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POWER TRANSFER How the Clarke Calculator has given rise to today's power grids

From Venus Kohli

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Clarke Calculator is a smart invention that facilitates electricity distribution over long-distance HVDC or HVAC transmission lines. Wondering about Clarke Calculator and its application? Understand all the details about the innovation that enabled seamless long-distance transmission in today’s smart grid technology!

Long transmission lines to support smart grid.
Long transmission lines to support smart grid.
(Source: ABCDstock -

History of Clarke Calculator

Edith Clarke was the world’s first woman electrical engineer and professor who invented a graphical calculator for long-distance transmission line calculations. She held numerous patents for her groundbreaking inventions and became a published author of various electrical engineering books. In 1921, Edith Clarke filed a patent for the graphical calculator in the US Patent office. She invented the Clarke Calculator to obtain error-free values of important transmission line parameters over long distances. The calculator was based on the uniform distribution of transmission line characteristics across its entire length. During the decade of the 1920s, the transmission line model was in the early stages of development. Although Warren P. Mason is heavily credited for the theory of distributed element circuits, Edith Clarke and her invention, contributed to its acceptance.

Clarke Calculator in detail

Around the 1920s, short transmission lines of about 50 miles were used to transfer electricity from the source generator to the load receiver. A 500-mile-long transmission line was considerably “futuristic” in the early twentieth century unlike 2019 inaugurated 1580-mile-long Xingu-Rio HVDC transmission line.

Several parameters of the same short-length transmission line must be calculated to understand the characteristics of the transmission line and effective power transfer. The important characteristics of such a transmission line are inductance, capacitance, reactance, resistance, etc. These values were believed to be concentrated on a single point across the short-length transmission line. But the single-point concentration model does not hold good when considering long transmission lines of about 500 miles. It leads to inaccurate calculations with errors in the inductance and capacitance values.

Edith Clarke developed a graphical calculator based on the distribution model. The calculator provides values of inductance, capacitance, reactance, and essential characteristics of a long transmission line with less than 1 % error. When the values of the output load receiver’s EMF, power factor, and current are known, the calculator shows accurate values of the input generator's EMF and current. The calculator determines the vector relationship between the EMF of the generator input and the EMF of the receiver output. It also helps to understand another vector relationship between the current at the input generator and the current at the receiver output.

Clarke Calculator uses the graphical representation of two pivoted arms that signify vectors to obtain relevant phase differences, ratios of input-output EMF, polar coordinates, and other transmission line parameters. The derivations include the expansion of hyperbolic sine and cosine functions that calculate the inductance, capacitance, susceptance, resistance, and reactance of a long transmission line for various cycles.

What is a power grid?

Power grid showcasing a network of power generators, transmission lines, and receivers.
Power grid showcasing a network of power generators, transmission lines, and receivers.
(Source: petovarga -

A power grid is a network of power generators, transmission lines, and consumers to deliver and receive electricity from a variety of locations. Nowadays, the smart grid system is preferable over the power grid because it enables even a small power generation source, such as a smart house, to participate in electricity production. A smart grid is an interconnected-network integration of small and large-scale electrical energy generation sources to deliver power at various loads across the nation. The electrical energy generation sources include thermal power plants, nuclear power plants, solar power plants, power stations, transmission lines, etc. Each source is capable to generate electricity and deliver it across the network. Whether small or large, each power-generating source participates in the network to contribute electricity so that there is no power outage.

How did Clarke Calculator contribute to a power grid?

  • The generated power is sent to the substation for processing. The substation increases the voltage using a step-up transformer.
  • The voltage is increased for fast transmission over long distances. The stepped-up power is further sent across HVDC (High Voltage Direct Current) or HVAC (High Voltage Alternating Current) transmission lines.
  • Another substation receives the power and steps it down.
  • Furthermore, the distribution line receives the power and distributes it to the consumers.

The transmission line system comprises a wide variety of transmission lines ranging from short lines (50 miles), medium length lines (125 miles), and long lines (200 miles onwards). Edith Clarke laid a foundation to understand the behavior of transmission line parameters. The Clarke Calculator facilitated the construction of long-distance transmission lines because it provides less than 1 % errors in important characteristic values that are responsible for power transfer over long distances. The entire system of the smart grid is possible because of long transmission lines. Hence, Clarke Calculator is one of the major reasons that led to the error-less operation of today’s smart grid technology!

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