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<ul><li><p>Topic 1: Basics of Power Systems</p><p>A.H.MohsenianRad(UofT) 1NetworkingandDistributedSystems</p><p>ECE5332:CommunicationsandControlforSmart</p><p>Spring2012</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 2</p><p> TheFourMainElementsinPowerSystems:</p><p> PowerProduction/Generation</p><p> PowerTransmission</p><p> PowerDistribution</p><p> PowerConsumption/Load</p><p> Ofcourse,wealsoneedmonitoringandcontrolsystems.</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 3</p><p> PowerProduction:</p><p> DifferentTypes:</p><p> Traditional</p><p> Renewable</p><p> Capacity,Cost,CarbonEmission</p><p> StepupTransformers</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 4</p><p> PowerTransmission:</p><p> HighVoltage(HV)TransmissionLines</p><p> SeveralHundredMiles</p><p> SwitchingStations</p><p> Transformers</p><p> CircuitBreakers</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 5</p><p> ThePowerTransmissionGridintheUnitedStates:</p><p>www.geni.org</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 6</p><p> MajorInterconnectionsintheUnitedStates:</p><p>www.geni.org</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 7</p><p> PowerDistribution:</p><p>MediumVoltage(MV)TransmissionLines(</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 8</p><p> PowerConsumption:</p><p> Industrial</p><p> Commercial</p><p> Residential</p><p> DemandResponse</p><p> ControllableLoad</p><p> NonControllable</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 9</p><p>Generation Transmission Distribution Load</p></li><li><p>Power Systems</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 10</p><p> PowerSystemControl:</p><p> DataCollection:Sensors,PMUs,etc.</p><p> DecisionMaking:Controllers</p><p> Actuators:CircuitBreakers,etc.</p></li><li><p>Power Grid Graph Representation</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 11</p><p>Nodes:Buses</p><p>Links:TransmissionLines</p><p>Generator</p><p>Load</p></li><li><p>Power Grid Graph Representation</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 12</p><p>Nodes:Buses</p><p>Links:TransmissionLines</p><p>Generator</p><p>Load</p><p>Buses (Voltage)</p></li><li><p>Power Grid Graph Representation</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 13</p><p>Nodes:Buses</p><p>Links:TransmissionLines</p><p>Generator</p><p>Load</p><p>TransmissionLines(PowerFlow,Loss)</p></li><li><p>Power Grid Graph Representation</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 14</p><p>Nodes:Buses</p><p>Links:TransmissionLines</p><p>Generator</p><p>Load</p><p>Consum</p><p>ers</p></li><li><p>Power Grid Graph Representation</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 15</p><p>Nodes:Buses</p><p>Links:TransmissionLines</p><p>Generator</p><p>Load</p><p>10MW 3MW</p><p>7MW</p></li><li><p>Transmission Line Admittance</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 16</p><p> Admittanceyisdefinedastheinverseofimpedancez:</p><p> z=r+jx (r:Resistance,x:Reactance)</p><p> y=g+jb (g:Conductance,b:Susceptance)</p><p> y=1/z</p><p> Parametergisusuallypositive</p><p> Parameterb:</p><p> Positive:Capacitor</p><p> Negative:Inductor</p></li><li><p>Transmission Line Admittance</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 17</p><p> Forthetransmissionlineconnectingbusi tobusk:</p><p> Addmitance:yik</p><p> Example:</p><p>yik =1 j4(perunit)</p><p> Notethat,yii isdenotedbyyi andindicates:</p><p> Susceptance foranyshuntelement(capacitor)togroundatbusi.