Max: 100 MW Cost: $20/MW Load: 50 MW G x1=0.2 p.u Cap: 50 MW. x2=0.2 Cap: 50 MW. x3=0.2 p.u. Cap: 50 MW. p.u. x4=0.2 p.u. Cap: 100 MW. 4 Max: 200 MW G Cost: $40/MW Load: 100 MW Load: 150 MW G Max: 250 MW Cost: $50/MW Example • Let's formulate the optimization problem for the following system. Max: 70 MW Cost: $30/MW Max: 80 MW Cost: $50/MW G x=0.1 p.u. Cap = 50 MW x=0.1 p.u. Cap = 50 MW x=0.1 p.u. Cap = 50 MW The VA base value is 100MVA 1 b = - = -10 p.u. x Objective: Subject to: Objective: Minimize (30P₁ +50P₂) Subject to: 0 ≤ P₁ ≤ 70 0 ≤ P₂ ≤ 80 −50 ≤ F₁3 ≤ 50 -50 ≤ F12 ≤ 50 -50 ≤ F23 ≤ 50 F1310 x 100(0₁ - 03) F12 10 x 100(0₁ - 0₂) F23 = 10 × 100(0₂ – 03) F12 = 0 P₁-F13 P₂ + F12 F23 = 0 F13 + F23 = 100 0₁ = 0 Load: 100 MW Minimize (30P₁ + 50P₂) 0 ≤ P₁ ≤ 70 0 ≤ P₂ ≤ 80 -50 ≤ F13 ≤ 50 -50 ≤ F12 ≤ 50 -50 ≤ F23 ≤ 50 F13 10 X 100 (0₁ - 03) F12 10 × 100(0₁ – 0₂) F23 = 10 x 100(02 - 03) F12 = 0 P₁ F13 P₂ + F12 Identify the variables and their ranges ● F23 = 0 F13 + F23 = 100 0₁ = 0 • Variables in this formulation: P1 P₂ F13 F12 • F23 0₁ (use a range of -1 to 1) 02 (use a range of -1 to 1) • 03 (use a range of -1 to 1)
Max: 100 MW Cost: $20/MW Load: 50 MW G x1=0.2 p.u Cap: 50 MW. x2=0.2 Cap: 50 MW. x3=0.2 p.u. Cap: 50 MW. p.u. x4=0.2 p.u. Cap: 100 MW. 4 Max: 200 MW G Cost: $40/MW Load: 100 MW Load: 150 MW G Max: 250 MW Cost: $50/MW Example • Let's formulate the optimization problem for the following system. Max: 70 MW Cost: $30/MW Max: 80 MW Cost: $50/MW G x=0.1 p.u. Cap = 50 MW x=0.1 p.u. Cap = 50 MW x=0.1 p.u. Cap = 50 MW The VA base value is 100MVA 1 b = - = -10 p.u. x Objective: Subject to: Objective: Minimize (30P₁ +50P₂) Subject to: 0 ≤ P₁ ≤ 70 0 ≤ P₂ ≤ 80 −50 ≤ F₁3 ≤ 50 -50 ≤ F12 ≤ 50 -50 ≤ F23 ≤ 50 F1310 x 100(0₁ - 03) F12 10 x 100(0₁ - 0₂) F23 = 10 × 100(0₂ – 03) F12 = 0 P₁-F13 P₂ + F12 F23 = 0 F13 + F23 = 100 0₁ = 0 Load: 100 MW Minimize (30P₁ + 50P₂) 0 ≤ P₁ ≤ 70 0 ≤ P₂ ≤ 80 -50 ≤ F13 ≤ 50 -50 ≤ F12 ≤ 50 -50 ≤ F23 ≤ 50 F13 10 X 100 (0₁ - 03) F12 10 × 100(0₁ – 0₂) F23 = 10 x 100(02 - 03) F12 = 0 P₁ F13 P₂ + F12 Identify the variables and their ranges ● F23 = 0 F13 + F23 = 100 0₁ = 0 • Variables in this formulation: P1 P₂ F13 F12 • F23 0₁ (use a range of -1 to 1) 02 (use a range of -1 to 1) • 03 (use a range of -1 to 1)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
Related questions
Question
Please write down the formulation of the DCOPF problem for the 4-bus system provided in the first figure. I have provided an example of the formulation in Figure 2. Hope that helps
![Max: 100 MW
Cost: $20/MW
Load: 50 MW
G
x1=0.2 p.u
Cap: 50 MW.
x2=0.2
Cap: 50 MW.
x3=0.2 p.u.
Cap: 50 MW.
p.u.
x4=0.2 p.u.
