffalo, New York, however, it is easy to see that we should choose a high voltage and a low current. After all, the wire has unavoidable resistance and, as we know, high currents deposit power in resistance. By choosing the current to be low (and therefore choosing the voltage to be high to compensate), we reduce the amount of power lost during transport from one place to another through the wires. (From another perspective, using low current permits smaller wire sizes and hence lowers the cost of construction, provided, of course, the costs for accommodating the higher voltage don't outrun the savings from smaller wire.) This choice results in the large high-voltage power lines that stretch between tall towers across the open country and carry large amounts of power from one place to another through the resistive wire. In practice, the voltages across these lines are at least several hundred thousand volts.

When it reaches a city, the power must be distributed for use. Of course, no one wants to plug a hair dryer into 100,000 volts, so the voltage must be reduced for safety during use. The voltage reduction is usually done in stages to maintain as much of the advantage of high voltages as is consistent with safety. First, transformers drop the voltage to perhaps a few ten thousand volts for transporting the power to various power distribution sub-stations scattered about the city. At the substations, the voltage level may be dropped further to a few thousand volts for distribution through business districts and neighborhoods. Transformers at each building lower the voltage to roughly one or two hundred volts for customer use. At each stage of distribution, transformers permit the voltage of AC power to be adjusted efficiently and inexpensively. Because adjustment of the voltage of DC power is much harder, Edison was locked, in practice, into low DC voltages for safety's sake. At first, when the power systems were small and distances were short, this limitation was not so severe. But as the very success of Edison's early electric power systems caused the demand for the systems, and thus their size, to grow, the low voltage caused the DC systems to be either costly (if you used big wire) or inefficient (if you used smaller wire).

The second reason AC power eventually won out over DC power in the electric utility industry is that good AC motors (and generators) are easier and cheaper to build than good DC motors (and generators). At first, electricity was used only for lighting. But soon, the availability of mechanical power without the heat, smoke, and noise from steam engines focussed attention on electric motors in addition to electric lights.

Although practical motors are available for either type of power, the structure and characteristics of AC and DC motors are quite different. AC power, particularly a common type known as three-phase AC power, makes it easy to produce a magnetic field whose direction rotates rapidly in space. Any electric conductor placed within the rotating magnetic field, a metal armature for example, rotates with the field. A simple physical picture is that the magnetic lines of force become essentially locked in place within a good electrical conductor. In a perfect electrical conductor, they simply could not move at all. In practical conductors such as metals, the magnetic lines of force can move only very slowly through the metal. Consequently, a metal armature rotates with the rotating magnetic field with little slippage and, through a shaft attached to the armature, can deliver mechanical power to a mechanical load such as a fan or a water pump. A motor such as we've just described, an AC induction motor, is a mechanically simple means of converting electric power to mechanical power. DC motors rely, in contrast, on a complex mechanical system of brushes and commutator switches to produce, in effect, only a fairly crude approximation to a rotating magnetic field. The mechanical complexity of DC motors, consequently, not only makes them more expensive to manufacture than AC motors, it also makes them more expensive to maintain.

Because they are simple, inexpensive and robust, three phase AC induction motors became the workhorses of industry and thus abetted the dominance of AC power over DC. Single-phase induction motors, though less efficient than their more powerful three-phase relatives, provide the comparatively smaller amounts of power required for air conditioners, water pumps, fans and other machines in small businesses and residences.

DC power still is the choice for autos, where distance is not a big factor and where DC power is the power type of choice for the increasing amount of electronic equipment, such as antilock braking systems and electronic ignitions, that autos now include. In recent decades, however, AC generators (alternators) in autos provide power that is converted to DC (by semiconductor rectifiers) to gain simplicity in comparison with the complexity of brushes and commutators in DC generators. Ironically, High Voltage DC also is the contemporary choice for some extremely long-distance electric power transport. The appeal of DC power in this instance is better use of the costly high voltage transmission lines than AC. A good part of the expense in constructing the high voltage transmission lines comes from providing large insulated towers that hold the wires far enough apart that electric arcs do not form and produce disruptive short-circuits. The higher the voltage, the larger and more expensive the towers become. The sinusoidal wave shape of AC means that the AC voltage value resides near its peak value during only a small fraction of the AC cycle. During most of the cycle, therefore, the voltage is lower than the peak value and some of the capability of the high voltage transmission system is underutilized. With DC, in contrast, the voltage can remain steady at the value for which the system is designed. As a result, DC can transport more electric power over a high voltage transmission line system than can AC. Of course, converting the AC voltage to high voltage DC at one end of the line is expensive, as is converting the high voltage DC to lower voltage AC at the other end. If the line is long enough, though, more economical use of the transmission line may justify the added costs at each end.

