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The no-three-in-line drawing of a complete graph is a special case of this result with =. [12] The no-three-in-line problem also has applications to another problem in discrete geometry, the Heilbronn triangle problem. In this problem, one must place points, anywhere in a unit square, not restricted to a grid. The goal of the placement is to ...
The electrical power grid that powers Northern America is not a single grid, but is instead divided into multiple wide area synchronous grids. [1] The Eastern Interconnection and the Western Interconnection are the largest. Three other regions include the Texas Interconnection, the Quebec Interconnection, and the Alaska Interconnection.
Solutions to the no-three-in-line problem, large sets of grid points with no three collinear points, can be scaled into a unit square with minimum triangle area (/). In the other direction, Paul Erdős found examples of point sets with minimum triangle area proportional to 1 / n 2 {\displaystyle 1/n^{2}} , demonstrating that, if true, Heilbronn ...
The electric power transmission grid of the contiguous United States consists of 120,000 miles (190,000 km) of lines operated by 500 companies. The Western Interconnection is a wide area synchronous grid and one of the two major alternating current (AC) power grids in the North American power transmission grid .
About 840 million people (mostly in Africa), which is ca. 11% of the World's population, had no access to grid electricity in 2017, down from 1.2 billion in 2010. [ 2 ] Electrical grids can be prone to malicious intrusion or attack; thus, there is a need for electric grid security .
[citation needed] In a traditional grid dominated by synchronous generators, a strong grid with SCR greater than 3.0 will have the desired voltage stability and active power reserves. [4] A weak grid (with SCR values between 2.0 and 3.0 [6]) can exhibit voltage instability and control problems. [5] A grid with SCR below 2.0 is very weak. [6]
This is an everyday occurrence in AC systems, but one that can become disrupted when AC system components fail and place unexpected loads on the grid. With an HVDC line instead, such an interconnection would: Convert AC in Seattle into HVDC; Use HVDC for the 3,000 miles (4,800 km) of cross-country transmission; and
The Texas Interconnection is an alternating current (AC) power grid – a wide area synchronous grid – that covers most of the state of Texas. The grid is managed by the Electric Reliability Council of Texas (ERCOT). The Texas Interconnection is one of the three minor grids in the North American power transmission grid.