Cap: 100 MW.
4
Max: 200 MW
G Cost: $40/MW
Load: 100 MW
Load: 150 MW
G Max: 250 MW
Cost: $50/MW](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9febe5d-8b15-43b8-b1a2-ee1d05ea5a44%2Fe73d9199-a448-4d59-bcdb-3b35e5dbf365%2F147i9sw_processed.png&w=3840&q=75)
Transcribed Image Text:Max: 100 MW
Cost: $20/MW
Load: 50 MW
G
x1=0.2 p.u
Cap: 50 MW.
x2=0.2
Cap: 50 MW.
x3=0.2 p.u.
Cap: 50 MW.
p.u.
x4=0.2 p.u.
Cap: 100 MW.
4
Max: 200 MW
G Cost: $40/MW
Load: 100 MW
Load: 150 MW
G Max: 250 MW
Cost: $50/MW
![Example
• Let's formulate the optimization problem for the following system.
Max: 70 MW
Cost: $30/MW
Max: 80 MW
Cost: $50/MW
G
x=0.1 p.u.
Cap = 50 MW
x=0.1 p.u.
Cap = 50 MW
x=0.1 p.u.
Cap = 50 MW
The VA base value is 100MVA
1
b = - = -10 p.u.
x
Objective:
Subject to:
Objective: Minimize (30P₁ +50P₂)
Subject to: 0 ≤ P₁ ≤ 70
0 ≤ P₂ ≤ 80
−50 ≤ F₁3 ≤ 50
-50 ≤ F12 ≤ 50
-50 ≤ F23 ≤ 50
F1310 x 100(0₁ - 03)
F12 10 x 100(0₁ - 0₂)
F23 = 10 × 100(0₂ – 03)
F12 = 0
P₁-F13
P₂ + F12
F23 = 0
F13 + F23 = 100
0₁ = 0
Load: 100 MW
Minimize (30P₁ + 50P₂)
0 ≤ P₁ ≤ 70
0 ≤ P₂ ≤ 80
-50 ≤ F13 ≤ 50
-50 ≤ F12 ≤ 50
-50 ≤ F23 ≤ 50
F13 10 X 100 (0₁ - 03)
F12 10 × 100(0₁ – 0₂)
F23 = 10 x 100(02 - 03)
F12 = 0
P₁ F13
P₂ + F12
Identify the variables and their ranges
●
F23 = 0
F13 + F23 = 100
0₁ = 0
• Variables in this formulation:
P1
P₂
F13
F12
• F23
0₁ (use a range of -1 to 1)
02 (use a range of -1 to 1)
• 03 (use a range of -1 to 1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9febe5d-8b15-43b8-b1a2-ee1d05ea5a44%2Fe73d9199-a448-4d59-bcdb-3b35e5dbf365%2Fc8a3l5d_processed.png&w=3840&q=75)
Transcribed Image Text:Example
• Let's formulate the optimization problem for the following system.
Max: 70 MW
Cost: $30/MW
Max: 80 MW
Cost: $50/MW
G
x=0.1 p.u.
Cap = 50 MW
x=0.1 p.u.
Cap = 50 MW
x=0.1 p.u.
Cap = 50 MW
The VA base value is 100MVA
1
b = - = -10 p.u.
x
Objective:
Subject to:
Objective: Minimize (30P₁ +50P₂)
Subject to: 0 ≤ P₁ ≤ 70
0 ≤ P₂ ≤ 80
−50 ≤ F₁3 ≤ 50
-50 ≤ F12 ≤ 50
-50 ≤ F23 ≤ 50
F1310 x 100(0₁ - 03)
F12 10 x 100(0₁ - 0₂)
F23 = 10 × 100(0₂ – 03)
F12 = 0
P₁-F13
P₂ + F12
F23 = 0
F13 + F23 = 100
0₁ = 0
Load: 100 MW
Minimize (30P₁ + 50P₂)
0 ≤ P₁ ≤ 70
0 ≤ P₂ ≤ 80
-50 ≤ F13 ≤ 50
-50 ≤ F12 ≤ 50
-50 ≤ F23 ≤ 50
F13 10 X 100 (0₁ - 03)
F12 10 × 100(0₁ – 0₂)
F23 = 10 x 100(02 - 03)
F12 = 0
P₁ F13
P₂ + F12
Identify the variables and their ranges
●
F23 = 0
F13 + F23 = 100
0₁ = 0
• Variables in this formulation:
P1
P₂
F13
F12
• F23
0₁ (use a range of -1 to 1)
02 (use a range of -1 to 1)
• 03 (use a range of -1 to 1)
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