</p></li><li><p>Y-Bus Matrix</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 18</p><p> Wedefine:</p><p> Ybus =[Yij ]where</p><p> DiagonalElements:</p><p> OffdiagonalElements:</p><p> NotethatYbas matrixdependsonthepowergridtopologyandtheadmittanceofalltransmissionlines.</p><p> Nisthenumberofbussesinthegrid.</p><p>N</p><p>ikkikiii yyY</p><p>,1</p><p>ijij yY </p></li><li><p>Y-Bus Matrix</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 19</p><p> Example:Foragridwith4buses,wehave:</p><p> Afterseparatingtherealandimaginaryparts:</p><p>4342414434241</p><p>3434323133231</p><p>2423242321221</p><p>1413121413121</p><p>yyyyyyyyyyyyyyyyyyyyyyyyyyyy</p><p>Ybus</p><p>BjGYbus </p></li><li><p>Bus Voltage</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 20</p><p> LetVi denotethevoltageatbusi:</p><p> Notethat,Vi isaphasor,withmagnitude andangle.</p><p> Inmostoperatingscenarioswehave:</p><p>iii VV </p><p>jiji VV </p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 21</p><p> LetSi denotethepowerinjection atbusi:</p><p>Si =Pi +jQi</p><p> GenerationBus: Pi &gt;0</p><p> LoadBus: Pi </p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 22</p><p> UsingKirchhofflaws,ACPowerFlowEquations become:</p><p> Doweknowallnotationshere?</p><p> Ifweknowenoughvariables,wecanobtaintherestofvariablesbysolvingasystemofnonlinearequations.</p><p>N</p><p>jjkkjjkkjjkk</p><p>N</p><p>jjkkjjkkjjkk</p><p>BGVVQ</p><p>BGVVP</p><p>1</p><p>1</p><p>)cos()sin(</p><p>)sin()cos(</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 23</p><p> TheACPowerFlowEquationsarecomplicatedtosolve.</p><p> Next,wetrytosimplifytheequationsinthreesteps.</p><p> Step1:Formostnetworks,G</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 24</p><p> Step2:Formostneighboringbuses:.</p><p> Asaresult,wehave:</p><p> 15 to10 ji </p><p>1)()(</p><p>jk</p><p>jkjk</p><p>CosSin</p><p>N</p><p>jkjjkk</p><p>N</p><p>jjkkjjkk</p><p>BVVQ</p><p>BVVP</p><p>1</p><p>1)( </p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 25</p><p> Step3:Inperunit,|Vi|isverycloseto1.0(0.95to1.05).</p><p> Asaresult,wehave:.</p><p> Pk hasalinearmodelandQk isalmostfixed.</p><p>1ji VV</p><p> kN</p><p>kjj</p><p>kjkk</p><p>N</p><p>jkjk</p><p>N</p><p>jjkkjk</p><p>bBBBQ</p><p>BP</p><p>,11</p><p>1)( </p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 26</p><p> Step3:Inperunit,|Vi|isverycloseto1.0(0.95to1.05).</p><p> Asaresult,wehave:.</p><p> Pk hasalinearmodelandQk isalmostfixed.</p><p>1ji VV</p><p> kN</p><p>kjj</p><p>kjkk</p><p>N</p><p>jkjk</p><p>N</p><p>jjkkjk</p><p>bBBBQ</p><p>BP</p><p>,11</p><p>1)( </p><p>DCPowerFlowEquations</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 27</p><p> Giventhepowerinjectionvalues atallbuses,wecanuse</p><p>toobtainthevoltageangles atallbuses.