Tree of primitive Pythagorean triples - Revision history

en>K9re11: removed Category:Number theory using HotCat as there is already the more specific category ''Diophantine equations''

2014-11-21T10:15:30Z

removed Category:Number theory using HotCat as there is already the more specific category ''Diophantine equations''

← Older revision		Revision as of 12:15, 21 November 2014
Line 1:		Line 1:
	~~[[File:Electricity Grid Schematic English~~.~~svg\|thumb\|right\|An electrical grid may have many types of generators and loads; generators~~ must ~~be controlled~~ to ~~maintain stable operation of the system~~.]]		A home has to be safe as well as good looking. That is why you must know what you're doing prior to embarking on any home improvement project. Follow the ideas presented here to become a good, all around general handyman.<br><br>It can be expensive to buy new furniture. Add some spice to your home by buying vintage furniture. Real treasures could be found among used items, such as furniture. Some pieces will be in great condition, while others may require a little work and elbow grease to make them just right for you house.<br><br>Think about using stain instead of paint on your baseboards for your next home improvement. In addition to being classic, the warm look of wood is natural in virtually any style of home. The stained baseboards will not make scuffs and dust as apparent as the painted would, and can easily be touched up. Wood stain comes in lots of different colors to coordinate with any color scheme.<br><br>When replacing baseboards, stained wood offers more appeal than painted baseboards. In addition to being classic, the warm look of wood is natural in virtually any style of home. Stained baseboards will also hide scuffs and dings better than painted wood, and touch-ups to scratches will blend in more easily. There are many options available in wood stains.<br><br>You can make a kitchen look new without spending a lot For more in regards to home makeover ideas, [http://www.homeimprovementdaily.com the full details], stop by our own internet site. of money. There is no reason to get rid of a properly working appliance just because it doesn't match the decor. You can buy some very affordable appliance spray paint and paint your appliances any color of your choosing. This can give your kitchen a more modern appearance in just one day.<br><br>Great quality materials don't have to break a homeowner's wallet; they just need to be long lasting and affordable. Those are the things that add value to the property. Quality fixtures stay in the home and increase the value of your home.<br><br>A good home improvement tip is to get a professional opinion before you ever try to fix anything serious on your own. The small cost of an initial consultation will seem nominal when compared to the costs of having a preventable mishap repaired. Without speaking with a professional prior to making home improvements, you may really mess things up.<br><br>Many building supplies for use in home improvement jobs are targets for theft. You should keep building supplies locked up when you are not working. If you have a secure home, your supplies can be kept in the home. An on-site storage container with a lock should be used when the house cannot provide adequate security.<br><br>Use fruit and flowers in order to provide your kitchen with a fresher look and smell. It will make any kitchen much more friendly. It is a very inexpensive fix to help brighten up your kitchen. Looking at those beautiful flowers can lift your spirits as soon as you see them.<br><br>Home improvement will serve to make your house look better as well as add value to your home. If you are willing to do the work, then you can easily turn your house into a home. Not only can doing your own home improvements save you money, but it can be something fun and enjoyable.
	~~In an [[Electrical grid\|electric power system]], '''automatic generation control (AGC) '''is a system for adjusting~~ the ~~power output of multiple generators at different [[Power station\|power plants]], in response~~ to ~~changes in the load. Since~~ a ~~power grid requires that generation and load closely balance moment by moment~~, ~~frequent adjustments to the output of generators are necessary~~. ~~The balance~~ can be ~~judged~~ by ~~measuring the [[Utility frequency\|system frequency]]; if it is increasing, more power is being generated than~~ used, ~~and all the machines~~ in ~~the system are accelerating. If the system frequency is decreasing~~, ~~more load is on the system than the instantaneous generation can provide, and all generators are slowing down.~~

	~~Before the use of automatic generation control, one generating unit in~~ a ~~system would be designated as the regulating unit~~ and ~~would be manually adjusted~~ to ~~control the balance between generation and load to maintain system frequency at the desired value~~. ~~The remaining units would be controlled with [[droop speed control\|speed droop]] to proportion their share~~ of ~~the load according to their ratings. With automatic systems, many units in a system can participate in regulation, reducing wear~~ on ~~a single unit's controls and improving overall system efficiency, stability, and economy~~.

