电子科技大学：《电力系统运行与控制 Power System Operation and Control》课程教学资源（课件讲稿）Lecture 03 Power System Economic Dispatch

Mathematic model of economic dispatch N generators supply to Pload ■Fi:fuel cost ■Pi:output pow F-→ 1 T G P F 2 > ■ ■ ■ ■ ■ ■ Optimization: F→ N G P→ minF,=∑F(E) s.t. =0=Poa-∑P i=l i=1 电力集镜广城测量乌控制四川省重点实脸室 家电

电力系统广域测量与控制四川省重点实验室 Mathematic model of economic dispatch  N generators supply to Pload  Fi: fuel cost  Pi: output power  Optimization: 1 min ( ) N T i i i F F P   s.t. 1 0 N load i i  P P    

Solution of Economic dispatch With Lagrange, 1=+0-空()--立月 aL dF(P)-2=0 OP dP =Pm-P=0 Mathematic model of Operation economic constraints: P.mn≤P≤P.nax dispatch 电力拿镜广城洲量写控制四川省重点实验蜜 家电

电力系统广域测量与控制四川省重点实验室 Solution of Economic dispatch  With Lagrange, 1 1 ( ) N N T i i load i i i L F F P P P                  ( ) 0 i i i i L dF P P dP       1 0 N load i i i L P P         P P P i i i ,min ,max   Operation constraints: Mathematic model of economic dispatch

Example#1 ·Example determine the economic operating point for the three generating units when delivering a total of 850 MW ●1 input-output curves unit 1:coal-fired steam unit:H =510+7.2P+0.00142P2 unit 2:oil-fired steam unit:H =310+7.85P +0.00194B2 unit 3:oil-fired steam unit:H3 =78+7.97P+0.00482P ●fuel costs ·coal:$3.30/MBtu oil:3.00/MBtu the individual unit cost rate functions F(B)=H1(E)×3.3=1683+23.76P+0.004686P E,(D)=HD)×3.0=930+23.55D+0.00582P F(P)=H()×3.0=234+23.70P+0.01446P2

电力系统广域测量与控制四川省重点实验室 Example#1

aL dF(P)-2=0 Example#1 (cont.) o dP aL .Example on i- .the conditions for an optimal dispatch dE/dP=23.76+0.009372P= dF2/dP=23.55+0.01164P=2 dF3/d=23.70+0.02892P=2 ?+P,+P=850 solving for A yields 元-23.76，元-23.55. 元-23.70 十 =850 0.009372 0.01164 0.02892 =27.41 then solving for the generator power values =(27.41-23.76)/0.009372=389.8 P=(27.41-23.55)/0.01164=331.8 P3=(27.41-23.70)/0.02892=128.4 家电

电力系统广域测量与控制四川省重点实验室 Example#1（cont.） ( ) 0 i i i i L dF P P dP       1 0 N load i i i L P P        

Over limit The equal incremental heat rate cannot be satisfied,if the output by economic dispatch is over the limit Pmn≤P≤P.max aL OP dE(E)_=0 for Pin≤P≤Px dP _drP)2元torL=Pam aL OP d BLdF(P forPm ap dp 电力镜广城测量乌控制四川省重点实验蜜 家电

电力系统广域测量与控制四川省重点实验室 Over limit  The equal incremental heat rate cannot be satisfied, if the output by economic dispatch is over the limit ,min ,max ( ) 0 for i i i i i i i L dF P P P P P dP         P P P i i i ,min ,max   ,min ( ) for i i i i i i L dF P P P P dP       ,max ( ) for i i i i i i L dF P P P P dP      