</p><p> LetPij denotethepowerflow frombusi tobusj,wehave:</p><p>N</p><p>jjkkjk BP</p><p>1)( </p><p>)( jiijij BP </p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 28</p><p> Example:Obtainpowerflowvaluesinthefollowinggrid:</p><p>puPg 21 puPg 22 </p><p>puPg 14 puPl 43 </p><p>puP l 12 1014 jy 1013 jy </p><p>1034 jy </p><p>1023 jy </p><p>1012 jy </p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 29</p><p> First,weobtaintheYbusmatrix:</p><p>44434241</p><p>34333231</p><p>24232221</p><p>14131211</p><p>4342414434241</p><p>3434323133231</p><p>2423242321221</p><p>1413121413121</p><p>BBBBBBBBBBBBBBBB</p><p>jBjj</p><p>bbbbbbbbbbbbbbbbbbbbbbbbbbbb</p><p>jYbus</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 30</p><p> Next,wewritethe(active)powerflowequations:</p><p> Thiscanbewrittenas:</p><p> 44342413432421414</p><p>43433432312321313</p><p>42432322423211212</p><p>41431321211413121</p><p>BBBBBBPBBBBBBPBBBBBBP</p><p>BBBBBBP</p><p>4</p><p>3</p><p>2</p><p>1</p><p>434241434241</p><p>343432313231</p><p>242324232121</p><p>141312141312</p><p>4</p><p>3</p><p>2</p><p>1</p><p>BBBBBBBBBBBBBBBBBBBBBBBB</p><p>PPPP</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 31</p><p> Fromthelasttwoslides,wefinallyobtain:</p><p> Therefore,thevoltageanglesareobtainedas:</p><p>4</p><p>3</p><p>2</p><p>1</p><p>1</p><p>4</p><p>3</p><p>2</p><p>1</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 32</p><p> However,thelastmatrixinthepreviousslideissingular!</p><p> Therefore,wecannottaketheinverse.</p><p> Thesystemofequationswouldhaveinfinitesolutions.</p><p> Theproblemisthatthefouranglesarenotindependent.</p><p> Whatmattersistheangular/phasedifference.</p><p> Wechooseonebus(e.g.,bus1)asreferencebus:.01 </p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 33</p><p> Weshouldalsoremovethecorrespondingrows/columns:</p><p> Theangulardifferences(withrespectto):</p><p>4</p><p>3</p><p>2</p><p>1</p><p>201001010301010010201010101030</p><p>14</p><p>12</p><p>4</p><p>3</p><p>2</p><p>2010010301001020</p><p>14</p><p>1</p><p>1</p><p>025.015.0</p><p>025.0</p><p>14</p><p>1</p><p>2010010301001020 1</p><p>4</p><p>3</p><p>2</p><p>025.015.0025.0</p><p>14</p><p>13</p><p>12</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 34</p><p> Finally,thepowerflowvaluesarecalculatedas:</p><p>puPg 21 puPg 22 </p><p>puPg 14 puPl 43 </p><p>puP l 12 </p><p>25.1)025.015.0(10)(25.1)15.0025.0(10)(</p><p>25.0)025.00(10)(5.1)15.00(10)(</p><p>25.0)025.00(10)(</p><p>433434</p><p>322323</p><p>411414</p><p>311313</p><p>211212</p><p>BPBPBPBPBP</p><p>0.25</p><p>1.25</p><p>1.250.25 1.5</p></li><li><p>Power Flow Equations</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 35</p><p> Whatifthegeneratorconnectedtobus1isrenewable?</p><p> Whatifthecapacity oftransmissionlink(1,3)is1pu?</p><p> Whatifwecanapplydemandresponse toloadbus3?</p><p> Whatifoneofthetransmissionlinesfails?</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 36</p><p> Intheexamplewediscussedearlier,wehad:</p><p> Inparticular,wehad:</p><p> However,generationlevelsandassumedgiven.</p><p> Q:Whatifthegeneratorshavedifferentgenerationcosts?