	~~Where the grid has tie interconnections~~ to ~~adjacent control areas~~, ~~automatic generation control helps maintain~~ the ~~power interchanges over the tie lines at the scheduled levels~~. ~~With computer-based control systems~~ and ~~multiple inputs, an automatic generation control system can take into account such matters~~ as the ~~most economical units to adjust, the coordination of thermal, hydroelectric~~, and ~~other generation types, and even constraints related to the stability~~ of ~~the system and capacity of interconnections~~ to ~~other power grids~~.<~~ref~~>~~Robert Herschel Miller~~, ~~James H~~. ~~Malinowski~~, ~~''Power system operation'', McGraw-Hill Professional, 1994 ISBN 0-07-041977-9, page 86-87</ref>~~

	~~==Types~~ of ~~Automatic Generation Control (AGC)==~~

	~~===Turbine-Governor Control (TGC)===~~
	~~Turbine generators~~ in ~~a power system have stored kinetic energy due to their large rotating masses. All the kinetic energy stored in a power system in such rotating masses is a part~~ of ~~the grid inertia~~. ~~When system load increases~~, ~~grid inertia is initially used~~ to ~~supply the load~~. ~~This, however, leads to a decrease~~ in ~~the stored kinetic energy of the turbine generators~~. ~~Since the mechanical power of these turbines correlates with the delivered electrical power, the turbine generators have~~ a ~~decrease~~ in ~~angular velocity~~, ~~which is directly proportional to a decrease in frequency in synchronous generators.~~
	[~~[File~~:~~Steady state frequency-power relation for a turbine governor~~.~~png\|thumb\|Steady state frequency-power relation for a turbine governor~~]]
	~~The purpose~~ of ~~the turbine-governor control~~ is to ~~maintain the desired system frequency by adjusting the mechanical power output~~ of the ~~turbine~~.~~<ref>Glover, Duncan J. et al. Power System Analysis~~ and ~~Design~~. ~~5th Edition. Cengage Learning. 2012. pp. 657-658~~.<~~/ref~~> ~~These controllers~~ have ~~become automated~~ and ~~at steady state,~~ the ~~frequency-power relation for turbine-governor control is,~~

	~~<math>\Delta p_m = \Delta p_{ref} - 1/R\times\Delta f</math>~~

	~~where,~~

	~~<math>\Delta p_m</math> is~~ the ~~change~~ in ~~turbine mechanical power output~~

	<~~math~~>~~\Delta p_{ref}~~<~~/math~~> is ~~the change in~~ a ~~reference power setting~~

	~~<math>R = -\Delta f/\Delta p_m = -slope</math> is~~ the ~~regulation constant which quantifies the sensitivity~~ of ~~the generator~~ to ~~a change in frequency~~

	<~~math~~>~~\Delta f~~<~~/math~~> ~~is the change~~ in ~~frequency~~.

	~~For steam turbines, [[steam turbine governing]] adjusts the mechanical output of the turbine by increasing or decreasing the amount of steam entering the turbine via~~ a ~~throttle valve.~~

	~~===[[Utility frequency#Load-Frequency Control\|Load-Frequency Control (LFC)]]===~~
	~~Load-frequency control is employed to allow an area to first meet its own load demands~~, ~~then to assist~~ in ~~returning~~ the ~~steady~~-~~state frequency of~~ the ~~system, Δf, to zero~~.<~~ref~~>~~Glover, Duncan J. et al. Power System Analysis and Design. 5th Edition. Cengage Learning. 2012. pp. 663.~~<~~/ref~~>

	~~===[[Economic dispatch\|Economic Dispatch]]===~~
	~~The goal of economic dispatch is~~ to ~~minimize total operating costs in an area by determining how the real power output of each generating unit will meet~~ a ~~given load.<ref>Glover, Duncan J. et al. Power System Analysis~~ and ~~Design~~. ~~5th Edition~~. ~~Cengage Learning~~. ~~2012. pp. 667~~.<~~/ref~~>

	~~===[[Power system simulation#Optimal power flow\|Optimal Power Flow]]===~~
	~~Optimal power flow combines economic dispatch with power flow~~ to ~~optimize generation and enforce transmission line limits~~.~~<ref>Glover~~, ~~Duncan J~~. ~~et al. Power System Analysis~~ and ~~Design~~. ~~5th Edition. Cengage Learning. 2012. pp. 680.</ref>~~

	~~==References==~~
	~~{{Reflist}}~~

	~~[[Category:Electric power distribution]]~~

en>Tobias Bergemann: /* Properties */ Link to excircle and inradius.

2013-06-22T19:33:56Z

Properties: Link to excircle and inradius.

