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 09 Power System Optimal Power Flow

Solution of OPF Lambda-iterative: Gradient:slow convergence;cannot handle inequality constraints Newton method:fast convergence;may have problem with inequality constraints Linear Programming:mature algorithm;linearize the nonlinear objective function and constraints ■ Non-linear programming:handle non-linear objective function and constraint (equality or inequality) Interior point method:widely used;easy for handling inequality constraints 电力拿镜广城洲量写控制四川省重点实验蜜 家电网

电力系统广域测量与控制四川省重点实验室 Solution of OPF  Lambda-iterative:  Gradient: slow convergence; cannot handle inequality constraints  Newton method: fast convergence; may have problem with inequality constraints  Linear Programming: mature algorithm; linearize the nonlinear objective function and constraints  Non-linear programming: handle non-linear objective function and constraint (equality or inequality)  Interior point method: widely used; easy for handling inequality constraints

Gradient method min ∑F(E)=∑(a,P+a,P+a) ieall gen. ieall gen. PQ bus X= on the reference bus IEI PV bus P y= on each PQ bus control or adjustable variables V- P > p fixed or constant variables on each QV bus 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 Gradient method 2 2 1 0 gen. gen. min ( ) ( ) i i Gi i Gi i i all i all F P a P a P a        PQ bus | | PV bus i i i E            x on the reference bus | | on each PQ bus on each QV bus | | k k net k net k net k sch k E P Q P E                       y control or adjustable variables fixed or constant variables        u y p

Gradient method P(El,0)-Pe for each PQ bus g(xy)=Q,E1,0)-g P.(1El0)-Pe for each PV bus w/ref bus cost=∑F(P)+Fgr(Per) gen =∑F(P)+Fer(Per(El,θ)=f(&,m) gen Lagrange function: L(x,u,p)(x,u)+g(x,y) 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 Gradient method (| |, ) for each PQ bus ( ) (| |, ) (| |, ) for each PV bus w/ ref bus net i i net i i net k k P P Q Q P P                E g x, y Ε E r r cost ( ) (P ) ( ) (P (| |, )) ( ) i i ref ef gen i i ref ef gen F P F F P F f         E x,u Lagrange function: L( , )= ( ) ( ) t x,u p x,u f  λ g x, y

Gradient method L(x,u,p)f(x,u)+g(x,y) L(x,u,p)=>F(P)+Fr(Prer(E,))+ gen P(E,0)-Pmet +[乃….n] Q,(E,0)-9"e P(El,)-Pme 电力康镜广城测量与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 Gradient method L( , )= ( ) ( ) t x,u p x,u f  λ g x, y   r 1 2 L( , )= ( ) (P (| |, )) (| |, ) (| |, ) (| |, ) i i ref ef gen net i i net i i m net k k F P F P P Q Q P P                          x,u p E  E Ε E

Gradient method VL 0g VL(x,u,p)-0 V 时 og Bu VL2-g(x,U,p) a 胎， OP OP aP Pret a01 lE,l a82 aE21 0x Pret 2 01 0Q1 01 aE:l 6JE,l a82 aE21 [ 码湖 OP2 alE,l a 0 a02 OP F(P) , alE:l of Qu 0P F2(P) 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 Gradient method L( , )=0 x,u p x u = = = ( , ) T T f g L x x f g L u u L                        g x,u p