</p><p>PowerSupply=PowerLoad</p><p>llggg PPPPP 32421 </p><p>ggg PPP 421 ,,</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 37</p><p> Forthermalpowerplants,generationcostisquadratic:</p><p> Example:agridwiththreepowerplants:</p><p> Eachpowerplanthassomeminandmaxgenerationlevels.</p><p>GenerationCost=C(P)=a1 +a2 xP+a3 xP2</p><p>C1(P1)=561+7.92xP1 +0.001562x(P1)2 150MWP1 600MW</p><p>C2(P2)=310+7.85xP2 +0.001940x(P2)2 100MWP2 400MW</p><p>C3(P3)=78+7.97xP3 +0.004820x(P3)2 50MWP3 200MW</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 38</p><p> Forthermalpowerplants,generationcostisquadratic:</p><p> Example:agridwiththreepowerplants:</p><p> Eachpowerplanthassomeminandmaxgenerationlevels.</p><p>GenerationCost=C(P)=a1 +a2 xP+a3 xP2</p><p>C1(P1)=561+7.92xP1 +0.001562x(P1)2 150MWP1 600MW</p><p>C2(P2)=310+7.85xP2 +0.001940x(P2)2 100MWP2 400MW</p><p>C3(P3)=78+7.97xP3 +0.004820x(P3)2 50MWP3 200MW</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 39</p><p> Forthermalpowerplants,generationcostisquadratic:</p><p> Example:agridwiththreepowerplants:</p><p> Eachpowerplanthassomeminandmaxgenerationlevels.</p><p>GenerationCost=C(P)=a1 +a2 xP+a3 xP2</p><p>C1(P1)=561+7.92xP1 +0.001562x(P1)2 150MWP1 600MW</p><p>C2(P2)=310+7.85xP2 +0.001940x(P2)2 100MWP2 400MW</p><p>C3(P3)=78+7.97xP3 +0.004820x(P3)2 50MWP3 200MW</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 40</p><p> Forthermalpowerplants,generationcostisquadratic:</p><p> Example:agridwiththreepowerplants:</p><p> Eachpowerplanthassomeminandmaxgenerationlevels.</p><p>GenerationCost=C(P)=a1 +a2 xP+a3 xP2</p><p>C1(P1)=561+7.92xP1 +0.001562x(P1)2 150MWP1 600MW</p><p>C2(P2)=310+7.85xP2 +0.001940x(P2)2 100MWP2 400MW</p><p>C3(P3)=78+7.97xP3 +0.004820x(P3)2 50MWP3 200MW</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 41</p><p> Forthermalpowerplants,generationcostisquadratic:</p><p> Example:agridwiththreepowerplants:</p><p> Eachpowerplanthassomeminandmaxgenerationlevels.</p><p>GenerationCost=C(P)=a1 +a2 xP+a3 xP2</p><p>C1(P1)=561+7.92xP1 +0.001562x(P1)2 150MWP1 600MW</p><p>C2(P2)=310+7.85xP2 +0.001940x(P2)2 100MWP2 400MW</p><p>C3(P3)=78+7.97xP3 +0.004820x(P3)2 50MWP3 200MW</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 42</p><p> WeshouldselectP1,P2,andP3 to:</p><p> Meettotalload Pload =850MW</p><p> Minimizethetotalcost ofgeneration</p><p> EconomicDispatchProblem:</p><p>85020050400100600150 subject to</p><p>CCC minimize</p><p>321</p><p>3</p><p>2</p><p>1</p><p>321 , , 321</p><p>PPPPPP</p><p>PPPPPP</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 43</p><p> Istheformulatedproblemaconvexprogram?Why?</p><p> Convexprogramscanbesolvedefficiently.</p><p> AnusefulsoftwareisCVXforMatlab (http://cvxr.com/cvx).</p><p> Theoptimal economicdispatchsolution:</p><p>P1 =393.2MW</p><p>P2 =334.6MW</p><p>P3 =122.2MW</p><p>Q:Dotheysatisfyallconstraints?</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 44</p><p> Istheformulatedproblemaconvexprogram?Why?</p><p> Convexprogramscanbesolvedefficiently.</p><p> AnusefulsoftwareisCVXforMatlab (http://cvxr.com/cvx).</p><p> Theoptimal economicdispatchsolution:</p><p>P1 =393.2MW</p><p>P2 =334.6MW</p><p>P3 =122.2MW</p><p>MinimumCost =3916.6+3153.8+1123.9=8194.3</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 45</p><p> Whatifwehavetosatisfytopologyconstraints?