← Older revision		Revision as of 21:33, 22 June 2013
Line 1:		Line 1:
	I'~~m Leesa~~ and ~~I live~~ in a ~~seaside city~~ in ~~northern Norway~~, ~~Stavanger. I~~'~~m 32~~ and ~~I'm will soon finish my study~~ at ~~Occupational Therapy~~.<br><br>~~Also visit my homepage :: home makeover ideas~~ ([~~http~~://~~www~~.~~homeimprovementdaily~~.~~com sneak~~ a ~~peek at this website~~])		[[File:Electricity Grid Schematic English.svg\|thumb\|right\|An electrical grid may have many types of generators and loads; generators must be controlled to maintain stable operation of the system.]]
			In an [[Electrical grid\|electric power system]], '''automatic generation control (AGC) '''is a system for adjusting the power output of multiple generators at different [[Power station\|power plants]], in response to changes in the load. Since a power grid requires that generation and load closely balance moment by moment, frequent adjustments to the output of generators are necessary. The balance can be judged by measuring the [[Utility frequency\|system frequency]]; if it is increasing, more power is being generated than used, and all the machines in the system are accelerating. If the system frequency is decreasing, more load is on the system than the instantaneous generation can provide, and all generators are slowing down.

			Before the use of automatic generation control, one generating unit in a system would be designated as the regulating unit and would be manually adjusted to control the balance between generation and load to maintain system frequency at the desired value. The remaining units would be controlled with [[droop speed control\|speed droop]] to proportion their share of the load according to their ratings. With automatic systems, many units in a system can participate in regulation, reducing wear on a single unit's controls and improving overall system efficiency, stability, and economy.

			Where the grid has tie interconnections to adjacent control areas, automatic generation control helps maintain the power interchanges over the tie lines at the scheduled levels. With computer-based control systems and multiple inputs, an automatic generation control system can take into account such matters as the most economical units to adjust, the coordination of thermal, hydroelectric, and other generation types, and even constraints related to the stability of the system and capacity of interconnections to other power grids.<ref>Robert Herschel Miller, James H. Malinowski, ''Power system operation'', McGraw-Hill Professional, 1994 ISBN 0-07-041977-9, page 86-87</ref>

			==Types of Automatic Generation Control (AGC)==

			===Turbine-Governor Control (TGC)===
			Turbine generators in a power system have stored kinetic energy due to their large rotating masses. All the kinetic energy stored in a power system in such rotating masses is a part of the grid inertia. When system load increases, grid inertia is initially used to supply the load. This, however, leads to a decrease in the stored kinetic energy of the turbine generators. Since the mechanical power of these turbines correlates with the delivered electrical power, the turbine generators have a decrease in angular velocity, which is directly proportional to a decrease in frequency in synchronous generators.
			[[File:Steady state frequency-power relation for a turbine governor.png\|thumb\|Steady state frequency-power relation for a turbine governor]]
			The purpose of the turbine-governor control is to maintain the desired system frequency by adjusting the mechanical power output of the turbine.<ref>Glover, Duncan J. et al. Power System Analysis and Design. 5th Edition. Cengage Learning. 2012. pp. 657-658.</ref> These controllers have become automated and at steady state, the frequency-power relation for turbine-governor control is,

			<math>\Delta p_m = \Delta p_{ref} - 1/R\times\Delta f</math>

			where,

			<math>\Delta p_m</math> is the change in turbine mechanical power output

			<math>\Delta p_{ref}</math> is the change in a reference power setting

			<math>R = -\Delta f/\Delta p_m = -slope</math> is the regulation constant which quantifies the sensitivity of the generator to a change in frequency

			<math>\Delta f</math> is the change in frequency.

			For steam turbines, [[steam turbine governing]] adjusts the mechanical output of the turbine by increasing or decreasing the amount of steam entering the turbine via a throttle valve.

			===[[Utility frequency#Load-Frequency Control\|Load-Frequency Control (LFC)]]===
			Load-frequency control is employed to allow an area to first meet its own load demands, then to assist in returning the steady-state frequency of the system, Δf, to zero.<ref>Glover, Duncan J. et al. Power System Analysis and Design. 5th Edition. Cengage Learning. 2012. pp. 663.</ref>

			===[[Economic dispatch\|Economic Dispatch]]===
			The goal of economic dispatch is to minimize total operating costs in an area by determining how the real power output of each generating unit will meet a given load.<ref>Glover, Duncan J. et al. Power System Analysis and Design. 5th Edition. Cengage Learning. 2012. pp. 667.</ref>

			===[[Power system simulation#Optimal power flow\|Optimal Power Flow]]===
			Optimal power flow combines economic dispatch with power flow to optimize generation and enforce transmission line limits.<ref>Glover, Duncan J. et al. Power System Analysis and Design. 5th Edition. Cengage Learning. 2012. pp. 680.</ref>

			==References==
			{{Reflist}}

			[[Category:Electric power distribution]]

en>Giftlite: −sp

2012-06-05T17:07:46Z

−sp

New page

I'm Leesa and I live in a seaside city in northern Norway, Stavanger. I'm 32 and I'm will soon finish my study at Occupational Therapy.<br><br>Also visit my homepage :: home makeover ideas ([http://www.homeimprovementdaily.com sneak a peek at this website])