Because AC power could be transported more cheaply than DC power over all but the longest distances and because AC motors are better than DC motors for most purposes, even General Electric, Edison's own company, embraced AC power rather than DC power for electric utilities before his death.

Edison and Ambiguity in Engineering

Edison's choice of a high-resistance electric power system (a key factor in the commercial success of his systems) and his choice of DC over AC for power systems (ultimately a bad choice) provide a couple of valuable insights.

First, Edison's choices, like most engineering choices, were not simple enough to be decided by plugging a few numbers into some set of magic equations. These choices involved a complex interwoven web of technical, business, economic, and social considerations. Such a diverse combination of issues, typical even of engineering projects much smaller than Edison's, ensure that engineering decisions are almost never black and white and almost never based on simple, unambiguous calculations. Many people outside engineering imagine that engineering is largely a matter of finding the right equation and evaluating it to obtain the answer to an engineering problem. It's easy to see that people with such a perspective can envision engineering as a mindless profession with little room for the ambiguity that they recognize instinctively as essential for creativity. The constraints imposed by the laws of science, mathematics, economics and society on engineering problem solving, however, leave much more to the imagination and creativity of an engineer than, for example, does a musical score to a performing artist.

Two things may account for the difficulty people have in understanding the ambiguity and creativty inherent in contemporary engineering:

Those without a good background in science and technolgy must rely on relatively scarce good-quality "popularizations" to access the concepts from which engineering ambiguities spring. Not only are effective popularizations rare, they demand a lot of effort from the reader -- more effort than most people with a casual interest in engineering are willing to commit.

Most of the introductory level courses in technology, science and mathematics that people may encounter in high school and college deal with topics mature enough that clever ways of circumventing the ambiguities that arose during development and refinement of the topics have been discovered and deployed long ago. As a consequence, a student in these courses can be excused for concluding that lack of ambiguity, and hence lack of opportunity for creativity, is a characteristic of technology, science and mathematics.

The subtleties and complexities of the choices faced by Edison can be understood, as we have seen, without an extensive background in technology, science or mathmatics. Thus, they can help a variety of people understand better the nature of engineering choices and, thereby, the nature of engineering.

Second, Edison did not always make the right engineering choices. No one does. Don't be surprised when you don't. All you can expect of yourself is to make the best engineering choice you can.

Edison's Legacy for Product Research and Development

Despite his limitations, flaws and occasional lapses in intuition, Edison is remembered deferentially, especially by historians of technology, for something we've not mentioned at all to this point. Edison conceived, and implemented with great and repeated success, the modern system of product research and development. Until Edison, inventors mainly worked alone. That approach meant that if they came up with something big, they shared the proceeds with only a few backers, or perhaps no one at all if they came from a wealthy family (rare) or could go without food and shelter for a sufficiently long period of time. This approach also meant, however, that the expertise available for the invention process was limited to that of a single inventor.

Edison was the first person to fund, build and staff an industrial laboratory for product research and development. It was at this laboratory in Menlo Park, New Jersey that Edison's team invented the electric lighting system. Edison's laboratory housed a remarkable variety of the latest equipment and supported a host of highly skilled technicians, as well as some formally educated engineers and scientists. Edison showed in practice how to bring an extraordinary concentration of expertise and capability, far beyond that of any single inventor, to the process of invention and product development. The funding came from what today would be called venture capitalists, people who invest in promising, but risky, projects in the hope of large returns from their investments. The success of his approach was unprecedented. Industries worldwide soon adopted Edison's concept, still the basic approach in industry today. Edison's last laboratory complex, still maintained much as it appeared at Edison's death, is a full-blown reminder of his approach to research and product development. It even included a technical library of several thousand volumes. Although the equipment and furnishings in the laboratory now seem quaint, the continued implementation of its basic system in contemporary industrial laboratories attests to the power that Edison's approach unleashed. The Edsonia portion of the Edison National Historical Site provides links to historic photos and sound recordings, including what is possibly the oldest surviving example of recorded music and an 1888 recording of Edison's voice.