</p><p>1P</p><p>3P MW 400</p><p>2P</p><p>MW 45020013 P</p><p>3</p><p>21</p><p>4</p><p>3</p><p>2</p><p>400450</p><p>2010010301001020</p><p>P</p><p>P</p><p>202010)( 33311313 BP</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 46</p><p> Thesame optimalsolutionsarestillvalid:</p><p>MW 393.21 P</p><p>MW 122.2 3 P MW 400</p><p>MW 334.6 2 P</p><p>MW 450</p><p>805.3830.19685.15</p><p>4</p><p>3</p><p>2</p><p>203 20013 P</p><p>156.8</p><p>160.3</p><p>41.438.1 198.3</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 47</p><p> Thesame optimalsolutionsarestillvalid:</p><p>MW 393.21 P</p><p>MW 122.2 3 P MW 400</p><p>MW 334.6 2 P</p><p>MW 450</p><p>805.3830.19685.15</p><p>4</p><p>3</p><p>2</p><p>203 20013 P</p><p>156.8</p><p>160.3</p><p>41.438.1 198.3</p><p>Whatif 17013 P</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 48</p><p> Thentheeconomicdispatchproblembecomes:</p><p>17 </p><p>400450</p><p>2010010301001020</p><p>850 20050 400100 600150 subject to </p><p>CCC minimize</p><p>3</p><p>3</p><p>21</p><p>4</p><p>3</p><p>2</p><p>321</p><p>3</p><p>2</p><p>1</p><p>321 , ,, , , 321321</p><p>P</p><p>P</p><p>PPPPPP</p><p>PPPPPP</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 49</p><p> Thentheeconomicdispatchproblembecomes:</p><p>17 </p><p>400450</p><p>2010010301001020</p><p>850 20050 400100 600150 subject to </p><p>CCC minimize</p><p>3</p><p>3</p><p>21</p><p>4</p><p>3</p><p>2</p><p>321</p><p>3</p><p>2</p><p>1</p><p>321 , ,, , , 321321</p><p>P</p><p>P</p><p>PPPPPP</p><p>PPPPPP StillaConvex</p><p>Program?</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 50</p><p> Thenewoptimalsolutionsareobtainedas:</p><p> Thetotalgenerationcostbecomes:$8,233.66&gt;$8,194.3</p><p> Here,wehadtosacrificecostforimplementation.</p><p>MW 2801 P</p><p>MW 170 3 P MW 400</p><p>MW 400 2 P</p><p>MW 450</p><p>110</p><p>170</p><p>600 170</p></li><li><p>Economic Dispatch Problem</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 51</p><p> Thenewoptimalsolutionsareobtainedas:</p><p> Thetotalgenerationcostbecomes:$8,233.66&gt;$8,194.3</p><p> Here,wehadtosacrificecostforimplementation.</p><p>MW 2801 P</p><p>MW 170 3 P MW 400</p><p>MW 400 2 P</p><p>MW 450</p><p>110</p><p>170</p><p>600 170</p><p>Whatif 15013 P</p></li><li><p>Unit Commitment</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 52</p><p> EconomicDispatchissolvedafewhoursahead ofoperation.</p><p> Ontheotherhand,weneedtodecideaboutthechoiceofpowerplantsthatwewanttoturnon forthenextday.</p><p> ThisisdonebysolvingtheUnitCommitment problem.</p><p> Weparticularlydecideonwhichslowstarting powerplantsweshouldturnonduringthenextdaygivenvariousconstraints.</p><p> ThemathematicalconceptsaresimilartotheEDproblem.</p></li><li><p>References</p><p>Dr. Hamed Mohsenian-Rad Texas Tech UniversityCommunications and Control in Smart Grid 53</p><p> W. J. Wood and B. F. Wollenberg, Power Generation,Operation, and Control, John Wiley &amp; Sons, 2nd Ed., 1996.</p><p> J. McCalley and L. Tesfatsion, "Power Flow Equations", LectureNotes, EE 458, Department of Electrical and ComputerEngineering, Iowa State University, Spring 2010.</p></li></ul>